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Group polynomials
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data.txt
Table for small non-Abelian groups
GAP id | exp | max deg | |Poly| | breakdown by degree
--------+------+---------+-----------+-------------------------------------------------------------------------------------------------------------------------------
6, 1 | 6 | 5 | 324 | 6, 36, 72, 108, 84, 18
8, 3 | 4 | 4 | 128 | 8, 32, 32, 32, 24
8, 4 | 4 | 4 | 128 | 8, 32, 32, 32, 24
10, 1 | 10 | 9 | 2500 | 10, 100, 200, 300, 440, 500, 400, 300, 200, 50
12, 1 | 12 | 7 | 1296 | 12, 72, 144, 216, 312, 252, 180, 108
12, 3 | 6 | 8 | 36864 | 12, 144, 1728, 5184, 6912, 9216, 7092, 5232, 1344
12, 4 | 6 | 5 | 648 | 12, 72, 144, 216, 168, 36
14, 1 | 14 | 13 | 9604 | 14, 196, 392, 588, 868, 980, 1176, 1372, 1176, 980, 784, 588, 392, 98
16, 3 | 4 | 4 | 256 | 16, 64, 64, 64, 48
16, 4 | 4 | 4 | 256 | 16, 64, 64, 64, 48
16, 6 | 8 | 4 | 256 | 16, 64, 64, 64, 48
16, 7 | 8 | 8 | 2048 | 16, 128, 256, 384, 432, 384, 256, 128, 64
16, 8 | 8 | 8 | 2048 | 16, 128, 256, 384, 432, 384, 256, 128, 64
16, 9 | 8 | 8 | 2048 | 16, 128, 256, 384, 432, 384, 256, 128, 64
16, 11 | 4 | 4 | 256 | 16, 64, 64, 64, 48
16, 12 | 4 | 4 | 256 | 16, 64, 64, 64, 48
16, 13 | 4 | 4 | 256 | 16, 64, 64, 64, 48
18, 1 | 18 | 17 | 26244 | 18, 324, 648, 972, 1440, 1620, 1944, 2268, 2592, 2916, 2592, 2268, 1944, 1620, 1296, 972, 648, 162
18, 3 | 6 | 9 | 2916 | 18, 108, 216, 324, 486, 486, 468, 378, 270, 162
18, 4 | 6 | 5 | 2916 | 18, 324, 648, 972, 792, 162
20, 1 | 20 | 11 | 10000 | 20, 200, 400, 600, 880, 1000, 1200, 1400, 1600, 1300, 900, 500
20, 3 | 20 | 11 | 6250000 | 20, 400, 8000, 160000, 640000, 800000, 1000000, 1250000, 922480, 762100, 554500, 152500
20, 4 | 10 | 9 | 5000 | 20, 200, 400, 600, 880, 1000, 800, 600, 400, 100
21, 1 | 21 | 11 | 1058841 | 21, 441, 9261, 27783, 55566, 111132, 194481, 203742, 191394, 130662, 93198, 41160
22, 1 | 22 | 21 | 58564 | 22, 484, 968, 1452, 2156, 2420, 2904, 3388, 3872, 4356, 4840, 5324, 4840, 4356, 3872, 3388, 2904, 2420, 1936, 1452, 968, 242
24, 1 | 24 | 11 | 5184 | 24, 144, 288, 432, 648, 648, 648, 648, 624, 504, 360, 216
24, 3 | 12 | 16 | 301989888 | 24, 288, 3456, 41472, 466560, 4497408, 23700480, 42332736, 47870304, 49503744, 49766784, 45834240, 26631144, 7998624, 2457888, 786432, 98304
24, 4 | 12 | 12 | 10368 | 24, 288, 576, 864, 1272, 1440, 1440, 1440, 1152, 864, 576, 288, 144
24, 5 | 12 | 7 | 2592 | 24, 144, 288, 432, 624, 504, 360, 216
24, 6 | 12 | 12 | 10368 | 24, 288, 576, 864, 1272, 1440, 1440, 1440, 1152, 864, 576, 288, 144
24, 7 | 12 | 7 | 2592 | 24, 144, 288, 432, 624, 504, 360, 216
24, 8 | 12 | 12 | 10368 | 24, 288, 576, 864, 1272, 1440, 1440, 1440, 1152, 864, 576, 288, 144
24, 10 | 12 | 12 | 1152 | 24, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 72
24, 11 | 12 | 12 | 1152 | 24, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 72
24, 12 | 12 | ? | ? | 24, 576, 13824, 331776, 6953472, 112961664, 896801904, ???
24, 13 | 6 | 11 | 147456 | 24, 288, 3456, 10368, 13824, 18432, 24552, 24288, 21120, 14208, 10752, 6144
24, 14 | 6 | 5 | 1296 | 24, 144, 288, 432, 336, 72
I haven't found a way to compute (24, 12) in only 16GB of RAM.
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