About this representation

Group Fi23
Group generators Standard generators
Number of points 31671
Primitivity information Primitive
Transitivity degree 1
Rank 3
Suborbit lengths 1, 3510, 28160
Character 1 + 782 + 30888
Point stabiliser 2.Fi22
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 31671
2A 3511 214080
2B 695 215488
2C 183 215744
3A 351 310440
3B 324 310449
3C 135 310512
3D 27 310548
4A 63 2316, 47744
4B 39 272, 47872
4C 31 2332, 47744
4D 7 288, 47872
5A 21 56330
6A 127 2112, 31128, 64656
6B 28 2148, 31161, 64644
6C 47 2152, 3216, 65112
6D 20 2152, 3225, 65112
6E 37 249, 31158, 64677
6F 36 2144, 349, 65200
6G 45 245, 346, 65233
6H 12 2156, 357, 65196
6I 15 2168, 356, 65192
6J 1 213, 31170, 64689
6K 11 262, 3228, 65142
6L 15 260, 356, 65228
6M 9 263, 358, 65227
6N 9 29, 358, 65245
6O 3 212, 360, 65244
7A 10 74523
8A 7 216, 436, 83936
8B 7 216, 436, 83936
8C 3 22, 444, 83936
9A 0 3108, 93483
9B 18 3102, 93483
9C 9 3105, 93483
9D 0 3108, 93483
9E 3 38, 93516
10A 11 25, 5700, 102815
10B 5 28, 5138, 103096
10C 3 29, 536, 103147
11A 2 112879
12A 15 216, 316, 476, 6100, 122556
12B 12 212, 39, 472, 620, 122600
12C 3 26, 312, 484, 622, 122596
12D 0 210, 321, 476, 6102, 122556
12E 12 39, 478, 624, 122598
12F 4 216, 3, 472, 624, 122600
12G 3 26, 312, 484, 622, 122596
12H 3 26, 312, 430, 622, 122614
12I 7 220, 38, 476, 6104, 122556
12J 3 24, 320, 431, 6104, 122571
12K 4 24, 3, 478, 628, 122598
12L 1 27, 32, 430, 627, 122614
12M 3 312, 46, 624, 122622
12N 1 25, 310, 431, 6109, 122571
12O 1 2, 32, 46, 629, 122622
13A 3 132436
13B 3 132436
14A 4 23, 7501, 142011
14B 2 24, 799, 142212
15A 6 35, 569, 152087
15B 0 37, 527, 152101
16A 1 2, 4, 822, 161968
16B 1 2, 4, 822, 161968
17A 0 171863
18A 7 2, 37, 649, 9387, 181548
18B 4 27, 38, 647, 9387, 181548
18C 3 23, 33, 651, 919, 181732
18D 0 34, 652, 919, 181732
18E 2 28, 36, 648, 975, 181704
18F 5 22, 35, 650, 975, 181704
18G 0 34, 652, 919, 181732
18H 1 2, 64, 9390, 181563
20A 3 2, 44, 512, 1063, 201548
20B 1 22, 44, 56, 1066, 201548
21A 1 33, 750, 211491
22A 2 1163, 221408
22B 2 11319, 221280
22C 2 11319, 221280
23A 0 231377
23B 0 231377
24A 1 2, 32, 43, 65, 842, 1211, 241298
24B 0 22, 3, 48, 836, 1212, 241300
24C 1 2, 32, 43, 65, 842, 1211, 241298
26A 1 2, 13270, 261083
26B 1 2, 13270, 261083
27A 0 936, 271161
28A 0 2, 42, 79, 1445, 281106
30A 2 22, 3, 59, 62, 1030, 1543, 301022
30B 2 22, 33, 525, 6, 1022, 15225, 30931
30C 0 3, 59, 63, 109, 159, 301046
35A 0 52, 73, 35904
36A 0 34, 93, 1226, 188, 36866
36B 0 2, 44, 63, 97, 1224, 1834, 36852
39A 0 3, 1327, 39803
39B 0 3, 1327, 39803
42A 1 3, 6, 718, 1416, 21161, 42665
60A 0 2, 3, 4, 53, 103, 12, 153, 2015, 3020, 60511

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 4, 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