(See the 2x3 calculation for more details of the method.)
Kjell Fredrik Pettersen has observed that representatives for the conjugacy classes can be taken to be formed from a permutation of the rows and a permutation of the columns. This simplifies the book-keeping hugely!
Size | Row representative | Column representative | Number of invariant grids |
---|---|---|---|
1 | 1 | 1 | 524640665777288616345600 |
1 | 1 | (1,2)(3,4)(5,6)(7,8)(9,10) | 227289669304320 |
20 | 1 | (1,2)(3,4)(5,6)(7,9)(8,10) | 164379135836160 |
60 | 1 | (1,2)(3,5)(4,6)(7,9)(8,10) | 108651431854080 |
384 | 1 | (1,3,5,7,9)(2,4,6,8,10) | 24883200 |
384 | 1 | (1,3,5,7,9,2,4,6,8,10) | 46080 |
20 | (9,10) | (1,2)(3,4)(5,6)(7,8)(9,10) | 93351114178560 |
400 | (9,10) | (1,2)(3,4)(5,6)(7,9)(8,10) | 47445631303680 |
1200 | (9,10) | (1,2)(3,5)(4,6)(7,9)(8,10) | 23716398366720 |
7680 | (9,10) | (1,3,5,7,9,2,4,6,8,10) | 23040 |
100 | (4,5)(9,10) | (1,2)(3,4)(5,6)(7,8)(9,10) | 38381102825472 |
2000 | (4,5)(9,10) | (1,2)(3,4)(5,6)(7,9)(8,10) | 14021843484672 |
6000 | (4,5)(9,10) | (1,2)(3,5)(4,6)(7,9)(8,10) | 5370871283712 |
38400 | (4,5)(9,10) | (1,3,5,7,9,2,4,6,8,10) | 12672 |
30 | (7,8)(9,10) | (1,2)(3,4)(5,6)(7,8)(9,10) | 36528696852480 |
600 | (7,8)(9,10) | (1,2)(3,4)(5,6)(7,9)(8,10) | 14069708881920 |
1800 | (7,8)(9,10) | (1,2)(3,5)(4,6)(7,9)(8,10) | 5575488307200 |
11520 | (7,8)(9,10) | (1,3,5,7,9,2,4,6,8,10) | 11520 |
300 | (4,5)(7,8)(9,10) | (1,2)(3,4)(5,6)(7,8)(9,10) | 15038794432512 |
6000 | (4,5)(7,8)(9,10) | (1,2)(3,4)(5,6)(7,9)(8,10) | 4232879013888 |
18000 | (4,5)(7,8)(9,10) | (1,2)(3,5)(4,6)(7,9)(8,10) | 1292658278400 |
115200 | (4,5)(7,8)(9,10) | (1,3,5,7,9,2,4,6,8,10) | 6912 |
225 | (2,3)(4,5)(7,8)(9,10) | (1,2)(3,4)(5,6)(7,8)(9,10) | 5953025998848 |
4500 | (2,3)(4,5)(7,8)(9,10) | (1,2)(3,4)(5,6)(7,9)(8,10) | 1304218828800 |
13500 | (2,3)(4,5)(7,8)(9,10) | (3,5)(4,6)(7,9)(8,10) | 1321425960960 |
13500 | (2,3)(4,5)(7,8)(9,10) | (1,2)(3,5)(4,6)(7,9)(8,10) | 319026102272 |
86400 | (2,3)(4,5)(7,8)(9,10) | (1,3,5,7,9,2,4,6,8,10) | 4608 |
32000 | (3,4,5)(8,9,10) | (5,7,9)(6,8,10) | 2356936704 |
32000 | (3,4,5)(8,9,10) | (1,2)(3,4)(5,7,9,6,8,10) | 884736 |
64000 | (3,4,5)(8,9,10) | (1,3)(2,4)(5,7,9,6,8,10) | 331776 |
64000 | (3,4,5)(6,7)(8,9,10) | (1,2)(3,4)(5,7,9,6,8,10) | 221184 |
128000 | (3,4,5)(6,7)(8,9,10) | (1,3)(2,4)(5,7,9,6,8,10) | 55296 |
32000 | (1,2)(3,4,5)(6,7)(8,9,10) | (1,2)(3,4)(5,7,9,6,8,10) | 147456 |
