About this representation

Group Fi22
Group generators Standard generators
Number of points 3510
Primitivity information Primitive
Transitivity degree 1
Rank 3
Suborbit lengths 1, 693, 2816
Character 1+429+3080
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 3510
2A 694 21408
2B 182 21664
2C 54 21728
3A 126 31128
3B 27 31161
3C 36 31158
3D 0 31170
4A 38 272, 4832
4B 30 276, 4832
4C 6 288, 4832
4D 6 224, 4864
4E 14 284, 4832
5A 10 5700
6A 46 240, 3216, 6456
6B 19 24, 3225, 6468
6C 11 28, 357, 6552
6D 14 256, 356, 6536
6E 10 213, 3228, 6465
6F 6 260, 316, 6556
6G 3 212, 317, 6572
6H 12 212, 314, 6572
6I 8 214, 358, 6550
6J 6 215, 316, 6571
6K 0 318, 6576
7A 3 7501
8A 6 216, 436, 8416
8B 6 216, 436, 8416
8C 2 22, 444, 8416
8D 2 22, 412, 8432
9A 6 37, 9387
9B 3 38, 9387
9C 0 9390
10A 4 23, 5138, 10281
10B 2 24, 536, 10332
11A 1 11319
11B 1 11319
12A 11 39, 44, 624, 12276
12B 2 26, 312, 428, 622, 12268
12C 2 26, 312, 428, 622, 12268
12D 6 24, 38, 428, 624, 12268
12E 3 3, 46, 68, 12286
12F 3 3, 46, 68, 12286
12G 0 26, 32, 46, 66, 12286
12H 3 24, 3, 44, 628, 12276
12I 2 26, 34, 428, 626, 12268
12J 0 24, 310, 47, 624, 12275
12K 0 32, 68, 12288
13A 0 13270
13B 0 13270
14A 1 2, 799, 14201
15A 1 33, 525, 15225
16A 0 2, 4, 822, 16208
16B 0 2, 4, 822, 16208
18A 4 2, 35, 6, 975, 18156
18B 4 2, 35, 6, 975, 18156
18C 1 2, 36, 6, 975, 18156
18D 2 22, 33, 62, 919, 18184
20A 0 2, 42, 56, 1015, 20166
21A 0 3, 718, 21161
22A 1 1163, 22128
22B 1 1163, 22128
24A 0 2, 32, 43, 65, 814, 1211, 24134
24B 0 2, 32, 43, 65, 814, 1211, 24134
30A 1 3, 59, 6, 108, 1543, 3091

Checks applied

Check Description Date Checked by Result
Presentation Check against the relations in a presentation. If this test passes, then the group is of the correct isomorphism type, and the generators are those stated. Note that the presentation itself is not checked here. Aug 2, 2006 certify.pl version 0.05 Pass
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