About this representation

Group Fi23
Group generators Standard generators
Number of points 137632
Primitivity information Primitive
Transitivity degree 1
Rank 3
Suborbit lengths 1, 28431, 109200
Character 1 + 30888 + 106743
Point stabiliser O8+(3):S3
Contributed by Not recorded

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This representation is available in the following formats:

MeatAxe a b
MeatAxe binary a b
GAP a b
GAP a, b
Magma a, b

On conjugacy classes

Conjugacy class Fixed points Cycle type
1A 137632
2A 14080 261776
2B 1408 268112
2C 416 268608
3A 1444 345396
3B 580 345684
3C 121 345837
3D 67 345855
4A 148 2630, 434056
4B 40 2188, 434304
4C 36 2686, 434056
4D 16 2200, 434304
5A 7 527525
6A 112 2666, 34656, 620370
6B 148 2216, 34644, 620520
6C 40 2702, 3456, 622470
6D 4 2288, 3468, 622608
6E 49 236, 34677, 620580
6F 68 2256, 3116, 622784
6G 41 240, 3125, 622856
6H 20 2280, 3132, 622776
6I 44 2700, 3124, 622636
6J 13 227, 34689, 620583
6K 13 254, 3465, 622686
6L 17 252, 3133, 622852
6M 5 258, 3137, 622850
6N 5 231, 3137, 622859
6O 11 228, 3135, 622860
7A 5 719661
8A 8 216, 494, 817152
8B 4 218, 494, 817152
8C 0 28, 4100, 817152
9A 13 3189, 915228
9B 13 3189, 915228
9C 13 3189, 915228
9D 4 3192, 915228
9E 1 322, 915285
10A 5 2, 52815, 1012355
10B 3 22, 5281, 1013622
10C 1 23, 583, 1013721
11A 0 1112512
12A 10 215, 346, 4351, 6205, 1211235
12B 4 232, 312, 4128, 652, 1211392
12C 16 214, 38, 4350, 658, 1211318
12D 4 348, 4144, 6210, 1211304
12E 4 28, 312, 4140, 660, 1211388
12F 4 232, 34, 4128, 656, 1211392
12G 4 220, 312, 4350, 656, 1211318
12H 1 28, 313, 426, 660, 1211426
12I 6 217, 310, 4351, 6223, 1211235
12J 7 23, 347, 427, 6209, 1211343
12K 4 28, 34, 4140, 664, 1211388
12L 1 28, 35, 426, 664, 1211426
12M 7 22, 311, 414, 662, 1211430
12N 3 25, 311, 427, 6227, 1211343
12O 1 25, 35, 414, 665, 1211430
13A 1 1310587
13B 1 1310587
14A 3 2, 72011, 148825
14B 1 22, 7201, 149730
15A 4 3, 5288, 159079
15B 1 32, 524, 159167
16A 0 44, 850, 168576
16B 0 44, 850, 168576
17A 0 178096
18A 1 26, 349, 670, 91548, 186840
18B 7 23, 347, 671, 91548, 186840
18C 5 24, 35, 692, 944, 187592
18D 5 24, 35, 692, 944, 187592
18E 1 26, 3, 694, 9156, 187536
18F 1 26, 3, 694, 9156, 187536
18G 2 2, 36, 693, 944, 187592
18H 1 34, 69, 91563, 186861
20A 3 4, 529, 10126, 206811
20B 1 2, 4, 57, 10137, 206811
21A 2 3, 7206, 216485
22A 0 11128, 226192
22B 0 111280, 225616
22C 0 111280, 225616
23A 0 235984
23B 0 235984
24A 4 26, 47, 64, 8175, 1229, 245659
24B 0 22, 416, 62, 864, 1228, 245696
24C 2 2, 32, 410, 65, 8175, 1228, 245659
26A 1 131083, 264752
26B 1 131083, 264752
27A 1 34, 963, 275076
28A 1 4, 721, 1490, 284865
30A 0 22, 3, 58, 10140, 1591, 304494
30B 2 2, 3, 522, 10133, 15931, 304074
30C 1 58, 6, 108, 1525, 304571
35A 0 5, 7, 353932
36A 1 22, 3, 42, 62, 94, 1246, 1820, 363796
36B 1 3, 43, 916, 1247, 1870, 363768
39A 1 13111, 393492
39B 1 13111, 393492
42A 0 2, 3, 716, 1495, 21665, 422910
60A 0 3, 4, 52, 103, 159, 2070, 3041, 602247

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
Order Check that the elements generate a group of the correct order. Jul 5, 2006 permanalyse version 0.03 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