About this representation

Group Fi24':2
Group generators Standard generators
Number of points 306936
Primitivity information Primitive
Transitivity degree 1
Rank 3
Suborbit lengths 1, 31671, 275264
Character 1+ + 57477+ + 249458+
Point stabiliser Fi23 × 2
Contributed by Not recorded

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This representation is available in the following formats:

MeatAxe c d
MeatAxe binary c d
GAP c d
GAP c, d
Magma c, d

On conjugacy classes

Conjugacy class Fixed points Cycle type
1A 306936
2A 3512 2151712
2B 504 2153216
3A 3240 3101232
3B 1485 3101817
3C 378 3102186
3D 162 3102258
3E 0 3102312
4A 120 2192, 476608
4B 64 21724, 475856
4C 8 2248, 476608
5A 36 561380
6A 128 21556, 31128, 650052
6B 126 2126, 3126, 651030
6C 29 2728, 31161, 650328
6D 72 21584, 3144, 650544
6E 45 2720, 3153, 650832
6F 38 2170, 31158, 650514
6G 2 280, 31170, 650544
6H 18 272, 3162, 651048
6I 18 2180, 3162, 651012
6J 18 272, 3162, 651048
6K 0 3168, 651072
7A 21 743845
7B 0 743848
8A 12 254, 496, 838304
8B 4 22, 4124, 838304
8C 0 24, 4124, 838304
9A 27 3486, 933939
9B 45 3480, 933939
9C 36 3483, 933939
9D 0 3495, 933939
9E 9 3492, 933939
9F 6 352, 934086
10A 12 212, 5700, 1030340
10B 4 216, 5100, 1030640
11A 3 1127903
12A 36 218, 328, 4792, 658, 1225272
12B 21 212, 333, 4360, 660, 1225416
12C 12 230, 336, 4792, 654, 1225272
12D 16 256, 316, 4778, 6556, 1225026
12E 6 26, 338, 490, 662, 1225506
12F 18 334, 436, 664, 1225524
12G 1 214, 321, 4364, 6570, 1225164
12H 5 220, 3, 4360, 676, 1225416
12I 0 340, 664, 1225536
12J 2 28, 32, 490, 680, 1225506
12K 4 217, 320, 485, 6569, 1225257
12L 2 28, 32, 436, 680, 1225524
13A 6 1323610
14A 5 28, 7501, 1421672
14B 0 772, 1421888
15A 15 37, 5645, 1520245
15B 0 312, 5297, 1520361
15C 3 311, 575, 1520435
16A 2 2, 4, 862, 1619152
17A 1 1718055
18A 12 212, 311, 6236, 951, 1816944
18B 8 214, 37, 6238, 9387, 1816776
18C 3 212, 314, 6236, 951, 1816944
18D 5 220, 38, 6236, 9387, 1816776
18E 3 23, 314, 6239, 951, 1816944
18F 2 22, 626, 9390, 1816848
18G 0 23, 36, 623, 954, 1817016
20A 4 24, 46, 512, 10344, 2015170
20B 0 22, 48, 524, 1038, 2015320
21A 6 35, 7462, 2114461
21B 0 37, 2114615
21C 0 754, 2114598
22A 3 11319, 2213792
23A 1 2313345
23B 1 2313345
24A 6 215, 32, 49, 613, 8396, 1229, 2412636
24B 6 23, 32, 415, 617, 8396, 1227, 2412636
24C 0 34, 618, 1232, 2412768
24D 1 22, 3, 410, 8180, 1238, 2412708
24E 0 2, 44, 6, 845, 1240, 2412753
26A 2 22, 13270, 2611670
27A 3 38, 9162, 2711313
27B 0 9165, 2711313
28A 1 22, 44, 79, 14246, 2810836
29A 0 2910584
30A 3 26, 33, 525, 62, 10310, 15225, 3010010
30B 1 2, 3, 525, 65, 1025, 1525, 3010205
33A 0 3, 11135, 339256
33B 0 3, 11135, 339256
35A 1 54, 75, 358768
36A 0 26, 37, 46, 62, 911, 12118, 1820, 368472
36B 3 36, 46, 64, 911, 12118, 1820, 368472
36C 1 22, 410, 64, 97, 12118, 18190, 368388
39A 3 3, 13249, 397787
39B 3 3, 13249, 397787
39C 0 32, 397870
42A 2 22, 3, 62, 718, 14222, 21161, 427150
42B 0 718, 1418, 2118, 427290
45A 0 59, 94, 1596, 456787
60A 1 2, 3, 43, 53, 6, 1011, 12, 153, 20155, 30111, 605005
2C 31672 2137632
2D 696 2153120
4D 360 21576, 475856
4E 72 21720, 475856
4F 40 2232, 476608
4G 0 2252, 476608
