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
|
Download
This representation is available in the following formats:
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
|