64000 | (1,2)(3,4,5)(6,7)(8,9,10) | (1,3)(2,4)(5,7,9,6,8,10) | 36864 |
216000 | (2,3,4,5)(7,8,9,10) | (3,5,7,9)(4,6,8,10) | 5242880 |
216000 | (2,3,4,5)(7,8,9,10) | (1,2)(3,5,7,9)(4,6,8,10) | 532480 |
18432 | (6,7,8,9,10) | (1,3,5,7,9)(2,4,6,8,10) | 619200 |
18432 | (6,7,8,9,10) | (1,3,5,7,9,2,4,6,8,10) | 5760 |
184320 | (4,5)(6,7,8,9,10) | (1,3,5,7,9,2,4,6,8,10) | 2880 |
276480 | (2,3)(4,5)(6,7,8,9,10) | (1,3,5,7,9,2,4,6,8,10) | 1440 |
576 | (1,2,3,4,5)(6,7,8,9,10) | 1 | 132710400 |
576 | (1,2,3,4,5)(6,7,8,9,10) | (1,2)(3,4)(5,6)(7,8)(9,10) | 46080 |
11520 | (1,2,3,4,5)(6,7,8,9,10) | (1,2)(3,4)(5,6)(7,9)(8,10) | 23040 |
34560 | (1,2,3,4,5)(6,7,8,9,10) | (1,2)(3,5)(4,6)(7,9)(8,10) | 11520 |
221184 | (1,2,3,4,5)(6,7,8,9,10) | (1,3,5,7,9)(2,4,6,8,10) | 114700 |
221184 | (1,2,3,4,5)(6,7,8,9,10) | (1,3,5,7,9,2,4,6,8,10) | 840 |
120 | (1,6)(2,7)(3,8)(4,9)(5,10) | 1 | 13580303155200 |
120 | (1,6)(2,7)(3,8)(4,9)(5,10) | (1,2)(3,4)(5,6)(7,8)(9,10) | 958060338610176 |
2400 | (1,6)(2,7)(3,8)(4,9)(5,10) | (7,9)(8,10) | 3171955138560 |
2400 | (1,6)(2,7)(3,8)(4,9)(5,10) | (1,2)(3,4)(5,6)(7,9)(8,10) | 22201474572288 |
7200 | (1,6)(2,7)(3,8)(4,9)(5,10) | (3,5)(4,6)(7,9)(8,10) | 770505216000 |
7200 | (1,6)(2,7)(3,8)(4,9)(5,10) | (1,2)(3,5)(4,6)(7,9)(8,10) | 4232109871104 |
46080 | (1,6)(2,7)(3,8)(4,9)(5,10) | (1,3,5,7,9)(2,4,6,8,10) | 8640 |
46080 | (1,6)(2,7)(3,8)(4,9)(5,10) | (1,3,5,7,9,2,4,6,8,10) | 9216 |
432000 | (1,6)(2,7,3,8)(4,9,5,10) | (3,5,7,9)(4,6,8,10) | 1300480 |
432000 | (1,6)(2,7,3,8)(4,9,5,10) | (1,2)(3,5,7,9)(4,6,8,10) | 632832 |
192000 | (1,6)(2,7)(3,8,4,9,5,10) | (5,7,9)(6,8,10) | 331776 |
192000 | (1,6)(2,7)(3,8,4,9,5,10) | (1,2)(3,4)(5,7,9,6,8,10) | 552960 |
384000 | (1,6)(2,7)(3,8,4,9,5,10) | (1,3)(2,4)(5,7,9)(6,8,10) | 82944 |
384000 | (1,6)(2,7)(3,8,4,9,5,10) | (1,3)(2,4)(5,7,9,6,8,10) | 175104 |
2880 | (1,6,2,7,3,8,4,9,5,10) | 1 | 46080 |
2880 | (1,6,2,7,3,8,4,9,5,10) | (1,2)(3,4)(5,6)(7,8)(9,10) | 9216 |
57600 | (1,6,2,7,3,8,4,9,5,10) | (7,9)(8,10) | 23040 |
57600 | (1,6,2,7,3,8,4,9,5,10) | (1,2)(3,4)(5,6)(7,9)(8,10) | 4608 |
172800 | (1,6,2,7,3,8,4,9,5,10) | (3,5)(4,6)(7,9)(8,10) | 11520 |
172800 | (1,6,2,7,3,8,4,9,5,10) | (1,2)(3,5)(4,6)(7,9)(8,10) | 2304 |
1105920 | (1,6,2,7,3,8,4,9,5,10) | (1,3,5,7,9)(2,4,6,8,10) | 320 |
1105920 | (1,6,2,7,3,8,4,9,5,10) | (1,3,5,7,9,2,4,6,8,10) | 2556 |
Total (red × green) = 524641104917993005056000 | |||
Total (red × green / 110592000) = 4743933602050718 |