6L 352 21444, 310440, 645396
6M 325 2580, 310449, 645684
6N 165 2660, 3177, 650820
6O 136 2121, 310512, 645837
6P 48 21596, 3216, 650508
6Q 21 2732, 3225, 650796
6R 28 267, 310548, 645855
6S 48 2165, 3216, 650985
6T 12 2183, 3228, 650979
6U 12 275, 3228, 651015
6V 0 3232, 651040
8D 20 250, 496, 838304
8E 12 254, 496, 838304
8F 4 22, 4124, 838304
10C 22 27, 56330, 1027525
10D 6 215, 5138, 1030621
12M 36 246, 3108, 4778, 6510, 1225026
12N 0 264, 3120, 4778, 6504, 1225026
12O 9 210, 3117, 4364, 6522, 1225164
12P 13 216, 39, 4360, 672, 1225416
12Q 18 210, 3114, 485, 6522, 1225257
12R 12 258, 320, 4778, 6554, 1225026
12S 4 234, 312, 4792, 666, 1225272
12T 13 216, 39, 4360, 672, 1225416
12U 0 2, 3120, 440, 6525, 1225272
12V 0 2, 324, 440, 6573, 1225272
12W 6 216, 322, 485, 6568, 1225257
12X 4 27, 312, 490, 675, 1225506
12Y 0 29, 436, 681, 1225524
12Z 4 27, 312, 436, 675, 1225524
12A1 0 684, 1225536
14C 11 25, 74523, 1419661
14D 3 29, 799, 1421873
16B 2 2, 4, 862, 1619152
18H 1 213, 3108, 6189, 93483, 1815228
18I 19 213, 3102, 6189, 93483, 1815228
18J 10 213, 3105, 6189, 93483, 1815228
18K 9 29, 34, 6241, 975, 1816932
18L 1 24, 3108, 6192, 93483, 1815228
18M 3 221, 36, 6237, 975, 1816932
18N 6 215, 35, 6239, 975, 1816932
18O 0 37, 6244, 975, 1816932
18P 3 23, 36, 6243, 975, 1816932
18Q 4 2, 38, 622, 93516, 1815285
20C 10 2, 46, 570, 10315, 2015170
20D 2 25, 46, 514, 10343, 2015170
22B 3 1163, 2213920
22C 3 112879, 2212512
24F 6 215, 32, 49, 613, 8396, 1229, 2412636
24G 2 25, 36, 415, 615, 8396, 1227, 2412636
24H 0 23, 34, 43, 617, 845, 1231, 2412753
24I 1 22, 3, 410, 8180, 1238, 2412708
26B 4 2, 132436, 2610587
26C 4 2, 132436, 2610587
28B 3 2, 44, 751, 14225, 2810836
28C 0 1436, 2810944
28D 0 1436, 2810944
30C 7 24, 35, 569, 6, 10288, 152087, 309079
30D 3 26, 3, 59, 63, 10318, 1543, 3010101
30E 1 2, 37, 527, 62, 1024, 152101, 309167
30F 3 3, 59, 65, 1033, 1543, 3010196
30G 0 32, 533, 65, 10132, 1535, 3010163
34A 1 171863, 348096
36D 0 24, 33, 47, 62, 939, 12119, 18174, 368388
36E 3 2, 32, 410, 63, 939, 12118, 18174, 368388
36F 1 2, 34, 46, 65, 93, 12118, 1824, 368472
36G 0 2, 4, 98, 1213, 18191, 368424
40A 0 4, 54, 84, 1010, 2019, 407660
42C 2 22, 33, 6, 750, 14206, 211491, 426485
42D 0 3, 63, 2133, 427291
46A 1 231377, 465984
46B 1 231377, 465984
54A 1 2, 64, 936, 1863, 271161, 545076
60B 1 2, 33, 43, 57, 109, 12, 1521, 20155, 30102, 605005
66A 0 3, 1115, 2260, 3316, 664620
66B 0 3, 1115, 2260, 3316, 664620
70A 1 52, 73, 10, 14, 35904, 703932
78A 1 2, 3, 1327, 26111, 39803, 783492
78B 1 2, 3, 1327, 26111, 39803, 783492
84A 0 2, 3, 4, 12, 149, 2117, 28111, 4272, 843575

Checks applied

Check Description Date Checked by Result
Semi-presentation Check against a semi-presentation. If this fails, then the representation is not on standard generators, and may generate the wrong group. Note that the semi-presentation itself is not checked here. Jul 4, 2006 certify.pl version 0.05 Pass
Number of points Check whether the permutation representation is acting on the stated number of points. Jul 4, 2006 certify.pl version 0.05 Pass
Files exist Check whether files exist (where stated). Jul 4, 2006 certify.pl version 0.05 Pass