gap> Read("sudoku");

gap> Centre(sudoku);
Group(())
gap> Exponent(sudoku);
72

gap> IsSolvableGroup(sudoku);
true
gap> IsNilpotentGroup(sudoku);
false
gap> IsSupersolvableGroup(sudoku);
false
gap> DerivedSeriesOfGroup(sudoku);
[ <permutation group with 17 generators>, 
  <permutation group with 14 generators>, 
  <permutation group with 12 generators>, 
  <permutation group with 10 generators>, 
  <permutation group with 6 generators>, Group(()) ]
gap> DerivedLength(sudoku);
5
gap> List(DerivedSeriesOfGroup(sudoku),Size);
[ 3359232, 419904, 104976, 11664, 729, 1 ]
gap> ElementaryAbelianSeriesLargeSteps(sudoku);
[ <permutation group with 17 generators>, 
  <permutation group of size 839808 with 15 generators>, 
  <permutation group of size 104976 with 12 generators>, 
  <permutation group of size 11664 with 10 generators>, 
  <permutation group of size 729 with 6 generators>, Group(()) ]

gap> NrConjugacyClasses(sudoku);
275
gap> ConjugacyClasses(sudoku);
[ ()^G, (7,8,9)(16,17,18)(25,26,27)(34,35,36)(43,44,45)(52,53,54)(55,64,
    73)(56,65,74)(57,66,75)(58,67,76)(59,68,77)(60,69,78)(61,71,81)(62,72,
    79)(63,70,80)^G, (55,73,64)(56,74,65)(57,75,66)(58,76,67)(59,77,68)(60,78,
    69)(61,79,70)(62,80,71)(63,81,72)^G, 
  (4,5,6)(7,8,9)(13,14,15)(16,17,18)(22,23,24)(25,26,27)(31,32,33)(34,35,
    36)(40,41,42)(43,44,45)(49,50,51)(52,53,54)(55,64,73)(56,65,74)(57,66,
    75)(58,68,78)(59,69,76)(60,67,77)(61,71,81)(62,72,79)(63,70,80)^G, 
  (4,5,6)(7,8,9)(13,14,15)(16,17,18)(22,23,24)(25,26,27)(31,32,33)(34,35,
    36)(40,41,42)(43,44,45)(49,50,51)(52,53,54)(58,59,60)(61,62,63)(67,68,
    69)(70,71,72)(76,77,78)(79,80,81)^G, 
  (4,5,6)(7,8,9)(13,14,15)(16,17,18)(22,23,24)(25,26,27)(28,37,46)(29,38,
    47)(30,39,48)(31,41,51)(32,42,49)(33,40,50)(34,44,54)(35,45,52)(36,43,
    53)(55,64,73)(56,65,74)(57,66,75)(58,68,78)(59,69,76)(60,67,77)(61,71,
    81)(62,72,79)(63,70,80)^G, (1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,
    17,18)(19,20,21)(22,23,24)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,
    39)(40,41,42)(43,44,45)(46,47,48)(49,50,51)(52,53,54)(55,74,66)(56,75,
    64)(57,73,65)(58,77,69)(59,78,67)(60,76,68)(61,80,72)(62,81,70)(63,79,
    71)^G, (1,2,3)(4,5,6)(7,9,8)(10,11,12)(13,14,15)(16,18,17)(19,20,21)(22,
    23,24)(25,27,26)(28,29,30)(31,32,33)(34,36,35)(37,38,39)(40,41,42)(43,45,
    44)(46,47,48)(49,50,51)(52,54,53)(55,56,57)(58,59,60)(61,63,62)(64,65,
    66)(67,68,69)(70,72,71)(73,74,75)(76,77,78)(79,81,80)^G, 
  (1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18)(19,20,21)(22,23,24)(25,
    26,27)(28,38,48)(29,39,46)(30,37,47)(31,41,51)(32,42,49)(33,40,50)(34,44,
    54)(35,45,52)(36,43,53)(55,74,66)(56,75,64)(57,73,65)(58,77,69)(59,78,
    67)(60,76,68)(61,80,72)(62,81,70)(63,79,71)^G, 
  (1,11,21)(2,12,19)(3,10,20)(4,14,24)(5,15,22)(6,13,23)(7,17,27)(8,18,25)(9,
    16,26)(28,38,48)(29,39,46)(30,37,47)(31,41,51)(32,42,49)(33,40,50)(34,44,
    54)(35,45,52)(36,43,53)(55,65,75)(56,66,73)(57,64,74)(58,68,78)(59,69,
    76)(60,67,77)(61,71,81)(62,72,79)(63,70,80)^G, 
  (5,6)(8,9)(14,15)(17,18)(23,24)(26,27)(32,33)(35,36)(37,46)(38,47)(39,
    48)(40,49)(41,51)(42,50)(43,52)(44,54)(45,53)(59,60)(62,63)(64,73)(65,
    74)(66,75)(67,76)(68,78)(69,77)(70,79)(71,81)(72,80)^G, 
  (1,2,3)(5,6)(8,9)(10,11,12)(14,15)(17,18)(19,20,21)(23,24)(26,27)(28,29,
    30)(32,33)(35,36)(37,47,39,46,38,48)(40,49)(41,51)(42,50)(43,52)(44,
    54)(45,53)(55,65,57,64,56,66)(58,67)(59,69)(60,68)(61,70)(62,72)(63,
    71)(73,74,75)(77,78)(80,81)^G, (1,11,21)(2,12,19)(3,10,20)(4,13,22)(5,15,
    23,6,14,24)(7,17,25,8,16,26)(9,18,27)(28,29,30)(32,33)(34,35)(37,47,39,46,
    38,48)(40,49)(41,51)(42,50)(43,53)(44,52)(45,54)(55,65,57,64,56,66)(58,
    67)(59,69)(60,68)(61,71)(62,70)(63,72)(73,74,75)(77,78)(79,80)^G, 
  (2,3)(5,6)(11,12)(14,15)(20,21)(23,24)(29,30)(32,33)(38,39)(41,42)(47,
    48)(50,51)(56,57)(59,60)(65,66)(68,69)(74,75)(77,78)^G, 
  (2,3)(5,6)(7,8,9)(11,12)(14,15)(16,17,18)(20,21)(23,24)(25,26,27)(29,30)(32,
    33)(34,35,36)(38,39)(41,42)(43,44,45)(47,48)(50,51)(52,53,54)(55,64,
    73)(56,66,74,57,65,75)(58,67,76)(59,69,77,60,68,78)(61,71,81)(62,72,
    79)(63,70,80)^G, (2,3)(5,6)(11,12)(14,15)(20,21)(23,24)(29,30)(32,33)(38,
    39)(41,42)(47,48)(50,51)(55,73,64)(56,75,65,57,74,66)(58,76,67)(59,78,68,
    60,77,69)(61,79,70)(62,80,71)(63,81,72)^G, 
  (2,3)(5,6)(7,8,9)(11,12)(14,15)(16,17,18)(20,21)(23,24)(25,26,27)(29,30)(32,
    33)(34,35,36)(38,39)(41,42)(43,44,45)(47,48)(50,51)(52,53,54)(56,57)(59,
    60)(61,62,63)(65,66)(68,69)(70,71,72)(74,75)(77,78)(79,80,81)^G, 
  (2,3)(5,6)(7,8,9)(11,12)(14,15)(16,17,18)(20,21)(23,24)(25,26,27)(28,37,
    46)(29,39,47,30,38,48)(31,40,49)(32,42,50,33,41,51)(34,44,54)(35,45,
    52)(36,43,53)(55,64,73)(56,66,74,57,65,75)(58,67,76)(59,69,77,60,68,
    78)(61,71,81)(62,72,79)(63,70,80)^G, (2,3)(5,6)(11,12)(14,15)(20,21)(23,
    24)(28,37,46)(29,39,47,30,38,48)(31,40,49)(32,42,50,33,41,51)(34,43,
    52)(35,44,53)(36,45,54)(55,73,64)(56,75,65,57,74,66)(58,76,67)(59,78,68,
    60,77,69)(61,79,70)(62,80,71)(63,81,72)^G, 
  (1,10,19)(2,12,20,3,11,21)(4,13,22)(5,15,23,6,14,24)(7,18,26)(8,16,27)(9,17,
    25)(28,37,46)(29,39,47,30,38,48)(31,40,49)(32,42,50,33,41,51)(34,45,
    53)(35,43,54)(36,44,52)(55,64,73)(56,66,74,57,65,75)(58,67,76)(59,69,77,
    60,68,78)(61,72,80)(62,70,81)(63,71,79)^G, 
  (1,10,19)(2,12,20,3,11,21)(4,13,22)(5,15,23,6,14,24)(7,16,25)(8,17,26)(9,18,
    27)(28,37,46)(29,39,47,30,38,48)(31,40,49)(32,42,50,33,41,51)(34,43,
    52)(35,44,53)(36,45,54)(55,73,64)(56,75,65,57,74,66)(58,76,67)(59,78,68,
    60,77,69)(61,79,70)(62,80,71)(63,81,72)^G, 
  (1,31,61)(2,32,62)(3,33,63)(4,34,55)(5,35,56)(6,36,57)(7,28,58)(8,29,59)(9,
    30,60)(10,40,70)(11,41,71)(12,42,72)(13,43,64)(14,44,65)(15,45,66)(16,37,
    67)(17,38,68)(18,39,69)(19,49,79)(20,50,80)(21,51,81)(22,52,73)(23,53,
    74)(24,54,75)(25,46,76)(26,47,77)(27,48,78)^G, 
  (1,31,71,11,41,81,21,51,61)(2,32,72,12,42,79,19,49,62)(3,33,70,10,40,80,20,
    50,63)(4,35,65,14,45,75,24,52,55)(5,36,66,15,43,73,22,53,56)(6,34,64,13,
    44,74,23,54,57)(7,28,67,17,38,77,27,48,60)(8,29,68,18,39,78,25,46,58)(9,
    30,69,16,37,76,26,47,59)^G, (1,31,79,19,49,70,10,40,61)(2,32,80,20,50,71,
    11,41,62)(3,33,81,21,51,72,12,42,63)(4,34,73,22,52,64,13,43,55)(5,35,74,
    23,53,65,14,44,56)(6,36,75,24,54,66,15,45,57)(7,28,76,25,46,67,16,37,
    58)(8,29,77,26,47,68,17,38,59)(9,30,78,27,48,69,18,39,60)^G, 
  (1,55,28)(2,56,29)(3,57,30)(4,58,31)(5,59,32)(6,60,33)(7,61,34)(8,62,35)(9,
    63,36)(10,64,37)(11,65,38)(12,66,39)(13,67,40)(14,68,41)(15,69,42)(16,70,
    43)(17,71,44)(18,72,45)(19,73,46)(20,74,47)(21,75,48)(22,76,49)(23,77,
    50)(24,78,51)(25,79,52)(26,80,53)(27,81,54)^G, 
  (1,64,37,10,73,46,19,55,28)(2,65,38,11,74,47,20,56,29)(3,66,39,12,75,48,21,
    57,30)(4,67,40,13,76,49,22,58,31)(5,68,41,14,77,50,23,59,32)(6,69,42,15,
    78,51,24,60,33)(7,71,45,16,80,54,25,62,36)(8,72,43,17,81,52,26,63,34)(9,
    70,44,18,79,53,27,61,35)^G, (1,73,46,19,64,37,10,55,28)(2,74,47,20,65,38,
    11,56,29)(3,75,48,21,66,39,12,57,30)(4,76,49,22,67,40,13,58,31)(5,77,50,
    23,68,41,14,59,32)(6,78,51,24,69,42,15,60,33)(7,79,52,25,70,43,16,61,
    34)(8,80,53,26,71,44,17,62,35)(9,81,54,27,72,45,18,63,36)^G, 
  (1,55,28)(2,56,29)(3,57,30)(4,58,31)(5,59,32)(6,60,33)(7,62,36)(8,63,34)(9,
    61,35)(10,64,37)(11,65,38)(12,66,39)(13,67,40)(14,68,41)(15,69,42)(16,71,
    45)(17,72,43)(18,70,44)(19,73,46)(20,74,47)(21,75,48)(22,76,49)(23,77,
    50)(24,78,51)(25,80,54)(26,81,52)(27,79,53)^G, 
  (1,64,37,10,73,46,19,55,28)(2,65,38,11,74,47,20,56,29)(3,66,39,12,75,48,21,
    57,30)(4,68,42,13,77,51,22,59,33)(5,69,40,14,78,49,23,60,31)(6,67,41,15,
    76,50,24,58,32)(7,71,45,16,80,54,25,62,36)(8,72,43,17,81,52,26,63,34)(9,
    70,44,18,79,53,27,61,35)^G, (1,55,28)(2,56,29)(3,57,30)(4,59,33)(5,60,
    31)(6,58,32)(7,62,36)(8,63,34)(9,61,35)(10,64,37)(11,65,38)(12,66,39)(13,
    68,42)(14,69,40)(15,67,41)(16,71,45)(17,72,43)(18,70,44)(19,73,46)(20,74,
    47)(21,75,48)(22,77,51)(23,78,49)(24,76,50)(25,80,54)(26,81,52)(27,79,
    53)^G, (1,74,48,19,65,39,10,56,30)(2,75,46,20,66,37,11,57,28)(3,73,47,21,
    64,38,12,55,29)(4,77,51,22,68,42,13,59,33)(5,78,49,23,69,40,14,60,31)(6,
    76,50,24,67,41,15,58,32)(7,80,54,25,71,45,16,62,36)(8,81,52,26,72,43,17,
    63,34)(9,79,53,27,70,44,18,61,35)^G, (1,56,30)(2,57,28)(3,55,29)(4,59,
    33)(5,60,31)(6,58,32)(7,63,35)(8,61,36)(9,62,34)(10,65,39)(11,66,37)(12,
    64,38)(13,68,42)(14,69,40)(15,67,41)(16,72,44)(17,70,45)(18,71,43)(19,74,
    48)(20,75,46)(21,73,47)(22,77,51)(23,78,49)(24,76,50)(25,81,53)(26,79,
    54)(27,80,52)^G, (1,55,28)(2,56,29)(3,57,30)(4,58,31)(5,60,32,6,59,33)(7,
    61,34)(8,63,35,9,62,36)(10,73,37)(11,74,38)(12,75,39)(13,76,40)(14,78,41,
    15,77,42)(16,79,43)(17,81,44,18,80,45)(19,64,46)(20,65,47)(21,66,48)(22,
    67,49)(23,69,50,24,68,51)(25,70,52)(26,72,53,27,71,54)^G, 
  (1,64,46,19,73,37,10,55,28)(2,65,47,20,74,38,11,56,29)(3,66,48,21,75,39,12,
    57,30)(4,67,49,22,76,40,13,58,31)(5,69,50,24,77,42,14,60,32,6,68,51,23,78,
    41,15,59,33)(7,71,52,26,79,44,16,62,34,8,70,53,25,80,43,17,61,35)(9,72,54,
    27,81,45,18,63,36)^G, (1,65,48,19,74,39,10,56,30)(2,66,46,20,75,37,11,57,
    28)(3,64,47,21,73,38,12,55,29)(4,67,49,22,76,40,13,58,31)(5,69,50,24,77,
    42,14,60,32,6,68,51,23,78,41,15,59,33)(7,70,52,25,79,43,16,61,34)(8,72,53,
    27,80,45,17,63,35,9,71,54,26,81,44,18,62,36)^G, 
  (1,56,30)(2,57,28)(3,55,29)(4,58,31)(5,60,32,6,59,33)(7,63,34,9,61,36)(8,62,
    35)(10,74,39)(11,75,37)(12,73,38)(13,76,40)(14,78,41,15,77,42)(16,81,43,
    18,79,45)(17,80,44)(19,65,48)(20,66,46)(21,64,47)(22,67,49)(23,69,50,24,
    68,51)(25,72,52,27,70,54)(26,71,53)^G, (1,34)(2,43)(3,52)(4,61)(5,70)(6,
    79)(8,16)(9,25)(10,35)(11,44)(12,53)(13,62)(14,71)(15,80)(18,26)(19,
    36)(20,45)(21,54)(22,63)(23,72)(24,81)(29,37)(30,46)(31,55)(32,64)(33,
    73)(39,47)(40,56)(41,65)(42,74)(49,57)(50,66)(51,75)(59,67)(60,76)(69,
    77)^G, (1,35,10,36,19,34)(2,44,11,45,20,43)(3,53,12,54,21,52)(4,71,14,81,
    24,61)(5,80,15,63,22,70)(6,62,13,72,23,79)(7,8,17,18,27,25)(9,26,16)(29,
    37)(30,46)(31,64,32,73,33,55)(39,47)(40,65,41,74,42,56)(49,66,50,75,51,
    57)(58,67,68,77,78,60)(59,76,69)^G, (1,34)(2,43)(3,52)(4,79,6,70,5,61)(8,
    16)(9,25)(10,35)(11,44)(12,53)(13,80,15,71,14,62)(18,26)(19,36)(20,45)(21,
    54)(22,81,24,72,23,63)(29,37)(30,46)(31,73,33,64,32,55)(39,47)(40,74,42,
    65,41,56)(49,75,51,66,50,57)(58,76,78,69,68,59)(60,67,77)^G, 
  (1,44,11,54,21,34)(2,53,12,36,19,43)(3,35,10,45,20,52)(4,71,14,81,24,61)(5,
    80,15,63,22,70)(6,62,13,72,23,79)(7,8,17,18,27,25)(9,26,16)(28,37,38,47,
    48,30)(29,46,39)(31,64,41,74,51,57)(32,73,42,56,49,66)(33,55,40,65,50,
    75)(58,67,68,77,78,60)(59,76,69)^G, (1,34)(2,52,3,43)(4,61)(5,79)(6,70)(8,
    16,9,25)(10,36,19,35)(11,54,21,44)(12,45,20,53)(13,63,22,62)(14,81,23,
    80)(15,72,24,71)(17,18,27,26)(29,46,30,37)(31,55)(32,73)(33,64)(38,47,48,
    39)(40,56,49,57)(41,74,50,75)(42,65,51,66)(59,76)(60,67)(68,78)^G, 
  (1,35,10,34)(2,53,12,43)(3,44,11,52)(4,71,15,79,5,62,13,70,6,80,14,61)(7,8,
    17,16)(9,26,18,25)(19,36)(20,54,21,45)(22,72,24,81,23,63)(29,46,30,37)(31,
    64,33,73,32,55)(38,47,48,39)(40,65,51,75,41,56,49,66,42,74,50,57)(58,67,
    69,78,77,59)(60,76,68)^G, (1,55,61,34,31,4)(2,64,62,43,32,13)(3,73,63,52,
    33,22)(5,10,56,70,35,40)(6,19,57,79,36,49)(7,28,58)(8,37,59,16,29,67)(9,
    46,60,25,30,76)(11,65,71,44,41,14)(12,74,72,53,42,23)(15,20,66,80,45,
    50)(17,38,68)(18,47,69,26,39,77)(21,75,81,54,51,24)(27,48,78)^G, 
  (1,64,72,54,51,24,21,57,62,44,41,14,11,74,79,34,31,4)(2,73,70,36,49,6,19,66,
    63,53,42,23,12,56,80,43,32,13)(3,55,71,45,50,15,20,75,61,35,40,5,10,65,81,
    52,33,22)(7,28,67,9,46,69,27,48,60,26,39,59,17,38,77,16,29,76)(8,37,68,18,
    47,78,25,30,58)^G, (8,9)(17,18)(26,27)(35,36)(44,45)(53,54)(62,63)(64,
    73)(65,74)(66,75)(67,76)(68,77)(69,78)(70,79)(71,81)(72,80)^G, 
  (4,5,6)(8,9)(13,14,15)(17,18)(22,23,24)(26,27)(31,32,33)(35,36)(40,41,
    42)(44,45)(49,50,51)(53,54)(58,59,60)(62,63)(64,73)(65,74)(66,75)(67,77,
    69,76,68,78)(70,79)(71,81)(72,80)^G, (4,5,6)(8,9)(13,14,15)(17,18)(22,23,
    24)(26,27)(28,37,46)(29,38,47)(30,39,48)(31,41,51)(32,42,49)(33,40,50)(34,
    43,52)(35,45,53,36,44,54)(58,59,60)(62,63)(64,73)(65,74)(66,75)(67,77,69,
    76,68,78)(70,79)(71,81)(72,80)^G, (1,2,3)(4,5,6)(8,9)(10,11,12)(13,14,
    15)(17,18)(19,20,21)(22,23,24)(26,27)(28,29,30)(31,32,33)(35,36)(37,38,
    39)(40,41,42)(44,45)(46,47,48)(49,50,51)(53,54)(55,65,57,64,56,66)(58,68,
    60,67,59,69)(61,70)(62,72)(63,71)(73,74,75)(76,77,78)(80,81)^G, 
  (1,2,3)(4,5,6)(8,9)(10,11,12)(13,14,15)(17,18)(19,20,21)(22,23,24)(26,
    27)(28,38,48)(29,39,46)(30,37,47)(31,41,51)(32,42,49)(33,40,50)(34,43,
    52)(35,45,53,36,44,54)(55,65,57,64,56,66)(58,68,60,67,59,69)(61,70)(62,
    72)(63,71)(73,74,75)(76,77,78)(80,81)^G, (1,11,21)(2,12,19)(3,10,20)(4,14,
    24)(5,15,22)(6,13,23)(7,17,25,8,16,26)(9,18,27)(28,38,48)(29,39,46)(30,37,
    47)(31,41,51)(32,42,49)(33,40,50)(34,44,52,35,43,53)(36,45,54)(55,65,57,
    64,56,66)(58,68,60,67,59,69)(61,71)(62,70)(63,72)(73,74,75)(76,77,78)(79,
    80)^G, (2,3)(5,6)(8,9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,
    30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,
    60)(62,63)(64,73)(65,75)(66,74)(67,76)(68,78)(69,77)(70,79)(71,81)(72,
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    44,54)(56,57)(59,60)(62,63)(64,73)(65,75)(66,74)(67,76)(68,78)(69,77)(70,
    79)(71,81)(72,80)^G, (1,10,19)(2,12,20,3,11,21)(4,13,22)(5,15,23,6,14,
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    42,50,33,41,51)(34,44,52,35,43,53)(36,45,54)(56,57)(59,60)(61,62)(64,
    73)(65,75)(66,74)(67,76)(68,78)(69,77)(70,80)(71,79)(72,81)^G, 
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    26)(29,30)(32,33)(35,36)(37,46)(38,48)(39,47)(40,49)(41,51)(42,50)(43,
    52)(44,54)(45,53)(56,57)(59,60)(62,63)(64,73)(65,75)(66,74)(67,76)(68,
    78)(69,77)(70,79)(71,81)(72,80)^G, (1,31,61)(2,32,62,3,33,63)(4,34,55)(5,
    35,57,6,36,56)(7,28,58)(8,30,60,9,29,59)(10,40,70,19,49,79)(11,41,71,21,
    51,81)(12,42,72,20,50,80)(13,43,64,22,52,73)(14,44,66,24,54,74)(15,45,65,
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    62,36)(10,64,46,19,73,37)(11,65,47,20,74,38)(12,66,48,21,75,39)(13,67,49,
    22,76,40)(14,68,50,23,77,41)(15,69,51,24,78,42)(16,70,52,25,79,43)(17,72,
    53,27,80,45)(18,71,54,26,81,44)^G, (1,55,28)(2,56,29)(3,57,30)(4,59,33)(5,
    60,31)(6,58,32)(7,61,34)(8,63,35,9,62,36)(10,64,46,19,73,37)(11,65,47,20,
    74,38)(12,66,48,21,75,39)(13,68,51,22,77,42)(14,69,49,23,78,40)(15,67,50,
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    69,49,23,60,31)(6,67,50,24,58,32)(7,70,52,25,61,34)(8,72,53,27,62,36)(9,
    71,54,26,63,35)(10,74,39)(11,75,37)(12,73,38)(13,77,42)(14,78,40)(15,76,
    41)(16,79,43)(17,81,44,18,80,45)^G, (1,55,28)(2,57,29,3,56,30)(4,58,31)(5,
    60,32,6,59,33)(7,61,34)(8,63,35,9,62,36)(10,64,46,19,73,37)(11,66,47,21,
    74,39)(12,65,48,20,75,38)(13,67,49,22,76,40)(14,69,50,24,77,42)(15,68,51,
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  (1,4)(2,5)(3,6)(10,13)(11,14)(12,15)(19,22)(20,23)(21,24)(28,58)(29,59)(30,
    60)(31,55)(32,56)(33,57)(34,61)(35,62)(36,63)(37,67)(38,68)(39,69)(40,
    64)(41,65)(42,66)(43,70)(44,71)(45,72)(46,76)(47,77)(48,78)(49,73)(50,
    74)(51,75)(52,79)(53,80)(54,81)^G, (1,4)(2,5)(3,6)(7,8,9)(10,13)(11,
    14)(12,15)(16,17,18)(19,22)(20,23)(21,24)(25,26,27)(28,67,37,76,46,58)(29,
    68,38,77,47,59)(30,69,39,78,48,60)(31,64,40,73,49,55)(32,65,41,74,50,
    56)(33,66,42,75,51,57)(34,71,45,79,53,63)(35,72,43,80,54,61)(36,70,44,81,
    52,62)^G, (1,4)(2,5)(3,6)(10,13)(11,14)(12,15)(19,22)(20,23)(21,24)(28,76,
    46,67,37,58)(29,77,47,68,38,59)(30,78,48,69,39,60)(31,73,49,64,40,55)(32,
    74,50,65,41,56)(33,75,51,66,42,57)(34,79,52,70,43,61)(35,80,53,71,44,
    62)(36,81,54,72,45,63)^G, (1,4)(2,5)(3,6)(7,8,9)(10,13)(11,14)(12,15)(16,
    17,18)(19,22)(20,23)(21,24)(25,26,27)(28,58)(29,59)(30,60)(31,55)(32,
    56)(33,57)(34,62,36,61,35,63)(37,67)(38,68)(39,69)(40,64)(41,65)(42,
    66)(43,71,45,70,44,72)(46,76)(47,77)(48,78)(49,73)(50,74)(51,75)(52,80,54,
    79,53,81)^G, (1,5,2,6,3,4)(7,8,9)(10,14,11,15,12,13)(16,17,18)(19,23,20,
    24,21,22)(25,26,27)(28,68,38,78,48,58)(29,69,39,76,46,59)(30,67,37,77,47,
    60)(31,64,41,74,51,57)(32,65,42,75,49,55)(33,66,40,73,50,56)(34,71,45,79,
    53,63)(35,72,43,80,54,61)(36,70,44,81,52,62)^G, 
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    78,48,67,37,59)(30,76,46,68,38,60)(31,73,50,65,42,57)(32,74,51,66,40,
    55)(33,75,49,64,41,56)(34,79,52,70,43,61)(35,80,53,71,44,62)(36,81,54,72,
    45,63)^G, (1,5,2,6,3,4)(7,8,9)(10,14,11,15,12,13)(16,17,18)(19,23,20,24,
    21,22)(25,26,27)(28,59,29,60,30,58)(31,55,32,56,33,57)(34,62,36,61,35,
    63)(37,68,38,69,39,67)(40,64,41,65,42,66)(43,71,45,70,44,72)(46,77,47,78,
    48,76)(49,73,50,74,51,75)(52,80,54,79,53,81)^G, 
  (1,13,19,4,10,22)(2,14,20,5,11,23)(3,15,21,6,12,24)(7,17,27)(8,18,25)(9,16,
    26)(28,58)(29,59)(30,60)(31,55)(32,56)(33,57)(34,62,36,61,35,63)(37,
    67)(38,68)(39,69)(40,64)(41,65)(42,66)(43,71,45,70,44,72)(46,76)(47,
    77)(48,78)(49,73)(50,74)(51,75)(52,80,54,79,53,81)^G, 
  (1,13,19,4,10,22)(2,14,20,5,11,23)(3,15,21,6,12,24)(7,18,26)(8,16,27)(9,17,
    25)(28,67,37,76,46,58)(29,68,38,77,47,59)(30,69,39,78,48,60)(31,64,40,73,
    49,55)(32,65,41,74,50,56)(33,66,42,75,51,57)(34,72,44,79,54,62)(35,70,45,
    80,52,63)(36,71,43,81,53,61)^G, (1,14,20,6,12,22)(2,15,21,4,10,23)(3,13,
    19,5,11,24)(7,18,26)(8,16,27)(9,17,25)(28,68,38,78,48,58)(29,69,39,76,46,
    59)(30,67,37,77,47,60)(31,64,41,74,51,57)(32,65,42,75,49,55)(33,66,40,73,
    50,56)(34,72,44,79,54,62)(35,70,45,80,52,63)(36,71,43,81,53,61)^G, 
  (1,4)(2,6,3,5)(8,9)(10,13)(11,15,12,14)(17,18)(19,22)(20,24,21,23)(26,
    27)(28,58)(29,60,30,59)(31,55)(32,56,33,57)(34,61)(35,63)(36,62)(37,
    76)(38,78,39,77)(40,73)(41,74,42,75)(43,79)(44,81)(45,80)(46,67)(47,69,48,
    68)(49,64)(50,65,51,66)(52,70)(53,72)(54,71)^G, 
  (1,4)(2,6,3,5)(7,8)(10,13)(11,15,12,14)(16,17)(19,22)(20,24,21,23)(25,
    26)(28,67,46,76,37,58)(29,69,48,77,38,60,30,68,47,78,39,59)(31,64,49,73,
    40,55)(32,65,51,75,41,56,33,66,50,74,42,57)(34,71,52,80,43,62)(35,70,53,
    79,44,61)(36,72,54,81,45,63)^G, (1,13,19,4,10,22)(2,15,21,5,11,24,3,14,20,
    6,12,23)(7,17,25,8,16,26)(9,18,27)(28,58)(29,60,30,59)(31,55)(32,56,33,
    57)(34,62)(35,61)(36,63)(37,76)(38,78,39,77)(40,73)(41,74,42,75)(43,
    80)(44,79)(45,81)(46,67)(47,69,48,68)(49,64)(50,65,51,66)(52,71)(53,
    70)(54,72)^G, (1,13,19,4,10,22)(2,15,21,5,11,24,3,14,20,6,12,23)(7,18,25,
    9,16,27)(8,17,26)(28,67,46,76,37,58)(29,69,48,77,38,60,30,68,47,78,39,
    59)(31,64,49,73,40,55)(32,65,51,75,41,56,33,66,50,74,42,57)(34,72,52,81,
    43,63)(35,71,53,80,44,62)(36,70,54,79,45,61)^G, 
  (1,4)(2,6,3,5)(8,9)(10,22)(11,24,12,23)(13,19)(14,20,15,21)(16,25)(17,
    27)(18,26)(28,58)(29,60,30,59)(31,55)(32,56,33,57)(34,61)(35,63)(36,
    62)(37,76,46,67)(38,78,48,68)(39,77,47,69)(40,73,49,64)(41,74,51,66)(42,
    75,50,65)(43,79,52,70)(44,81,53,72)(45,80,54,71)^G, 
  (1,4)(2,6,3,5)(10,22)(11,24,12,23)(13,19)(14,20,15,21)(16,25)(17,26)(18,
    27)(28,58)(29,60,30,59)(31,55)(32,56,33,57)(34,61)(35,62)(36,63)(37,
    67)(38,69,39,68)(40,64)(41,65,42,66)(43,70)(44,71)(45,72)(46,76)(47,78,48,
    77)(49,73)(50,74,51,75)(52,79)(53,80)(54,81)^G, 
  (1,4)(2,6,3,5)(7,8,9)(10,22)(11,24,12,23)(13,19)(14,20,15,21)(16,26,18,25,
    17,27)(28,67,37,76,46,58)(29,69,39,77,47,60,30,68,38,78,48,59)(31,64,40,
    73,49,55)(32,65,42,75,50,56,33,66,41,74,51,57)(34,71,45,79,53,63)(35,72,
    43,80,54,61)(36,70,44,81,52,62)^G, (1,4)(2,6,3,5)(10,22)(11,24,12,23)(13,
    19)(14,20,15,21)(16,25)(17,26)(18,27)(28,76,46,67,37,58)(29,78,48,68,38,
    60,30,77,47,69,39,59)(31,73,49,64,40,55)(32,74,51,66,41,56,33,75,50,65,42,
    57)(34,79,52,70,43,61)(35,80,53,71,44,62)(36,81,54,72,45,63)^G, 
  (1,4)(2,6,3,5)(7,8,9)(10,22)(11,24,12,23)(13,19)(14,20,15,21)(16,26,18,25,
    17,27)(28,58)(29,60,30,59)(31,55)(32,56,33,57)(34,62,36,61,35,63)(37,
    67)(38,69,39,68)(40,64)(41,65,42,66)(43,71,45,70,44,72)(46,76)(47,78,48,
    77)(49,73)(50,74,51,75)(52,80,54,79,53,81)^G, 
  (1,4)(2,5)(3,6)(8,9)(10,22)(11,23)(12,24)(13,19)(14,20)(15,21)(16,25)(17,
    27)(18,26)(28,58)(29,59)(30,60)(31,55)(32,56)(33,57)(34,61)(35,63)(36,
    62)(37,76)(38,77)(39,78)(40,73)(41,74)(42,75)(43,79)(44,81)(45,80)(46,
    67)(47,68)(48,69)(49,64)(50,65)(51,66)(52,70)(53,72)(54,71)^G, 
  (1,4)(2,5)(3,6)(7,8)(10,22)(11,23)(12,24)(13,19)(14,20)(15,21)(16,26)(17,
    25)(18,27)(28,67,46,76,37,58)(29,68,47,77,38,59)(30,69,48,78,39,60)(31,64,
    49,73,40,55)(32,65,50,74,41,56)(33,66,51,75,42,57)(34,71,52,80,43,62)(35,
    70,53,79,44,61)(36,72,54,81,45,63)^G, (1,5,2,6,3,4)(7,8)(10,23,11,24,12,
    22)(13,19,14,20,15,21)(16,26)(17,25)(18,27)(28,68,47,78,39,58)(29,69,48,
    76,37,59)(30,67,46,77,38,60)(31,64,50,74,42,57)(32,65,51,75,40,55)(33,66,
    49,73,41,56)(34,71,52,80,43,62)(35,70,53,79,44,61)(36,72,54,81,45,63)^G, 
  (1,4)(2,6,3,5)(10,13)(11,15,12,14)(19,22)(20,24,21,23)(28,58)(29,60,30,
    59)(31,55)(32,56,33,57)(34,61)(35,62)(36,63)(37,67,46,76)(38,69,48,77)(39,
    68,47,78)(40,64,49,73)(41,65,51,75)(42,66,50,74)(43,70,52,79)(44,71,53,
    80)(45,72,54,81)^G, (1,4)(2,6,3,5)(7,8,9)(10,13)(11,15,12,14)(16,17,
    18)(19,22)(20,24,21,23)(25,26,27)(28,67,46,58)(29,69,48,59)(30,68,47,
    60)(31,64,49,55)(32,65,51,57)(33,66,50,56)(34,71,54,61,35,72,52,62,36,70,
    53,63)(37,76)(38,78,39,77)(40,73)(41,74,42,75)(43,80,45,79,44,81)^G, 
  (1,13,19,4,10,22)(2,15,21,5,11,24,3,14,20,6,12,23)(7,17,27)(8,18,25)(9,16,
    26)(28,58)(29,60,30,59)(31,55)(32,56,33,57)(34,62,36,61,35,63)(37,67,46,
    76)(38,69,48,77)(39,68,47,78)(40,64,49,73)(41,65,51,75)(42,66,50,74)(43,
    71,54,79,44,72,52,80,45,70,53,81)^G, (1,34,6,61,3,52,4,70,2,43,5,79)(8,16,
    9,25)(10,36,24,62,12,54,22,71,11,45,23,80)(13,72,20,44,14,81,19,35,15,63,
    21,53)(17,18,27,26)(28,33,60,57,48,49,67,65,38,41,77,73)(29,42,59,75,46,
    31,69,56,39,50,76,64)(30,51,58,66,47,40,68,74,37,32,78,55)^G, 
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    9,27,25)(8,18,26,16)(10,35,15,80)(11,44,14,71)(12,53,13,62)(28,33,78,
    73)(29,42,77,64)(30,51,76,55)(31,60,75,46)(32,69,74,37)(38,41,68,65)(39,
    50,67,56)(40,59,66,47)(48,49,58,57)^G, (1,34,5,70,2,52,4,79)(3,43,6,61)(8,
    16)(9,25)(10,35,14,71,11,53,13,80)(12,44,15,62)(18,26)(19,36,23,72,20,54,
    22,81)(21,45,24,63)(28,32,68,65,47,49,76,73)(29,50,67,74,46,31,77,64)(30,
    41,69,56,48,40,78,55)(33,59,66,38,51,58,75,37)(39,42,60,57)^G, 
  (1,35,14,81,19,34,5,80,10,36,23,79)(2,53,13,63,21,43,6,71,11,54,22,61,3,44,
    15,72,20,52,4,62,12,45,24,70)(7,8,17,18,27,25)(9,26,16)(28,32,77,73)(29,
    50,76,55,30,41,78,64)(31,59,75,37,33,68,74,46)(38,51,67,56,48,40,60,
    66)(39,42,69,65,47,49,58,57)^G, (4,5,6)(10,19)(11,20)(12,21)(13,23,15,22,
    14,24)(16,25)(17,26)(18,27)(28,73)(29,74)(30,75)(31,77,33,76,32,78)(34,
    79)(35,80)(36,81)(37,64)(38,65)(39,66)(40,68,42,67,41,69)(43,70)(44,
    71)(45,72)(46,55)(47,56)(48,57)(49,59,51,58,50,60)(52,61)(53,62)(54,63)^G,
  (4,5,6)(7,8,9)(10,19)(11,20)(12,21)(13,23,15,22,14,24)(16,26,18,25,17,
    27)(28,55,46,64,37,73)(29,56,47,65,38,74)(30,57,48,66,39,75)(31,59,51,67,
    41,78)(32,60,49,68,42,76)(33,58,50,69,40,77)(34,62,54,70,44,81)(35,63,52,
    71,45,79)(36,61,53,72,43,80)^G, (4,5,6)(10,19)(11,20)(12,21)(13,23,15,22,
    14,24)(16,25)(17,26)(18,27)(28,64,37,55,46,73)(29,65,38,56,47,74)(30,66,
    39,57,48,75)(31,68,42,58,50,78)(32,69,40,59,51,76)(33,67,41,60,49,77)(34,
    70,43,61,52,79)(35,71,44,62,53,80)(36,72,45,63,54,81)^G, 
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    27)(28,73)(29,74)(30,75)(31,77,33,76,32,78)(34,80,36,79,35,81)(37,64)(38,
    65)(39,66)(40,68,42,67,41,69)(43,71,45,70,44,72)(46,55)(47,56)(48,57)(49,
    59,51,58,50,60)(52,62,54,61,53,63)^G, (10,19)(11,20)(12,21)(13,22)(14,
    23)(15,24)(16,25)(17,26)(18,27)(28,73)(29,74)(30,75)(31,76)(32,77)(33,
    78)(34,79)(35,80)(36,81)(37,64)(38,65)(39,66)(40,67)(41,68)(42,69)(43,
    70)(44,71)(45,72)(46,55)(47,56)(48,57)(49,58)(50,59)(51,60)(52,61)(53,
    62)(54,63)^G, (10,19)(11,20)(12,21)(13,22)(14,23)(15,24)(16,25)(17,26)(18,
    27)(28,64,37,55,46,73)(29,65,38,56,47,74)(30,66,39,57,48,75)(31,67,40,58,
    49,76)(32,68,41,59,50,77)(33,69,42,60,51,78)(34,70,43,61,52,79)(35,71,44,
    62,53,80)(36,72,45,63,54,81)^G, (1,2,3)(4,5,6)(7,8,9)(10,20,12,19,11,
    21)(13,23,15,22,14,24)(16,26,18,25,17,27)(28,65,39,55,47,75)(29,66,37,56,
    48,73)(30,64,38,57,46,74)(31,68,42,58,50,78)(32,69,40,59,51,76)(33,67,41,
    60,49,77)(34,71,45,61,53,81)(35,72,43,62,54,79)(36,70,44,63,52,80)^G, 
  (1,2,3)(4,5,6)(7,9,8)(10,20,12,19,11,21)(13,23,15,22,14,24)(16,27,17,25,18,
    26)(28,74,30,73,29,75)(31,77,33,76,32,78)(34,81,35,79,36,80)(37,65,39,64,
    38,66)(40,68,42,67,41,69)(43,72,44,70,45,71)(46,56,48,55,47,57)(49,59,51,
    58,50,60)(52,63,53,61,54,62)^G, (4,6)(8,9)(10,19)(11,20)(12,21)(13,24)(14,
    23)(15,22)(16,25)(17,27)(18,26)(28,64,46,55,37,73)(29,65,47,56,38,74)(30,
    66,48,57,39,75)(31,69,49,60,40,78)(32,68,50,59,41,77)(33,67,51,58,42,
    76)(34,70,52,61,43,79)(35,72,53,63,44,81)(36,71,54,62,45,80)^G, 
  (4,6)(7,8)(10,19)(11,20)(12,21)(13,24)(14,23)(15,22)(16,26)(17,25)(18,
    27)(28,73)(29,74)(30,75)(31,78)(32,77)(33,76)(34,80)(35,79)(36,81)(37,
    55)(38,56)(39,57)(40,60)(41,59)(42,58)(43,62)(44,61)(45,63)(46,64)(47,
    65)(48,66)(49,69)(50,68)(51,67)(52,71)(53,70)(54,72)^G, 
  (1,2,3)(4,6)(8,9)(10,20,12,19,11,21)(13,24)(14,23)(15,22)(16,25)(17,27)(18,
    26)(28,74,30,73,29,75)(31,78)(32,77)(33,76)(34,79)(35,81)(36,80)(37,56,39,
    55,38,57)(40,60)(41,59)(42,58)(43,61)(44,63)(45,62)(46,65,48,64,47,66)(49,
    69)(50,68)(51,67)(52,70)(53,72)(54,71)^G, 
  (1,2,3)(4,6)(7,8)(10,20,12,19,11,21)(13,24)(14,23)(15,22)(16,26)(17,25)(18,
    27)(28,56,39,64,47,75)(29,57,37,65,48,73)(30,55,38,66,46,74)(31,60,40,69,
    49,78)(32,59,41,68,50,77)(33,58,42,67,51,76)(34,62,43,71,52,80)(35,61,44,
    70,53,79)(36,63,45,72,54,81)^G, (4,5,6)(13,14,15)(22,23,24)(28,73)(29,
    74)(30,75)(31,77,33,76,32,78)(34,79)(35,80)(36,81)(37,64,46,55)(38,65,47,
    56)(39,66,48,57)(40,68,51,58,41,69,49,59,42,67,50,60)(43,70,52,61)(44,71,
    53,62)(45,72,54,63)^G, (4,5,6)(7,8,9)(13,14,15)(16,17,18)(22,23,24)(25,26,
    27)(28,55,37,73)(29,56,38,74)(30,57,39,75)(31,59,42,76,32,60,40,77,33,58,
    41,78)(34,62,45,79,35,63,43,80,36,61,44,81)(46,64)(47,65)(48,66)(49,68,51,
    67,50,69)(52,71,54,70,53,72)^G, (28,73)(29,74)(30,75)(31,76)(32,77)(33,
    78)(34,79)(35,80)(36,81)(37,64,46,55)(38,65,47,56)(39,66,48,57)(40,67,49,
    58)(41,68,50,59)(42,69,51,60)(43,70,52,61)(44,71,53,62)(45,72,54,63)^G, 
  (1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18)(19,20,21)(22,23,24)(25,
    26,27)(28,65,48,73,29,66,46,74,30,64,47,75)(31,68,51,76,32,69,49,77,33,67,
    50,78)(34,71,54,79,35,72,52,80,36,70,53,81)(37,56,39,55,38,57)(40,59,42,
    58,41,60)(43,62,45,61,44,63)^G, (1,10,19)(2,11,20)(3,12,21)(4,14,24)(5,15,
    22)(6,13,23)(7,17,27)(8,18,25)(9,16,26)(28,73)(29,74)(30,75)(31,77,33,76,
    32,78)(34,80,36,79,35,81)(37,64,46,55)(38,65,47,56)(39,66,48,57)(40,68,51,
    58,41,69,49,59,42,67,50,60)(43,71,54,61,44,72,52,62,45,70,53,63)^G, 
  (1,10,19)(2,11,20)(3,12,21)(4,14,24)(5,15,22)(6,13,23)(7,16,25)(8,17,26)(9,
    18,27)(28,64,46,73)(29,65,47,74)(30,66,48,75)(31,68,51,76,32,69,49,77,33,
    67,50,78)(34,70,52,79)(35,71,53,80)(36,72,54,81)(37,55)(38,56)(39,57)(40,
    59,42,58,41,60)(43,61)(44,62)(45,63)^G, (1,10,19)(2,11,20)(3,12,21)(4,13,
    22)(5,14,23)(6,15,24)(7,16,25)(8,17,26)(9,18,27)(28,64,46,73)(29,65,47,
    74)(30,66,48,75)(31,67,49,76)(32,68,50,77)(33,69,51,78)(34,70,52,79)(35,
    71,53,80)(36,72,54,81)(37,55)(38,56)(39,57)(40,58)(41,59)(42,60)(43,
    61)(44,62)(45,63)^G, (1,11,21)(2,12,19)(3,10,20)(4,14,24)(5,15,22)(6,13,
    23)(7,17,27)(8,18,25)(9,16,26)(28,56,39,73,29,57,37,74,30,55,38,75)(31,59,
    42,76,32,60,40,77,33,58,41,78)(34,62,45,79,35,63,43,80,36,61,44,81)(46,65,
    48,64,47,66)(49,68,51,67,50,69)(52,71,54,70,53,72)^G, 
  (4,6)(8,9)(13,15)(17,18)(22,24)(26,27)(28,64,37,73)(29,65,38,74)(30,66,39,
    75)(31,69,40,78)(32,68,41,77)(33,67,42,76)(34,70,43,79)(35,72,44,81)(36,
    71,45,80)(46,55)(47,56)(48,57)(49,60)(50,59)(51,58)(52,61)(53,63)(54,62)^G
    , (1,2,3)(4,6)(8,9)(10,11,12)(13,15)(17,18)(19,20,21)(22,24)(26,27)(28,74,
    30,73,29,75)(31,78)(32,77)(33,76)(34,79)(35,81)(36,80)(37,56,48,64,38,57,
    46,65,39,55,47,66)(40,60,49,69)(41,59,50,68)(42,58,51,67)(43,61,52,70)(44,
    63,53,72)(45,62,54,71)^G, (1,10,19)(2,11,20)(3,12,21)(4,15,22,6,13,24)(5,
    14,23)(7,17,25,8,16,26)(9,18,27)(28,64,37,73)(29,65,38,74)(30,66,39,
    75)(31,69,40,78)(32,68,41,77)(33,67,42,76)(34,71,43,80)(35,70,44,79)(36,
    72,45,81)(46,55)(47,56)(48,57)(49,60)(50,59)(51,58)(52,62)(53,61)(54,63)^G
    , (1,11,21)(2,12,19)(3,10,20)(4,15,22,6,13,24)(5,14,23)(7,17,25,8,16,
    26)(9,18,27)(28,74,30,73,29,75)(31,78)(32,77)(33,76)(34,80)(35,79)(36,
    81)(37,56,48,64,38,57,46,65,39,55,47,66)(40,60,49,69)(41,59,50,68)(42,58,
    51,67)(43,62,52,71)(44,61,53,70)(45,63,54,72)^G, 
  (1,31,26,38,14,54,3,33,25,37,13,53,2,32,27,39,15,52)(4,35,20,41,18,48,6,34,
    19,40,17,47,5,36,21,42,16,46)(7,28,22,44,11,50,9,30,24,43,10,49,8,29,23,
    45,12,51)(55,76,62,74,59,81,57,78,61,73,58,80,56,77,63,75,60,79)(64,67,71,
    65,68,72,66,69,70)^G, (1,31,25,37,13,52)(2,32,26,38,14,53)(3,33,27,39,15,
    54)(4,34,19,40,16,46)(5,35,20,41,17,47)(6,36,21,42,18,48)(7,28,22,43,10,
    49)(8,29,23,44,11,50)(9,30,24,45,12,51)(55,67,61,64,58,70)(56,68,62,65,59,
    71)(57,69,63,66,60,72)(73,76,79)(74,77,80)(75,78,81)^G, 
  (1,49,8,47,5,54,3,51,7,46,4,53,2,50,9,48,6,52)(10,40,17,38,14,45,12,42,16,
    37,13,44,11,41,18,39,15,43)(19,31,26,29,23,36,21,33,25,28,22,35,20,32,27,
    30,24,34)(55,76,62,74,59,81,57,78,61,73,58,80,56,77,63,75,60,79)(64,67,71,
    65,68,72,66,69,70)^G, (1,49,7,46,4,52)(2,50,8,47,5,53)(3,51,9,48,6,54)(10,
    40,16,37,13,43)(11,41,17,38,14,44)(12,42,18,39,15,45)(19,31,25,28,22,
    34)(20,32,26,29,23,35)(21,33,27,30,24,36)(55,67,61,64,58,70)(56,68,62,65,
    59,71)(57,69,63,66,60,72)(73,76,79)(74,77,80)(75,78,81)^G, 
  (1,31,27,48,5,35,20,51,7,28,22,54,3,32,26,47,6,34,19,49,9,30,23,53,2,33,25,
    46,4,36,21,50,8,29,24,52)(10,40,18,39,14,44,11,42,16,37,13,45,12,41,17,38,
    15,43)(55,67,81,57,68,80,56,69,79)(58,72,75,59,71,74,60,70,73)(61,64,76,
    63,66,77,62,65,78)^G, (1,31,25,46,4,34,19,49,7,28,22,52)(2,33,26,47,6,35,
    20,51,8,29,24,53)(3,32,27,48,5,36,21,50,9,30,23,54)(10,40,16,37,13,43)(11,
    42,17,38,15,44)(12,41,18,39,14,45)(55,76,70)(56,78,71)(57,77,72)(58,79,
    64)(59,81,66)(60,80,65)(61,73,67)(62,74,69)(63,75,68)^G, 
  (1,31,26,47,6,36,21,50,7,28,22,53,2,33,27,48,5,34,19,49,8,29,24,54,3,32,25,
    46,4,35,20,51,9,30,23,52)(10,40,17,38,15,45,12,41,16,37,13,44,11,42,18,39,
    14,43)(55,58,62,56,60,63,57,59,61)(64,67,71,65,69,72,66,68,70)(73,76,80,
    74,78,81,75,77,79)^G, (1,31,25,46,4,34,19,49,7,28,22,52)(2,33,26,47,6,35,
    20,51,8,29,24,53)(3,32,27,48,5,36,21,50,9,30,23,54)(10,40,16,37,13,43)(11,
    42,17,38,15,44)(12,41,18,39,14,45)(55,58,61)(56,60,62)(57,59,63)(64,67,
    70)(65,69,71)(66,68,72)(73,76,79)(74,78,80)(75,77,81)^G, 
  (4,6)(13,15)(22,24)(28,73)(29,74)(30,75)(31,78)(32,77)(33,76)(34,79)(35,
    80)(36,81)(37,64)(38,65)(39,66)(40,69)(41,68)(42,67)(43,70)(44,71)(45,
    72)(46,55)(47,56)(48,57)(49,60)(50,59)(51,58)(52,61)(53,62)(54,63)^G, 
  (4,6)(7,8,9)(13,15)(16,17,18)(22,24)(25,26,27)(28,55,46,64,37,73)(29,56,47,
    65,38,74)(30,57,48,66,39,75)(31,60,49,69,40,78)(32,59,50,68,41,77)(33,58,
    51,67,42,76)(34,62,54,70,44,81)(35,63,52,71,45,79)(36,61,53,72,43,80)^G, 
  (4,6)(13,15)(22,24)(28,64,37,55,46,73)(29,65,38,56,47,74)(30,66,39,57,48,
    75)(31,69,40,60,49,78)(32,68,41,59,50,77)(33,67,42,58,51,76)(34,70,43,61,
    52,79)(35,71,44,62,53,80)(36,72,45,63,54,81)^G, 
  (4,6)(7,8,9)(13,15)(16,17,18)(22,24)(25,26,27)(28,73)(29,74)(30,75)(31,
    78)(32,77)(33,76)(34,80,36,79,35,81)(37,64)(38,65)(39,66)(40,69)(41,
    68)(42,67)(43,71,45,70,44,72)(46,55)(47,56)(48,57)(49,60)(50,59)(51,
    58)(52,62,54,61,53,63)^G, (1,2,3)(4,6)(7,8,9)(10,11,12)(13,15)(16,17,
    18)(19,20,21)(22,24)(25,26,27)(28,65,39,55,47,75)(29,66,37,56,48,73)(30,
    64,38,57,46,74)(31,69,40,60,49,78)(32,68,41,59,50,77)(33,67,42,58,51,
    76)(34,71,45,61,53,81)(35,72,43,62,54,79)(36,70,44,63,52,80)^G, 
  (1,2,3)(4,6)(7,9,8)(10,11,12)(13,15)(16,18,17)(19,20,21)(22,24)(25,27,
    26)(28,74,30,73,29,75)(31,78)(32,77)(33,76)(34,81,35,79,36,80)(37,65,39,
    64,38,66)(40,69)(41,68)(42,67)(43,72,44,70,45,71)(46,56,48,55,47,57)(49,
    60)(50,59)(51,58)(52,63,53,61,54,62)^G, (1,10,19)(2,11,20)(3,12,21)(4,15,
    22,6,13,24)(5,14,23)(7,17,27)(8,18,25)(9,16,26)(28,73)(29,74)(30,75)(31,
    78)(32,77)(33,76)(34,80,36,79,35,81)(37,64)(38,65)(39,66)(40,69)(41,
    68)(42,67)(43,71,45,70,44,72)(46,55)(47,56)(48,57)(49,60)(50,59)(51,
    58)(52,62,54,61,53,63)^G, (1,10,19)(2,11,20)(3,12,21)(4,15,22,6,13,24)(5,
    14,23)(7,18,26)(8,16,27)(9,17,25)(28,55,46,64,37,73)(29,56,47,65,38,
    74)(30,57,48,66,39,75)(31,60,49,69,40,78)(32,59,50,68,41,77)(33,58,51,67,
    42,76)(34,63,53,70,45,80)(35,61,54,71,43,81)(36,62,52,72,44,79)^G, 
  (1,10,19)(2,11,20)(3,12,21)(4,15,22,6,13,24)(5,14,23)(7,16,25)(8,17,26)(9,
    18,27)(28,64,37,55,46,73)(29,65,38,56,47,74)(30,66,39,57,48,75)(31,69,40,
    60,49,78)(32,68,41,59,50,77)(33,67,42,58,51,76)(34,70,43,61,52,79)(35,71,
    44,62,53,80)(36,72,45,63,54,81)^G, (1,10,19)(2,11,20)(3,12,21)(4,15,22,6,
    13,24)(5,14,23)(7,16,25)(8,17,26)(9,18,27)(28,73)(29,74)(30,75)(31,78)(32,
    77)(33,76)(34,79)(35,80)(36,81)(37,64)(38,65)(39,66)(40,69)(41,68)(42,
    67)(43,70)(44,71)(45,72)(46,55)(47,56)(48,57)(49,60)(50,59)(51,58)(52,
    61)(53,62)(54,63)^G, (1,11,21)(2,12,19)(3,10,20)(4,15,22,6,13,24)(5,14,
    23)(7,17,27)(8,18,25)(9,16,26)(28,56,48,64,38,75)(29,57,46,65,39,73)(30,
    55,47,66,37,74)(31,60,49,69,40,78)(32,59,50,68,41,77)(33,58,51,67,42,
    76)(34,62,54,70,44,81)(35,63,52,71,45,79)(36,61,53,72,43,80)^G, 
  (1,11,21)(2,12,19)(3,10,20)(4,15,22,6,13,24)(5,14,23)(7,17,27)(8,18,25)(9,
    16,26)(28,74,30,73,29,75)(31,78)(32,77)(33,76)(34,80,36,79,35,81)(37,65,
    39,64,38,66)(40,69)(41,68)(42,67)(43,71,45,70,44,72)(46,56,48,55,47,
    57)(49,60)(50,59)(51,58)(52,62,54,61,53,63)^G, 
  (2,3)(4,6)(8,9)(11,12)(13,15)(17,18)(20,21)(22,24)(26,27)(28,64,46,55,37,
    73)(29,66,47,57,38,75)(30,65,48,56,39,74)(31,69,49,60,40,78)(32,68,50,59,
    41,77)(33,67,51,58,42,76)(34,70,52,61,43,79)(35,72,53,63,44,81)(36,71,54,
    62,45,80)^G, (2,3)(4,6)(7,8)(11,12)(13,15)(16,17)(20,21)(22,24)(25,26)(28,
    73)(29,75)(30,74)(31,78)(32,77)(33,76)(34,80)(35,79)(36,81)(37,55)(38,
    57)(39,56)(40,60)(41,59)(42,58)(43,62)(44,61)(45,63)(46,64)(47,66)(48,
    65)(49,69)(50,68)(51,67)(52,71)(53,70)(54,72)^G, 
  (1,10,19)(2,12,20,3,11,21)(4,15,22,6,13,24)(5,14,23)(7,17,25,8,16,26)(9,18,
    27)(28,64,46,55,37,73)(29,66,47,57,38,75)(30,65,48,56,39,74)(31,69,49,60,
    40,78)(32,68,50,59,41,77)(33,67,51,58,42,76)(34,71,52,62,43,80)(35,70,53,
    61,44,79)(36,72,54,63,45,81)^G, (1,10,19)(2,12,20,3,11,21)(4,15,22,6,13,
    24)(5,14,23)(7,18,25,9,16,27)(8,17,26)(28,73)(29,75)(30,74)(31,78)(32,
    77)(33,76)(34,81)(35,80)(36,79)(37,55)(38,57)(39,56)(40,60)(41,59)(42,
    58)(43,63)(44,62)(45,61)(46,64)(47,66)(48,65)(49,69)(50,68)(51,67)(52,
    72)(53,71)(54,70)^G, (4,6)(10,19)(11,20)(12,21)(13,24)(14,23)(15,22)(16,
    25)(17,26)(18,27)(28,73)(29,74)(30,75)(31,78)(32,77)(33,76)(34,79)(35,
    80)(36,81)(37,64,46,55)(38,65,47,56)(39,66,48,57)(40,69,49,60)(41,68,50,
    59)(42,67,51,58)(43,70,52,61)(44,71,53,62)(45,72,54,63)^G, 
  (4,6)(7,8,9)(10,19)(11,20)(12,21)(13,24)(14,23)(15,22)(16,26,18,25,17,
    27)(28,55,37,73)(29,56,38,74)(30,57,39,75)(31,60,40,78)(32,59,41,77)(33,
    58,42,76)(34,62,45,79,35,63,43,80,36,61,44,81)(46,64)(47,65)(48,66)(49,
    69)(50,68)(51,67)(52,71,54,70,53,72)^G, (1,2,3)(4,6)(7,8,9)(10,20,12,19,
    11,21)(13,24)(14,23)(15,22)(16,26,18,25,17,27)(28,65,48,73,29,66,46,74,30,
    64,47,75)(31,69,49,78)(32,68,50,77)(33,67,51,76)(34,71,54,79,35,72,52,80,
    36,70,53,81)(37,56,39,55,38,57)(40,60)(41,59)(42,58)(43,62,45,61,44,63)^G,
  (2,3)(4,6)(8,9)(10,19)(11,21)(12,20)(13,24)(14,23)(15,22)(16,25)(17,27)(18,
    26)(28,64,37,73)(29,66,38,75)(30,65,39,74)(31,69,40,78)(32,68,41,77)(33,
    67,42,76)(34,70,43,79)(35,72,44,81)(36,71,45,80)(46,55)(47,57)(48,56)(49,
    60)(50,59)(51,58)(52,61)(53,63)(54,62)^G, 
  (1,31,27,48,6,34,19,49,9,30,24,52)(2,32,26,47,5,35,20,50,8,29,23,53)(3,33,
    25,46,4,36,21,51,7,28,22,54)(10,40,18,39,15,43)(11,41,17,38,14,44)(12,42,
    16,37,13,45)(55,76,63,75,60,79)(56,77,62,74,59,80)(57,78,61,73,58,81)(64,
    67,72,66,69,70)(65,68,71)^G, (1,31,26,38,15,52)(2,33,25,37,13,53)(3,32,27,
    39,14,54)(4,35,20,42,16,46)(5,36,21,41,18,48)(6,34,19,40,17,47)(7,28,22,
    44,11,51)(8,29,24,43,10,49)(9,30,23,45,12,50)(55,67,80,56,69,79)(57,68,
    81)(58,71,74,60,70,73)(59,72,75)(61,64,76,62,65,78)(63,66,77)^G, 
  (1,31,25,37,13,52)(2,33,27,39,14,53)(3,32,26,38,15,54)(4,34,19,40,16,46)(5,
    35,20,42,18,48)(6,36,21,41,17,47)(7,28,22,43,10,49)(8,29,24,45,12,50)(9,
    30,23,44,11,51)(55,58,61)(56,60,63,57,59,62)(64,67,70)(65,69,72,66,68,
    71)(73,76,79)(74,78,81,75,77,80)^G, (1,49,8,47,6,52)(2,51,7,46,4,53)(3,50,
    9,48,5,54)(10,40,17,38,15,43)(11,42,16,37,13,44)(12,41,18,39,14,45)(19,31,
    26,29,24,34)(20,33,25,28,22,35)(21,32,27,30,23,36)(55,67,80,56,69,79)(57,
    68,81)(58,71,74,60,70,73)(59,72,75)(61,64,76,62,65,78)(63,66,77)^G, 
  (1,49,7,46,4,52)(2,51,9,48,5,53)(3,50,8,47,6,54)(10,40,16,37,13,43)(11,42,
    18,39,14,44)(12,41,17,38,15,45)(19,31,25,28,22,34)(20,33,27,30,23,35)(21,
    32,26,29,24,36)(55,58,61)(56,60,63,57,59,62)(64,67,70)(65,69,72,66,68,
    71)(73,76,79)(74,78,81,75,77,80)^G, (64,73)(65,74)(66,75)(67,76)(68,
    77)(69,78)(70,79)(71,80)(72,81)^G, (7,8,9)(16,17,18)(25,26,27)(34,35,
    36)(43,44,45)(52,53,54)(55,64)(56,65)(57,66)(58,67)(59,68)(60,69)(61,71,
    63,70,62,72)(79,80,81)^G, (4,5,6)(7,8,9)(13,14,15)(16,17,18)(22,23,24)(25,
    26,27)(31,32,33)(34,35,36)(40,41,42)(43,44,45)(49,50,51)(52,53,54)(55,
    64)(56,65)(57,66)(58,68,60,67,59,69)(61,71,63,70,62,72)(76,77,78)(79,80,
    81)^G, (28,37,46)(29,38,47)(30,39,48)(31,40,49)(32,41,50)(33,42,51)(34,43,
    52)(35,44,53)(36,45,54)(64,73)(65,74)(66,75)(67,76)(68,77)(69,78)(70,
    79)(71,80)(72,81)^G, (7,8,9)(16,17,18)(25,26,27)(28,37,46)(29,38,47)(30,
    39,48)(31,40,49)(32,41,50)(33,42,51)(34,44,54)(35,45,52)(36,43,53)(55,
    64)(56,65)(57,66)(58,67)(59,68)(60,69)(61,71,63,70,62,72)(79,80,81)^G, 
  (4,5,6)(7,8,9)(13,14,15)(16,17,18)(22,23,24)(25,26,27)(28,37,46)(29,38,
    47)(30,39,48)(31,41,51)(32,42,49)(33,40,50)(34,44,54)(35,45,52)(36,43,
    53)(55,64)(56,65)(57,66)(58,68,60,67,59,69)(61,71,63,70,62,72)(76,77,
    78)(79,80,81)^G, (1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18)(19,
    20,21)(22,23,24)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,
    42)(43,44,45)(46,47,48)(49,50,51)(52,53,54)(55,74,57,73,56,75)(58,77,60,
    76,59,78)(61,80,63,79,62,81)(64,65,66)(67,68,69)(70,71,72)^G, 
  (1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18)(19,20,21)(22,23,24)(25,
    26,27)(28,38,48)(29,39,46)(30,37,47)(31,41,51)(32,42,49)(33,40,50)(34,44,
    54)(35,45,52)(36,43,53)(55,74,57,73,56,75)(58,77,60,76,59,78)(61,80,63,79,
    62,81)(64,65,66)(67,68,69)(70,71,72)^G, (1,10,19)(2,11,20)(3,12,21)(4,13,
    22)(5,14,23)(6,15,24)(7,17,27)(8,18,25)(9,16,26)(28,37,46)(29,38,47)(30,
    39,48)(31,40,49)(32,41,50)(33,42,51)(34,44,54)(35,45,52)(36,43,53)(61,62,
    63)(64,73)(65,74)(66,75)(67,76)(68,77)(69,78)(70,80,72,79,71,81)^G, 
  (1,10,19)(2,11,20)(3,12,21)(4,13,22)(5,14,23)(6,15,24)(7,16,25)(8,17,26)(9,
    18,27)(28,37,46)(29,38,47)(30,39,48)(31,40,49)(32,41,50)(33,42,51)(34,43,
    52)(35,44,53)(36,45,54)(55,73)(56,74)(57,75)(58,76)(59,77)(60,78)(61,
    79)(62,80)(63,81)^G, (1,10,19)(2,11,20)(3,12,21)(4,14,24)(5,15,22)(6,13,
    23)(7,17,27)(8,18,25)(9,16,26)(28,37,46)(29,38,47)(30,39,48)(31,41,51)(32,
    42,49)(33,40,50)(34,44,54)(35,45,52)(36,43,53)(58,59,60)(61,62,63)(64,
    73)(65,74)(66,75)(67,77,69,76,68,78)(70,80,72,79,71,81)^G, 
  (1,11,21)(2,12,19)(3,10,20)(4,14,24)(5,15,22)(6,13,23)(7,17,27)(8,18,25)(9,
    16,26)(28,38,48)(29,39,46)(30,37,47)(31,41,51)(32,42,49)(33,40,50)(34,44,
    54)(35,45,52)(36,43,53)(55,65,57,64,56,66)(58,68,60,67,59,69)(61,71,63,70,
    62,72)(73,74,75)(76,77,78)(79,80,81)^G, 
  (5,6)(8,9)(14,15)(17,18)(23,24)(26,27)(32,33)(35,36)(37,46)(38,47)(39,
    48)(40,49)(41,51)(42,50)(43,52)(44,54)(45,53)(59,60)(62,63)(68,69)(71,
    72)(77,78)(80,81)^G, (5,6)(7,8)(14,15)(16,17)(23,24)(25,26)(32,33)(34,
    35)(37,46)(38,47)(39,48)(40,49)(41,51)(42,50)(43,53)(44,52)(45,54)(55,64,
    73)(56,65,74)(57,66,75)(58,67,76)(59,69,77,60,68,78)(61,71,79,62,70,
    80)(63,72,81)^G, (1,2,3)(5,6)(8,9)(10,11,12)(14,15)(17,18)(19,20,21)(23,
    24)(26,27)(28,29,30)(32,33)(35,36)(37,47,39,46,38,48)(40,49)(41,51)(42,
    50)(43,52)(44,54)(45,53)(55,65,75)(56,66,73)(57,64,74)(58,67,76)(59,69,77,
    60,68,78)(61,70,79)(62,72,80,63,71,81)^G, 
  (1,2,3)(5,6)(7,9)(10,11,12)(14,15)(16,18)(19,20,21)(23,24)(25,27)(28,29,
    30)(32,33)(34,36)(37,47,39,46,38,48)(40,49)(41,51)(42,50)(43,54)(44,
    53)(45,52)(55,56,57)(59,60)(61,63)(64,65,66)(68,69)(70,72)(73,74,75)(77,
    78)(79,81)^G, (1,10,19)(2,11,20)(3,12,21)(4,13,22)(5,15,23,6,14,24)(7,18,
    25,9,16,27)(8,17,26)(32,33)(34,36)(37,46)(38,47)(39,48)(40,49)(41,51)(42,
    50)(43,54)(44,53)(45,52)(55,64,73)(56,65,74)(57,66,75)(58,67,76)(59,69,77,
    60,68,78)(61,72,79,63,70,81)(62,71,80)^G, 
  (1,11,21)(2,12,19)(3,10,20)(4,13,22)(5,15,23,6,14,24)(7,17,25,8,16,26)(9,18,
    27)(28,29,30)(32,33)(34,35)(37,47,39,46,38,48)(40,49)(41,51)(42,50)(43,
    53)(44,52)(45,54)(55,65,75)(56,66,73)(57,64,74)(58,67,76)(59,69,77,60,68,
    78)(61,71,79,62,70,80)(63,72,81)^G, (10,19)(11,20)(12,21)(13,22)(14,
    23)(15,24)(16,25)(17,26)(18,27)(37,46)(38,47)(39,48)(40,49)(41,50)(42,
    51)(43,52)(44,53)(45,54)(64,73)(65,74)(66,75)(67,76)(68,77)(69,78)(70,
    79)(71,80)(72,81)^G, (7,8,9)(10,19)(11,20)(12,21)(13,22)(14,23)(15,24)(16,
    26,18,25,17,27)(34,35,36)(37,46)(38,47)(39,48)(40,49)(41,50)(42,51)(43,53,
    45,52,44,54)(55,64)(56,65)(57,66)(58,67)(59,68)(60,69)(61,71,63,70,62,
    72)(79,80,81)^G, (4,5,6)(7,8,9)(10,19)(11,20)(12,21)(13,23,15,22,14,
    24)(16,26,18,25,17,27)(31,32,33)(34,35,36)(37,46)(38,47)(39,48)(40,50,42,
    49,41,51)(43,53,45,52,44,54)(55,64)(56,65)(57,66)(58,68,60,67,59,69)(61,
    71,63,70,62,72)(76,77,78)(79,80,81)^G, (1,2,3)(4,5,6)(7,8,9)(10,20,12,19,
    11,21)(13,23,15,22,14,24)(16,26,18,25,17,27)(28,29,30)(31,32,33)(34,35,
    36)(37,47,39,46,38,48)(40,50,42,49,41,51)(43,53,45,52,44,54)(55,74,57,73,
    56,75)(58,77,60,76,59,78)(61,80,63,79,62,81)(64,65,66)(67,68,69)(70,71,
    72)^G, (2,3)(5,6)(10,19)(11,21)(12,20)(13,22)(14,24)(15,23)(16,25)(17,
    26)(18,27)(29,30)(32,33)(37,46)(38,48)(39,47)(40,49)(41,51)(42,50)(43,
    52)(44,53)(45,54)(56,57)(59,60)(64,73)(65,75)(66,74)(67,76)(68,78)(69,
    77)(70,79)(71,80)(72,81)^G, (2,3)(5,6)(7,8,9)(10,19)(11,21)(12,20)(13,
    22)(14,24)(15,23)(16,26,18,25,17,27)(29,30)(32,33)(34,35,36)(37,46)(38,
    48)(39,47)(40,49)(41,51)(42,50)(43,53,45,52,44,54)(55,64)(56,66)(57,
    65)(58,67)(59,69)(60,68)(61,71,63,70,62,72)(74,75)(77,78)(79,80,81)^G, 
  (1,31,61)(2,32,62)(3,33,63)(4,34,55)(5,35,56)(6,36,57)(7,28,58)(8,29,59)(9,
    30,60)(10,40,70,19,49,79)(11,41,71,20,50,80)(12,42,72,21,51,81)(13,43,64,
    22,52,73)(14,44,65,23,53,74)(15,45,66,24,54,75)(16,37,67,25,46,76)(17,38,
    68,26,47,77)(18,39,69,27,48,78)^G, (1,31,71,20,50,63,3,33,70,19,49,62,2,
    32,72,21,51,61)(4,35,65,23,54,57,6,34,64,22,53,56,5,36,66,24,52,55)(7,28,
    67,26,47,59,9,30,69,25,46,58,8,29,68,27,48,60)(10,40,80,11,41,81,12,42,
    79)(13,44,74,14,45,75,15,43,73)(16,37,76,17,38,77,18,39,78)^G, 
  (1,55,28)(2,56,29)(3,57,30)(4,58,31)(5,59,32)(6,60,33)(7,61,34)(8,62,35)(9,
    63,36)(10,64,46,19,73,37)(11,65,47,20,74,38)(12,66,48,21,75,39)(13,67,49,
    22,76,40)(14,68,50,23,77,41)(15,69,51,24,78,42)(16,70,52,25,79,43)(17,71,
    53,26,80,44)(18,72,54,27,81,45)^G, (1,64,46,19,55,28)(2,65,47,20,56,29)(3,
    66,48,21,57,30)(4,67,49,22,58,31)(5,68,50,23,59,32)(6,69,51,24,60,33)(7,
    71,54,25,62,36)(8,72,52,26,63,34)(9,70,53,27,61,35)(10,73,37)(11,74,
    38)(12,75,39)(13,76,40)(14,77,41)(15,78,42)(16,80,45)(17,81,43)(18,79,
    44)^G, (1,64,46,19,55,28)(2,65,47,20,56,29)(3,66,48,21,57,30)(4,68,51,22,
    59,33)(5,69,49,23,60,31)(6,67,50,24,58,32)(7,71,54,25,62,36)(8,72,52,26,
    63,34)(9,70,53,27,61,35)(10,73,37)(11,74,38)(12,75,39)(13,77,42)(14,78,
    40)(15,76,41)(16,80,45)(17,81,43)(18,79,44)^G, 
  (1,74,39,10,56,30)(2,75,37,11,57,28)(3,73,38,12,55,29)(4,77,42,13,59,33)(5,
    78,40,14,60,31)(6,76,41,15,58,32)(7,80,45,16,62,36)(8,81,43,17,63,34)(9,
    79,44,18,61,35)(19,65,48)(20,66,46)(21,64,47)(22,68,51)(23,69,49)(24,67,
    50)(25,71,54)(26,72,52)(27,70,53)^G, (1,55,28)(2,56,29)(3,57,30)(4,58,
    31)(5,60,32,6,59,33)(7,61,34)(8,63,35,9,62,36)(10,73,46,19,64,37)(11,74,
    47,20,65,38)(12,75,48,21,66,39)(13,76,49,22,67,40)(14,78,50,24,68,42)(15,
    77,51,23,69,41)(16,79,52,25,70,43)(17,81,53,27,71,45)(18,80,54,26,72,44)^G
    , (1,65,39,10,56,30)(2,66,37,11,57,28)(3,64,38,12,55,29)(4,67,40,13,58,
    31)(5,69,41,15,59,33)(6,68,42,14,60,32)(7,70,43,16,61,34)(8,72,44,18,62,
    36)(9,71,45,17,63,35)(19,74,48)(20,75,46)(21,73,47)(22,76,49)(23,78,50,24,
    77,51)(25,79,52)(26,81,53,27,80,54)^G, (1,4,7)(2,5,8)(3,6,9)(10,13,16)(11,
    14,17)(12,15,18)(19,22,25)(20,23,26)(21,24,27)(28,31,34)(29,32,35)(30,33,
    36)(37,40,43)(38,41,44)(39,42,45)(46,49,52)(47,50,53)(48,51,54)(55,58,
    61)(56,59,62)(57,60,63)(64,76,70,73,67,79)(65,77,71,74,68,80)(66,78,72,75,
    69,81)^G, (1,4,8,2,5,9,3,6,7)(10,13,17,11,14,18,12,15,16)(19,22,26,20,23,
    27,21,24,25)(28,31,35,29,32,36,30,33,34)(37,40,44,38,41,45,39,42,43)(46,
    49,53,47,50,54,48,51,52)(55,67,62,65,59,72,57,69,61,64,58,71,56,68,63,66,
    60,70)(73,76,80,74,77,81,75,78,79)^G, (1,4,7)(2,5,8)(3,6,9)(10,13,16)(11,
    14,17)(12,15,18)(19,22,25)(20,23,26)(21,24,27)(28,40,52)(29,41,53)(30,42,
    54)(31,43,46)(32,44,47)(33,45,48)(34,37,49)(35,38,50)(36,39,51)(55,58,
    61)(56,59,62)(57,60,63)(64,76,70,73,67,79)(65,77,71,74,68,80)(66,78,72,75,
    69,81)^G, (1,4,8,2,5,9,3,6,7)(10,13,17,11,14,18,12,15,16)(19,22,26,20,23,
    27,21,24,25)(28,40,53,29,41,54,30,42,52)(31,44,47,32,45,48,33,43,46)(34,
    37,49,35,38,50,36,39,51)(55,67,62,65,59,72,57,69,61,64,58,71,56,68,63,66,
    60,70)(73,76,80,74,77,81,75,78,79)^G, (1,13,26,2,14,27,3,15,25)(4,17,20,5,
    18,21,6,16,19)(7,10,22,8,11,23,9,12,24)(28,40,53,29,41,54,30,42,52)(31,44,
    47,32,45,48,33,43,46)(34,37,49,35,38,50,36,39,51)(55,58,62,56,59,63,57,60,
    61)(64,76,71,74,68,81,66,78,70,73,67,80,65,77,72,75,69,79)^G, 
  (1,13,25)(2,14,26)(3,15,27)(4,16,19)(5,17,20)(6,18,21)(7,10,22)(8,11,23)(9,
    12,24)(28,40,52)(29,41,53)(30,42,54)(31,43,46)(32,44,47)(33,45,48)(34,37,
    49)(35,38,50)(36,39,51)(55,76,61,73,58,79)(56,77,62,74,59,80)(57,78,63,75,
    60,81)(64,67,70)(65,68,71)(66,69,72)^G, (1,4,7)(2,5,8)(3,6,9)(10,22,16,19,
    13,25)(11,23,17,20,14,26)(12,24,18,21,15,27)(28,31,34)(29,32,35)(30,33,
    36)(37,49,43,46,40,52)(38,50,44,47,41,53)(39,51,45,48,42,54)(55,58,61)(56,
    59,62)(57,60,63)(64,76,70,73,67,79)(65,77,71,74,68,80)(66,78,72,75,69,
    81)^G, (1,4,8,2,5,9,3,6,7)(10,22,17,20,14,27,12,24,16,19,13,26,11,23,18,
    21,15,25)(28,31,35,29,32,36,30,33,34)(37,49,44,47,41,54,39,51,43,46,40,53,
    38,50,45,48,42,52)(55,67,62,65,59,72,57,69,61,64,58,71,56,68,63,66,60,
    70)(73,76,80,74,77,81,75,78,79)^G, (1,34)(2,43)(3,52)(4,61)(5,70,6,79)(8,
    16)(9,25)(10,35)(11,44)(12,53)(13,62)(14,71,15,80)(18,26)(19,36)(20,
    45)(21,54)(22,63)(23,72,24,81)(29,37)(30,46)(31,55)(32,64,33,73)(39,
    47)(40,56)(41,65,42,74)(49,57)(50,66,51,75)(59,67,60,76)(68,69,78,77)^G, 
  (1,35,10,36,19,34)(2,44,11,45,20,43)(3,53,12,54,21,52)(4,71,15,63,22,70,6,
    62,13,72,24,61)(5,80,14,81,23,79)(7,8,17,18,27,25)(9,26,16)(29,37)(30,
    46)(31,64,33,55)(32,73)(39,47)(40,65,42,56)(41,74)(49,66,51,57)(50,75)(58,
    67,69,60)(59,76,68,78)^G, (1,44,11,54,21,34)(2,53,12,36,19,43)(3,35,10,45,
    20,52)(4,71,15,63,22,70,6,62,13,72,24,61)(5,80,14,81,23,79)(7,8,17,18,27,
    25)(9,26,16)(28,37,38,47,48,30)(29,46,39)(31,64,42,56,49,66,33,55,40,65,
    51,57)(32,73,41,74,50,75)(58,67,69,60)(59,76,68,78)^G, 
  (1,34)(2,52,3,43)(4,61)(5,79,6,70)(8,16,9,25)(10,36,19,35)(11,54,21,44)(12,
    45,20,53)(13,63,22,62)(14,81,24,71)(15,72,23,80)(17,18,27,26)(29,46,30,
    37)(31,55)(32,73,33,64)(38,47,48,39)(40,56,49,57)(41,74,51,66)(42,65,50,
    75)(59,76,60,67)(68,77,78,69)^G, (1,55,61,34,31,4)(2,64,63,52,33,22,3,73,
    62,43,32,13)(5,10,56,70,36,49,6,19,57,79,35,40)(7,28,58)(8,37,59,16,29,67,
    9,46,60,25,30,76)(11,65,72,54,51,24,21,75,80,44,41,14)(12,74,71,45,50,15,
    20,66,81,53,42,23)(17,38,68,18,47,69,27,48,78,26,39,77)^G, 
  (1,4)(2,5)(3,6)(10,13)(11,14)(12,15)(19,22)(20,23)(21,24)(28,58)(29,59)(30,
    60)(31,55)(32,56)(33,57)(34,61)(35,62)(36,63)(37,67,46,76)(38,68,47,
    77)(39,69,48,78)(40,64,49,73)(41,65,50,74)(42,66,51,75)(43,70,52,79)(44,
    71,53,80)(45,72,54,81)^G, (1,4)(2,5)(3,6)(7,8,9)(10,13)(11,14)(12,15)(16,
    17,18)(19,22)(20,23)(21,24)(25,26,27)(28,67,46,58)(29,68,47,59)(30,69,48,
    60)(31,64,49,55)(32,65,50,56)(33,66,51,57)(34,71,54,61,35,72,52,62,36,70,
    53,63)(37,76)(38,77)(39,78)(40,73)(41,74)(42,75)(43,80,45,79,44,81)^G, 
  (1,5,2,6,3,4)(10,14,11,15,12,13)(19,23,20,24,21,22)(28,59,29,60,30,58)(31,
    55,32,56,33,57)(34,61)(35,62)(36,63)(37,68,47,78,39,67,46,77,38,69,48,
    76)(40,64,50,74,42,66,49,73,41,65,51,75)(43,70,52,79)(44,71,53,80)(45,72,
    54,81)^G, (1,5,2,6,3,4)(7,8,9)(10,14,11,15,12,13)(16,17,18)(19,23,20,24,
    21,22)(25,26,27)(28,68,47,60,30,67,46,59,29,69,48,58)(31,64,50,56,33,66,
    49,55,32,65,51,57)(34,71,54,61,35,72,52,62,36,70,53,63)(37,77,38,78,39,
    76)(40,73,41,74,42,75)(43,80,45,79,44,81)^G, 
  (1,13,19,4,10,22)(2,14,20,5,11,23)(3,15,21,6,12,24)(7,17,27)(8,18,25)(9,16,
    26)(28,58)(29,59)(30,60)(31,55)(32,56)(33,57)(34,62,36,61,35,63)(37,67,46,
    76)(38,68,47,77)(39,69,48,78)(40,64,49,73)(41,65,50,74)(42,66,51,75)(43,
    71,54,79,44,72,52,80,45,70,53,81)^G, (1,13,19,4,10,22)(2,14,20,5,11,23)(3,
    15,21,6,12,24)(7,16,25)(8,17,26)(9,18,27)(28,76,37,58)(29,77,38,59)(30,78,
    39,60)(31,73,40,55)(32,74,41,56)(33,75,42,57)(34,79,43,61)(35,80,44,
    62)(36,81,45,63)(46,67)(47,68)(48,69)(49,64)(50,65)(51,66)(52,70)(53,
    71)(54,72)^G, (1,14,20,6,12,22)(2,15,21,4,10,23)(3,13,19,5,11,24)(7,17,
    27)(8,18,25)(9,16,26)(28,59,29,60,30,58)(31,55,32,56,33,57)(34,62,36,61,
    35,63)(37,68,47,78,39,67,46,77,38,69,48,76)(40,64,50,74,42,66,49,73,41,65,
    51,75)(43,71,54,79,44,72,52,80,45,70,53,81)^G, 
  (1,14,20,6,12,22)(2,15,21,4,10,23)(3,13,19,5,11,24)(7,16,25)(8,17,26)(9,18,
    27)(28,77,38,60,30,76,37,59,29,78,39,58)(31,73,41,56,33,75,40,55,32,74,42,
    57)(34,79,43,61)(35,80,44,62)(36,81,45,63)(46,68,47,69,48,67)(49,64,50,65,
    51,66)(52,70)(53,71)(54,72)^G, (1,4)(2,6,3,5)(8,9)(10,13)(11,15,12,14)(17,
    18)(19,22)(20,24,21,23)(26,27)(28,58)(29,60,30,59)(31,55)(32,56,33,57)(34,
    61)(35,63)(36,62)(37,76,46,67)(38,78,48,68)(39,77,47,69)(40,73,49,64)(41,
    74,51,66)(42,75,50,65)(43,79,52,70)(44,81,53,72)(45,80,54,71)^G, 
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    27)(28,58)(29,60,30,59)(31,55)(32,56,33,57)(34,62)(35,61)(36,63)(37,76,46,
    67)(38,78,48,68)(39,77,47,69)(40,73,49,64)(41,74,51,66)(42,75,50,65)(43,
    80,52,71)(44,79,53,70)(45,81,54,72)^G, (1,4)(2,5)(3,6)(10,22)(11,23)(12,
    24)(13,19)(14,20)(15,21)(16,25)(17,26)(18,27)(28,58)(29,59)(30,60)(31,
    55)(32,56)(33,57)(34,61)(35,62)(36,63)(37,67)(38,68)(39,69)(40,64)(41,
    65)(42,66)(43,70)(44,71)(45,72)(46,76)(47,77)(48,78)(49,73)(50,74)(51,
    75)(52,79)(53,80)(54,81)^G, (1,4)(2,5)(3,6)(7,8,9)(10,22)(11,23)(12,
    24)(13,19)(14,20)(15,21)(16,26,18,25,17,27)(28,67,37,76,46,58)(29,68,38,
    77,47,59)(30,69,39,78,48,60)(31,64,40,73,49,55)(32,65,41,74,50,56)(33,66,
    42,75,51,57)(34,71,45,79,53,63)(35,72,43,80,54,61)(36,70,44,81,52,62)^G, 
  (1,4)(2,5)(3,6)(10,22)(11,23)(12,24)(13,19)(14,20)(15,21)(16,25)(17,26)(18,
    27)(28,76,46,67,37,58)(29,77,47,68,38,59)(30,78,48,69,39,60)(31,73,49,64,
    40,55)(32,74,50,65,41,56)(33,75,51,66,42,57)(34,79,52,70,43,61)(35,80,53,
    71,44,62)(36,81,54,72,45,63)^G, (1,4)(2,5)(3,6)(7,8,9)(10,22)(11,23)(12,
    24)(13,19)(14,20)(15,21)(16,26,18,25,17,27)(28,58)(29,59)(30,60)(31,
    55)(32,56)(33,57)(34,62,36,61,35,63)(37,67)(38,68)(39,69)(40,64)(41,
    65)(42,66)(43,71,45,70,44,72)(46,76)(47,77)(48,78)(49,73)(50,74)(51,
    75)(52,80,54,79,53,81)^G, (1,5,2,6,3,4)(10,23,11,24,12,22)(13,19,14,20,15,
    21)(16,25)(17,26)(18,27)(28,59,29,60,30,58)(31,55,32,56,33,57)(34,61)(35,
    62)(36,63)(37,68,38,69,39,67)(40,64,41,65,42,66)(43,70)(44,71)(45,72)(46,
    77,47,78,48,76)(49,73,50,74,51,75)(52,79)(53,80)(54,81)^G, 
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    27)(28,68,38,78,48,58)(29,69,39,76,46,59)(30,67,37,77,47,60)(31,64,41,74,
    51,57)(32,65,42,75,49,55)(33,66,40,73,50,56)(34,71,45,79,53,63)(35,72,43,
    80,54,61)(36,70,44,81,52,62)^G, (1,5,2,6,3,4)(10,23,11,24,12,22)(13,19,14,
    20,15,21)(16,25)(17,26)(18,27)(28,77,47,69,39,58)(29,78,48,67,37,59)(30,
    76,46,68,38,60)(31,73,50,65,42,57)(32,74,51,66,40,55)(33,75,49,64,41,
    56)(34,79,52,70,43,61)(35,80,53,71,44,62)(36,81,54,72,45,63)^G, 
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    27)(28,59,29,60,30,58)(31,55,32,56,33,57)(34,62,36,61,35,63)(37,68,38,69,
    39,67)(40,64,41,65,42,66)(43,71,45,70,44,72)(46,77,47,78,48,76)(49,73,50,
    74,51,75)(52,80,54,79,53,81)^G, (1,4)(2,6,3,5)(8,9)(10,22)(11,24,12,
    23)(13,19)(14,20,15,21)(16,25)(17,27)(18,26)(28,58)(29,60,30,59)(31,
    55)(32,56,33,57)(34,61)(35,63)(36,62)(37,76)(38,78,39,77)(40,73)(41,74,42,
    75)(43,79)(44,81)(45,80)(46,67)(47,69,48,68)(49,64)(50,65,51,66)(52,
    70)(53,72)(54,71)^G, (1,4)(2,6,3,5)(7,8)(10,22)(11,24,12,23)(13,19)(14,20,
    15,21)(16,26)(17,25)(18,27)(28,67,46,76,37,58)(29,69,48,77,38,60,30,68,47,
    78,39,59)(31,64,49,73,40,55)(32,65,51,75,41,56,33,66,50,74,42,57)(34,71,
    52,80,43,62)(35,70,53,79,44,61)(36,72,54,81,45,63)^G, 
  (1,34,6,61,3,52,4,70)(2,43,5,79)(8,16,9,25)(10,36,24,62,12,54,22,71)(11,45,
    23,80)(13,72,19,35,15,63,21,53)(14,81,20,44)(17,18,27,26)(28,33,60,57,48,
    49,67,64)(29,42,59,75,47,40,68,73)(30,51,58,66,46,31,69,55)(32,78,56,39,
    50,76,65,37)(38,41,77,74)^G, (1,34,5,70)(2,52,4,79)(3,43,6,61)(8,16)(9,
    25)(10,35,14,71)(11,53,13,80)(12,44,15,62)(18,26)(19,36,23,72)(20,54,22,
    81)(21,45,24,63)(28,32,68,64)(29,50,67,73)(30,41,69,55)(31,77,65,46)(33,
    59,66,37)(38,51,58,75)(39,42,60,57)(40,78,56,48)(47,49,76,74)^G, 
  (1,35,14,81,20,52,4,62,12,45,24,70)(2,53,13,63,21,43,6,71,10,36,23,79)(3,44,
    15,72,19,34,5,80,11,54,22,61)(7,8,17,18,27,25)(9,26,16)(28,32,77,74,47,49,
    58,57,39,42,69,64)(29,50,76,56,48,40,60,66,37,33,68,73)(30,41,78,65,46,31,
    59,75,38,51,67,55)^G, (1,34,5,61,3,43,6,79,2,52,4,70)(8,16)(9,25)(10,35,
    14,62,12,44,15,80,11,53,13,71)(18,26)(19,36,23,63,21,45,24,81,20,54,22,
    72)(28,32,59,57,39,42,78,74,47,49,67,64)(29,50,58,66,37,33,77,56,48,40,69,
    73)(30,41,60,75,38,51,76,65,46,31,68,55)^G, 
  (1,35,14,72,19,34,5,71,10,36,23,70)(2,53,13,81,20,52,4,80,11,54,22,79)(3,44,
    15,63,21,43,6,62,12,45,24,61)(7,8,17,18,27,25)(9,26,16)(28,32,68,64)(29,
    50,67,73)(30,41,69,55)(31,77,65,46)(33,59,66,37)(38,51,58,75)(39,42,60,
    57)(40,78,56,48)(47,49,76,74)^G, (4,5,6)(10,19)(11,20)(12,21)(13,23,15,22,
    14,24)(16,25)(17,26)(18,27)(28,73,37,64)(29,74,38,65)(30,75,39,66)(31,77,
    42,67,32,78,40,68,33,76,41,69)(34,79,43,70)(35,80,44,71)(36,81,45,72)(46,
    55)(47,56)(48,57)(49,59,51,58,50,60)(52,61)(53,62)(54,63)^G, 
  (4,5,6)(7,8,9)(10,19)(11,20)(12,21)(13,23,15,22,14,24)(16,26,18,25,17,
    27)(28,55,46,64)(29,56,47,65)(30,57,48,66)(31,59,51,67,32,60,49,68,33,58,
    50,69)(34,62,54,70,35,63,52,71,36,61,53,72)(37,73)(38,74)(39,75)(40,77,42,
    76,41,78)(43,80,45,79,44,81)^G, (10,19)(11,20)(12,21)(13,22)(14,23)(15,
    24)(16,25)(17,26)(18,27)(28,73,37,64)(29,74,38,65)(30,75,39,66)(31,76,40,
    67)(32,77,41,68)(33,78,42,69)(34,79,43,70)(35,80,44,71)(36,81,45,72)(46,
    55)(47,56)(48,57)(49,58)(50,59)(51,60)(52,61)(53,62)(54,63)^G, 
  (1,2,3)(4,5,6)(7,8,9)(10,20,12,19,11,21)(13,23,15,22,14,24)(16,26,18,25,17,
    27)(28,65,30,64,29,66)(31,68,33,67,32,69)(34,71,36,70,35,72)(37,56,48,73,
    38,57,46,74,39,55,47,75)(40,59,51,76,41,60,49,77,42,58,50,78)(43,62,54,79,
    44,63,52,80,45,61,53,81)^G, (4,6)(8,9)(10,19)(11,20)(12,21)(13,24)(14,
    23)(15,22)(16,25)(17,27)(18,26)(28,64)(29,65)(30,66)(31,69)(32,68)(33,
    67)(34,70)(35,72)(36,71)(37,73,46,55)(38,74,47,56)(39,75,48,57)(40,78,49,
    60)(41,77,50,59)(42,76,51,58)(43,79,52,61)(44,81,53,63)(45,80,54,62)^G, 
  (1,2,3)(4,6)(8,9)(10,20,12,19,11,21)(13,24)(14,23)(15,22)(16,25)(17,27)(18,
    26)(28,74,48,64,29,75,46,65,30,73,47,66)(31,78,49,69)(32,77,50,68)(33,76,
    51,67)(34,79,52,70)(35,81,53,72)(36,80,54,71)(37,56,39,55,38,57)(40,
    60)(41,59)(42,58)(43,61)(44,63)(45,62)^G, 
  (4,5,6)(13,14,15)(22,23,24)(28,73,46,55,37,64)(29,74,47,56,38,65)(30,75,48,
    57,39,66)(31,77,51,58,41,69)(32,78,49,59,42,67)(33,76,50,60,40,68)(34,79,
    52,61,43,70)(35,80,53,62,44,71)(36,81,54,63,45,72)^G, 
  (4,5,6)(7,8,9)(13,14,15)(16,17,18)(22,23,24)(25,26,27)(28,55,37,73,46,
    64)(29,56,38,74,47,65)(30,57,39,75,48,66)(31,59,42,76,50,69)(32,60,40,77,
    51,67)(33,58,41,78,49,68)(34,62,45,79,53,72)(35,63,43,80,54,70)(36,61,44,
    81,52,71)^G, (4,5,6)(7,9,8)(13,14,15)(16,18,17)(22,23,24)(25,27,26)(28,
    64)(29,65)(30,66)(31,68,33,67,32,69)(34,72,35,70,36,71)(37,55)(38,56)(39,
    57)(40,59,42,58,41,60)(43,63,44,61,45,62)(46,73)(47,74)(48,75)(49,77,51,
    76,50,78)(52,81,53,79,54,80)^G, (4,5,6)(13,14,15)(22,23,24)(28,64)(29,
    65)(30,66)(31,68,33,67,32,69)(34,70)(35,71)(36,72)(37,55)(38,56)(39,
    57)(40,59,42,58,41,60)(43,61)(44,62)(45,63)(46,73)(47,74)(48,75)(49,77,51,
    76,50,78)(52,79)(53,80)(54,81)^G, (28,73,46,55,37,64)(29,74,47,56,38,
    65)(30,75,48,57,39,66)(31,76,49,58,40,67)(32,77,50,59,41,68)(33,78,51,60,
    42,69)(34,79,52,61,43,70)(35,80,53,62,44,71)(36,81,54,63,45,72)^G, 
  (28,64)(29,65)(30,66)(31,67)(32,68)(33,69)(34,70)(35,71)(36,72)(37,55)(38,
    56)(39,57)(40,58)(41,59)(42,60)(43,61)(44,62)(45,63)(46,73)(47,74)(48,
    75)(49,76)(50,77)(51,78)(52,79)(53,80)(54,81)^G, 
  (1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18)(19,20,21)(22,23,24)(25,
    26,27)(28,65,30,64,29,66)(31,68,33,67,32,69)(34,71,36,70,35,72)(37,56,39,
    55,38,57)(40,59,42,58,41,60)(43,62,45,61,44,63)(46,74,48,73,47,75)(49,77,
    51,76,50,78)(52,80,54,79,53,81)^G, (1,2,3)(4,5,6)(7,9,8)(10,11,12)(13,14,
    15)(16,18,17)(19,20,21)(22,23,24)(25,27,26)(28,74,48,55,38,66)(29,75,46,
    56,39,64)(30,73,47,57,37,65)(31,77,51,58,41,69)(32,78,49,59,42,67)(33,76,
    50,60,40,68)(34,81,53,61,45,71)(35,79,54,62,43,72)(36,80,52,63,44,70)^G, 
  (1,10,19)(2,11,20)(3,12,21)(4,14,24)(5,15,22)(6,13,23)(7,17,27)(8,18,25)(9,
    16,26)(28,73,46,55,37,64)(29,74,47,56,38,65)(30,75,48,57,39,66)(31,77,51,
    58,41,69)(32,78,49,59,42,67)(33,76,50,60,40,68)(34,80,54,61,44,72)(35,81,
    52,62,45,70)(36,79,53,63,43,71)^G, (1,10,19)(2,11,20)(3,12,21)(4,14,24)(5,
    15,22)(6,13,23)(7,16,25)(8,17,26)(9,18,27)(28,64)(29,65)(30,66)(31,68,33,
    67,32,69)(34,70)(35,71)(36,72)(37,55)(38,56)(39,57)(40,59,42,58,41,60)(43,
    61)(44,62)(45,63)(46,73)(47,74)(48,75)(49,77,51,76,50,78)(52,79)(53,
    80)(54,81)^G, (1,10,19)(2,11,20)(3,12,21)(4,14,24)(5,15,22)(6,13,23)(7,17,
    27)(8,18,25)(9,16,26)(28,64)(29,65)(30,66)(31,68,33,67,32,69)(34,71,36,70,
    35,72)(37,55)(38,56)(39,57)(40,59,42,58,41,60)(43,62,45,61,44,63)(46,
    73)(47,74)(48,75)(49,77,51,76,50,78)(52,80,54,79,53,81)^G, 
  (1,10,19)(2,11,20)(3,12,21)(4,14,24)(5,15,22)(6,13,23)(7,16,25)(8,17,26)(9,
    18,27)(28,55,37,73,46,64)(29,56,38,74,47,65)(30,57,39,75,48,66)(31,59,42,
    76,50,69)(32,60,40,77,51,67)(33,58,41,78,49,68)(34,61,43,79,52,70)(35,62,
    44,80,53,71)(36,63,45,81,54,72)^G, (1,10,19)(2,11,20)(3,12,21)(4,13,22)(5,
    14,23)(6,15,24)(7,16,25)(8,17,26)(9,18,27)(28,64)(29,65)(30,66)(31,67)(32,
    68)(33,69)(34,70)(35,71)(36,72)(37,55)(38,56)(39,57)(40,58)(41,59)(42,
    60)(43,61)(44,62)(45,63)(46,73)(47,74)(48,75)(49,76)(50,77)(51,78)(52,
    79)(53,80)(54,81)^G, (1,10,19)(2,11,20)(3,12,21)(4,13,22)(5,14,23)(6,15,
    24)(7,16,25)(8,17,26)(9,18,27)(28,55,37,73,46,64)(29,56,38,74,47,65)(30,
    57,39,75,48,66)(31,58,40,76,49,67)(32,59,41,77,50,68)(33,60,42,78,51,
    69)(34,61,43,79,52,70)(35,62,44,80,53,71)(36,63,45,81,54,72)^G, 
  (1,11,21)(2,12,19)(3,10,20)(4,14,24)(5,15,22)(6,13,23)(7,17,27)(8,18,25)(9,
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    76,50,69)(32,60,40,77,51,67)(33,58,41,78,49,68)(34,62,45,79,53,72)(35,63,
    43,80,54,70)(36,61,44,81,52,71)^G, (1,11,21)(2,12,19)(3,10,20)(4,14,24)(5,
    15,22)(6,13,23)(7,18,26)(8,16,27)(9,17,25)(28,65,30,64,29,66)(31,68,33,67,
    32,69)(34,72,35,70,36,71)(37,56,39,55,38,57)(40,59,42,58,41,60)(43,63,44,
    61,45,62)(46,74,48,73,47,75)(49,77,51,76,50,78)(52,81,53,79,54,80)^G, 
  (4,6)(8,9)(13,15)(17,18)(22,24)(26,27)(28,64)(29,65)(30,66)(31,69)(32,
    68)(33,67)(34,70)(35,72)(36,71)(37,73)(38,74)(39,75)(40,78)(41,77)(42,
    76)(43,79)(44,81)(45,80)(46,55)(47,56)(48,57)(49,60)(50,59)(51,58)(52,
    61)(53,63)(54,62)^G, (4,6)(7,8)(13,15)(16,17)(22,24)(25,26)(28,73,37,55,
    46,64)(29,74,38,56,47,65)(30,75,39,57,48,66)(31,78,40,60,49,69)(32,77,41,
    59,50,68)(33,76,42,58,51,67)(34,80,43,62,52,71)(35,79,44,61,53,70)(36,81,
    45,63,54,72)^G, (1,2,3)(4,6)(8,9)(10,11,12)(13,15)(17,18)(19,20,21)(22,
    24)(26,27)(28,74,39,55,47,66)(29,75,37,56,48,64)(30,73,38,57,46,65)(31,78,
    40,60,49,69)(32,77,41,59,50,68)(33,76,42,58,51,67)(34,79,43,61,52,70)(35,
    81,44,63,53,72)(36,80,45,62,54,71)^G, 
  (1,2,3)(4,6)(7,9)(10,11,12)(13,15)(16,18)(19,20,21)(22,24)(25,27)(28,65,30,
    64,29,66)(31,69)(32,68)(33,67)(34,72)(35,71)(36,70)(37,74,39,73,38,75)(40,
    78)(41,77)(42,76)(43,81)(44,80)(45,79)(46,56,48,55,47,57)(49,60)(50,
    59)(51,58)(52,63)(53,62)(54,61)^G, (1,10,19)(2,11,20)(3,12,21)(4,15,22,6,
    13,24)(5,14,23)(7,17,25,8,16,26)(9,18,27)(28,64)(29,65)(30,66)(31,69)(32,
    68)(33,67)(34,71)(35,70)(36,72)(37,73)(38,74)(39,75)(40,78)(41,77)(42,
    76)(43,80)(44,79)(45,81)(46,55)(47,56)(48,57)(49,60)(50,59)(51,58)(52,
    62)(53,61)(54,63)^G, (1,10,19)(2,11,20)(3,12,21)(4,15,22,6,13,24)(5,14,
    23)(7,18,25,9,16,27)(8,17,26)(28,73,37,55,46,64)(29,74,38,56,47,65)(30,75,
    39,57,48,66)(31,78,40,60,49,69)(32,77,41,59,50,68)(33,76,42,58,51,67)(34,
    81,43,63,52,72)(35,80,44,62,53,71)(36,79,45,61,54,70)^G, 
  (1,11,21)(2,12,19)(3,10,20)(4,15,22,6,13,24)(5,14,23)(7,17,25,8,16,26)(9,18,
    27)(28,74,39,55,47,66)(29,75,37,56,48,64)(30,73,38,57,46,65)(31,78,40,60,
    49,69)(32,77,41,59,50,68)(33,76,42,58,51,67)(34,80,43,62,52,71)(35,79,44,
    61,53,70)(36,81,45,63,54,72)^G, (1,11,21)(2,12,19)(3,10,20)(4,15,22,6,13,
    24)(5,14,23)(7,16,25)(8,18,26,9,17,27)(28,65,30,64,29,66)(31,69)(32,
    68)(33,67)(34,70)(35,72)(36,71)(37,74,39,73,38,75)(40,78)(41,77)(42,
    76)(43,79)(44,81)(45,80)(46,56,48,55,47,57)(49,60)(50,59)(51,58)(52,
    61)(53,63)(54,62)^G, (1,31,26,38,14,54,3,33,25,37,13,53,2,32,27,39,15,
    52)(4,35,20,41,18,48,6,34,19,40,17,47,5,36,21,42,16,46)(7,28,22,44,11,50,
    9,30,24,43,10,49,8,29,23,45,12,51)(55,76,71,56,77,72,57,78,70)(58,80,65,
    59,81,66,60,79,64)(61,73,67,62,74,68,63,75,69)^G, 
  (1,31,27,39,15,53,2,32,25,37,13,54,3,33,26,38,14,52)(4,36,21,42,17,47,5,34,
    19,40,18,48,6,35,20,41,16,46)(7,28,22,45,12,51,8,29,23,43,10,49,9,30,24,
    44,11,50)(55,58,63,57,60,62,56,59,61)(64,67,72,66,69,71,65,68,70)(73,76,
    81,75,78,80,74,77,79)^G, (1,31,25,37,13,52)(2,32,26,38,14,53)(3,33,27,39,
    15,54)(4,34,19,40,16,46)(5,35,20,41,17,47)(6,36,21,42,18,48)(7,28,22,43,
    10,49)(8,29,23,44,11,50)(9,30,24,45,12,51)(55,67,79)(56,68,80)(57,69,
    81)(58,70,73)(59,71,74)(60,72,75)(61,64,76)(62,65,77)(63,66,78)^G, 
  (1,31,25,37,13,52)(2,32,26,38,14,53)(3,33,27,39,15,54)(4,34,19,40,16,46)(5,
    35,20,41,17,47)(6,36,21,42,18,48)(7,28,22,43,10,49)(8,29,23,44,11,50)(9,
    30,24,45,12,51)(55,58,61)(56,59,62)(57,60,63)(64,67,70)(65,68,71)(66,69,
    72)(73,76,79)(74,77,80)(75,78,81)^G, (1,49,8,47,5,54,3,51,7,46,4,53,2,50,
    9,48,6,52)(10,40,17,38,14,45,12,42,16,37,13,44,11,41,18,39,15,43)(19,31,
    26,29,23,36,21,33,25,28,22,35,20,32,27,30,24,34)(55,76,71,56,77,72,57,78,
    70)(58,80,65,59,81,66,60,79,64)(61,73,67,62,74,68,63,75,69)^G, 
  (1,49,9,48,6,53,2,50,7,46,4,54,3,51,8,47,5,52)(10,40,18,39,15,44,11,41,16,
    37,13,45,12,42,17,38,14,43)(19,31,27,30,24,35,20,32,25,28,22,36,21,33,26,
    29,23,34)(55,58,63,57,60,62,56,59,61)(64,67,72,66,69,71,65,68,70)(73,76,
    81,75,78,80,74,77,79)^G, (1,49,7,46,4,52)(2,50,8,47,5,53)(3,51,9,48,6,
    54)(10,40,16,37,13,43)(11,41,17,38,14,44)(12,42,18,39,15,45)(19,31,25,28,
    22,34)(20,32,26,29,23,35)(21,33,27,30,24,36)(55,67,79)(56,68,80)(57,69,
    81)(58,70,73)(59,71,74)(60,72,75)(61,64,76)(62,65,77)(63,66,78)^G, 
  (1,49,7,46,4,52)(2,50,8,47,5,53)(3,51,9,48,6,54)(10,40,16,37,13,43)(11,41,
    17,38,14,44)(12,42,18,39,15,45)(19,31,25,28,22,34)(20,32,26,29,23,35)(21,
    33,27,30,24,36)(55,58,61)(56,59,62)(57,60,63)(64,67,70)(65,68,71)(66,69,
    72)(73,76,79)(74,77,80)(75,78,81)^G, (1,31,27,48,5,35,20,51,7,28,22,54,3,
    32,26,47,6,34,19,49,9,30,23,53,2,33,25,46,4,36,21,50,8,29,24,52)(10,40,18,
    39,14,44,11,42,16,37,13,45,12,41,17,38,15,43)(55,67,63,66,59,71,56,69,61,
    64,58,72,57,68,62,65,60,70)(73,76,81,75,77,80,74,78,79)^G, 
  (1,31,25,46,4,34,19,49,7,28,22,52)(2,33,26,47,6,35,20,51,8,29,24,53)(3,32,
    27,48,5,36,21,50,9,30,23,54)(10,40,16,37,13,43)(11,42,17,38,15,44)(12,41,
    18,39,14,45)(55,76,61,73,58,79)(56,78,62,74,60,80)(57,77,63,75,59,81)(64,
    67,70)(65,69,71)(66,68,72)^G, (4,6)(13,15)(22,24)(28,73,37,64)(29,74,38,
    65)(30,75,39,66)(31,78,40,69)(32,77,41,68)(33,76,42,67)(34,79,43,70)(35,
    80,44,71)(36,81,45,72)(46,55)(47,56)(48,57)(49,60)(50,59)(51,58)(52,
    61)(53,62)(54,63)^G, (4,6)(7,8,9)(13,15)(16,17,18)(22,24)(25,26,27)(28,55,
    46,64)(29,56,47,65)(30,57,48,66)(31,60,49,69)(32,59,50,68)(33,58,51,
    67)(34,62,54,70,35,63,52,71,36,61,53,72)(37,73)(38,74)(39,75)(40,78)(41,
    77)(42,76)(43,80,45,79,44,81)^G, (1,2,3)(4,6)(7,8,9)(10,11,12)(13,15)(16,
    17,18)(19,20,21)(22,24)(25,26,27)(28,65,30,64,29,66)(31,69)(32,68)(33,
    67)(34,71,36,70,35,72)(37,56,48,73,38,57,46,74,39,55,47,75)(40,60,49,
    78)(41,59,50,77)(42,58,51,76)(43,62,54,79,44,63,52,80,45,61,53,81)^G, 
  (1,10,19)(2,11,20)(3,12,21)(4,15,22,6,13,24)(5,14,23)(7,17,27)(8,18,25)(9,
    16,26)(28,73,37,64)(29,74,38,65)(30,75,39,66)(31,78,40,69)(32,77,41,
    68)(33,76,42,67)(34,80,45,70,35,81,43,71,36,79,44,72)(46,55)(47,56)(48,
    57)(49,60)(50,59)(51,58)(52,62,54,61,53,63)^G, 
  (1,10,19)(2,11,20)(3,12,21)(4,15,22,6,13,24)(5,14,23)(7,16,25)(8,17,26)(9,
    18,27)(28,64)(29,65)(30,66)(31,69)(32,68)(33,67)(34,70)(35,71)(36,72)(37,
    55,46,73)(38,56,47,74)(39,57,48,75)(40,60,49,78)(41,59,50,77)(42,58,51,
    76)(43,61,52,79)(44,62,53,80)(45,63,54,81)^G, 
  (1,11,21)(2,12,19)(3,10,20)(4,15,22,6,13,24)(5,14,23)(7,17,27)(8,18,25)(9,
    16,26)(28,56,48,64,29,57,46,65,30,55,47,66)(31,60,49,69)(32,59,50,68)(33,
    58,51,67)(34,62,54,70,35,63,52,71,36,61,53,72)(37,74,39,73,38,75)(40,
    78)(41,77)(42,76)(43,80,45,79,44,81)^G, (2,3)(4,6)(8,9)(11,12)(13,15)(17,
    18)(20,21)(22,24)(26,27)(28,64)(29,66)(30,65)(31,69)(32,68)(33,67)(34,
    70)(35,72)(36,71)(37,73,46,55)(38,75,47,57)(39,74,48,56)(40,78,49,60)(41,
    77,50,59)(42,76,51,58)(43,79,52,61)(44,81,53,63)(45,80,54,62)^G, 
  (1,10,19)(2,12,20,3,11,21)(4,15,22,6,13,24)(5,14,23)(7,17,25,8,16,26)(9,18,
    27)(28,64)(29,66)(30,65)(31,69)(32,68)(33,67)(34,71)(35,70)(36,72)(37,73,
    46,55)(38,75,47,57)(39,74,48,56)(40,78,49,60)(41,77,50,59)(42,76,51,
    58)(43,80,52,62)(44,79,53,61)(45,81,54,63)^G, 
  (4,6)(10,19)(11,20)(12,21)(13,24)(14,23)(15,22)(16,25)(17,26)(18,27)(28,73,
    46,55,37,64)(29,74,47,56,38,65)(30,75,48,57,39,66)(31,78,49,60,40,69)(32,
    77,50,59,41,68)(33,76,51,58,42,67)(34,79,52,61,43,70)(35,80,53,62,44,
    71)(36,81,54,63,45,72)^G, (4,6)(7,8,9)(10,19)(11,20)(12,21)(13,24)(14,
    23)(15,22)(16,26,18,25,17,27)(28,55,37,73,46,64)(29,56,38,74,47,65)(30,57,
    39,75,48,66)(31,60,40,78,49,69)(32,59,41,77,50,68)(33,58,42,76,51,67)(34,
    62,45,79,53,72)(35,63,43,80,54,70)(36,61,44,81,52,71)^G, 
  (4,6)(7,9,8)(10,19)(11,20)(12,21)(13,24)(14,23)(15,22)(16,27,17,25,18,
    26)(28,64)(29,65)(30,66)(31,69)(32,68)(33,67)(34,72,35,70,36,71)(37,
    55)(38,56)(39,57)(40,60)(41,59)(42,58)(43,63,44,61,45,62)(46,73)(47,
    74)(48,75)(49,78)(50,77)(51,76)(52,81,53,79,54,80)^G, 
  (4,6)(10,19)(11,20)(12,21)(13,24)(14,23)(15,22)(16,25)(17,26)(18,27)(28,
    64)(29,65)(30,66)(31,69)(32,68)(33,67)(34,70)(35,71)(36,72)(37,55)(38,
    56)(39,57)(40,60)(41,59)(42,58)(43,61)(44,62)(45,63)(46,73)(47,74)(48,
    75)(49,78)(50,77)(51,76)(52,79)(53,80)(54,81)^G, 
  (1,2,3)(4,6)(7,8,9)(10,20,12,19,11,21)(13,24)(14,23)(15,22)(16,26,18,25,17,
    27)(28,65,30,64,29,66)(31,69)(32,68)(33,67)(34,71,36,70,35,72)(37,56,39,
    55,38,57)(40,60)(41,59)(42,58)(43,62,45,61,44,63)(46,74,48,73,47,75)(49,
    78)(50,77)(51,76)(52,80,54,79,53,81)^G, (1,2,3)(4,6)(7,9,8)(10,20,12,19,
    11,21)(13,24)(14,23)(15,22)(16,27,17,25,18,26)(28,74,48,55,38,66)(29,75,
    46,56,39,64)(30,73,47,57,37,65)(31,78,49,60,40,69)(32,77,50,59,41,68)(33,
    76,51,58,42,67)(34,81,53,61,45,71)(35,79,54,62,43,72)(36,80,52,63,44,70)^G
    , (2,3)(4,6)(8,9)(10,19)(11,21)(12,20)(13,24)(14,23)(15,22)(16,25)(17,
    27)(18,26)(28,64)(29,66)(30,65)(31,69)(32,68)(33,67)(34,70)(35,72)(36,
    71)(37,73)(38,75)(39,74)(40,78)(41,77)(42,76)(43,79)(44,81)(45,80)(46,
    55)(47,57)(48,56)(49,60)(50,59)(51,58)(52,61)(53,63)(54,62)^G, 
  (2,3)(4,6)(7,8)(10,19)(11,21)(12,20)(13,24)(14,23)(15,22)(16,26)(17,25)(18,
    27)(28,73,37,55,46,64)(29,75,38,57,47,66)(30,74,39,56,48,65)(31,78,40,60,
    49,69)(32,77,41,59,50,68)(33,76,42,58,51,67)(34,80,43,62,52,71)(35,79,44,
    61,53,70)(36,81,45,63,54,72)^G, (1,31,27,48,6,34,19,49,9,30,24,52)(2,32,
    26,47,5,35,20,50,8,29,23,53)(3,33,25,46,4,36,21,51,7,28,22,54)(10,40,18,
    39,15,43)(11,41,17,38,14,44)(12,42,16,37,13,45)(55,76,72,57,78,70)(56,77,
    71)(58,81,66,60,79,64)(59,80,65)(61,73,67,63,75,69)(62,74,68)^G, 
  (1,31,25,46,4,34,19,49,7,28,22,52)(2,32,27,48,6,35,20,50,9,30,24,53)(3,33,
    26,47,5,36,21,51,8,29,23,54)(10,40,16,37,13,43)(11,41,18,39,15,44)(12,42,
    17,38,14,45)(55,58,61)(56,59,63,57,60,62)(64,67,70)(65,68,72,66,69,71)(73,
    76,79)(74,77,81,75,78,80)^G, (1,31,26,38,15,52)(2,33,25,37,13,53)(3,32,27,
    39,14,54)(4,35,20,42,16,46)(5,36,21,41,18,48)(6,34,19,40,17,47)(7,28,22,
    44,11,51)(8,29,24,43,10,49)(9,30,23,45,12,50)(55,67,62,65,60,70)(56,69,61,
    64,58,71)(57,68,63,66,59,72)(73,76,80,74,78,79)(75,77,81)^G, 
  (1,49,8,47,6,52)(2,51,7,46,4,53)(3,50,9,48,5,54)(10,40,17,38,15,43)(11,42,
    16,37,13,44)(12,41,18,39,14,45)(19,31,26,29,24,34)(20,33,25,28,22,35)(21,
    32,27,30,23,36)(55,67,62,65,60,70)(56,69,61,64,58,71)(57,68,63,66,59,
    72)(73,76,80,74,78,79)(75,77,81)^G ]
gap> List(ConjugacyClasses(sudoku),Size);
[ 1, 36, 12, 144, 24, 144, 96, 16, 192, 64, 729, 2916, 2916, 54, 648, 324, 
  108, 1296, 648, 864, 432, 5184, 20736, 20736, 144, 1728, 288, 864, 3456, 
  1728, 2304, 1152, 3888, 7776, 15552, 7776, 1296, 15552, 7776, 10368, 34992, 
  69984, 93312, 186624, 81, 648, 1296, 648, 2592, 1296, 486, 1944, 1944, 729, 
  46656, 3888, 15552, 15552, 11664, 324, 2592, 1296, 1296, 5184, 1296, 2592, 
  1296, 5184, 5184, 5832, 11664, 11664, 23328, 26244, 5832, 23328, 11664, 
  11664, 2916, 11664, 11664, 2916, 11664, 11664, 139968, 69984, 69984, 
  139968, 648, 2592, 1296, 1296, 108, 216, 1728, 864, 5832, 2916, 5832, 
  11664, 648, 1296, 108, 864, 2592, 1296, 216, 1728, 2916, 5832, 5832, 11664, 
  31104, 15552, 15552, 7776, 31104, 15552, 15552, 7776, 324, 2592, 648, 1296, 
  2592, 1296, 2592, 5184, 1296, 648, 5184, 2592, 1944, 972, 3888, 1944, 2916, 
  11664, 11664, 8748, 69984, 31104, 15552, 15552, 7776, 18, 108, 216, 72, 
  432, 864, 144, 576, 432, 72, 864, 576, 486, 1944, 3888, 972, 1944, 3888, 
  54, 324, 648, 432, 1458, 2916, 31104, 62208, 432, 2592, 5184, 3456, 11664, 
  23328, 1296, 2592, 5184, 10368, 10368, 5184, 3888, 7776, 11664, 46656, 
  46656, 34992, 279936, 1944, 3888, 3888, 7776, 7776, 3888, 15552, 7776, 
  17496, 34992, 1944, 7776, 3888, 3888, 3888, 15552, 7776, 7776, 17496, 
  34992, 209952, 23328, 93312, 46656, 46656, 1944, 3888, 324, 2592, 8748, 
  17496, 432, 864, 432, 216, 72, 36, 288, 576, 1728, 432, 864, 864, 72, 144, 
  1152, 576, 972, 1944, 3888, 1944, 1944, 3888, 7776, 3888, 20736, 10368, 
  10368, 5184, 10368, 5184, 5184, 2592, 46656, 23328, 972, 3888, 3888, 7776, 
  1944, 7776, 2916, 5832, 1944, 7776, 3888, 972, 3888, 7776, 2916, 5832, 
  46656, 23328, 46656, 23328 ]
gap> SmallGeneratingSet(sudoku);
[ (1,44,13,61)(2,53,15,79)(3,35,14,70)(4,62,10,43)(5,71,12,34)(6,80,11,52)(7,
    8,17,16)(9,26,18,25)(19,45,22,63)(20,54,24,81)(21,36,23,72)(28,41,67,
    57)(29,50,69,75)(30,32,68,66)(31,59,64,39)(33,77,65,48)(37,40,58,55)(38,
    49,60,73)(42,76,56,46)(47,51,78,74), 
  (1,43)(2,52)(3,34)(4,61)(5,70)(6,
    79)(8,16)(9,25)(10,44)(11,53)(12,35)(13,62)(14,71)(15,80)(18,26)(19,
    45)(20,54)(21,36)(22,63)(23,72)(24,81)(28,39)(29,48)(31,57)(32,66)(33,
    75)(38,46)(40,55)(41,64)(42,73)(49,56)(50,65)(51,74)(59,67)(60,76)(69,77),
  (1,46,64,19,37,55)(2,47,65,20,38,56)(3,48,66,21,39,57)(4,49,67,22,40,58)(5,
    50,68,23,41,59)(6,51,69,24,42,60)(7,52,70,25,43,61)(8,53,71,26,44,62)(9,
    54,72,27,45,63)(10,28,73)(11,29,74)(12,30,75)(13,31,76)(14,32,77)(15,33,
    78)(16,34,79)(17,35,80)(18,36,81) ]
gap> Size(SmallGeneratingSet(sudoku));
3
gap> SmallerDegreePermutationRepresentation(sudoku);
IdentityMapping( <permutation group of size 3359232 with 10 generators> )