About this representation
| Group
| Fi22
|
| Group generators
| Standard generators
|
| Number of points
| 14080
|
| Distinguishing letter
| b
|
| Primitivity information
| Primitive
|
| Transitivity degree
| 1
|
| Rank
| 3
|
| Suborbit lengths
| 1, 3159, 10920
|
| Character
| 1+429+13650
|
| Contributed by
| Not recorded
|
Download
This representation is available in the following formats:
On conjugacy classes
| Conjugacy class |
Fixed points |
Cycle type |
| 1A
| 14080
|
|
| 2A
| 1408
| 26336
|
| 2B
| 256
| 26912
|
| 2C
| 128
| 26976
|
| 3A
| 112
| 34656
|
| 3B
| 148
| 34644
|
| 3C
| 49
| 34677
|
| 3D
| 13
| 34689
|
| 4A
| 0
| 2128, 43456
|
| 4B
| 16
| 2120, 43456
|
| 4C
| 0
| 2128, 43456
|
| 4D
| 16
| 256, 43488
|
| 4E
| 16
| 2120, 43456
|
| 5A
| 5
| 52815
|
| 6A
| 40
| 236, 3456, 62100
|
| 6B
| 4
| 272, 3468, 62088
|
| 6C
| 4
| 272, 384, 62280
|
| 6D
| 16
| 248, 380, 62288
|
| 6E
| 13
| 218, 3465, 62106
|
| 6F
| 8
| 252, 340, 62308
|
| 6G
| 20
| 264, 336, 62304
|
| 6H
| 17
| 216, 337, 62320
|
| 6I
| 1
| 224, 385, 62296
|
| 6J
| 5
| 222, 341, 62318
|
| 6K
| 5
| 24, 341, 62324
|
| 7A
| 3
| 72011
|
| 8A
| 0
| 464, 81728
|
| 8B
| 0
| 464, 81728
|
| 8C
| 0
| 464, 81728
|
| 8D
| 4
| 26, 428, 81744
|
| 9A
| 1
| 349, 91548
|
| 9B
| 7
| 347, 91548
|
| 9C
| 1
| 34, 91563
|
| 10A
| 3
| 2, 5281, 101267
|
| 10B
| 1
| 22, 551, 101382
|
| 11A
| 0
| 111280
|
| 11B
| 0
| 111280
|
| 12A
| 0
| 22, 436, 642, 121140
|
| 12B
| 0
| 28, 424, 640, 121144
|
| 12C
| 0
| 28, 424, 640, 121144
|
| 12D
| 4
| 26, 34, 424, 638, 121144
|
| 12E
| 4
| 28, 34, 432, 616, 121152
|
| 12F
| 4
| 28, 34, 432, 616, 121152
|
| 12G
| 1
| 28, 35, 48, 616, 121160
|
| 12H
| 0
| 22, 436, 642, 121140
|
| 12I
| 4
| 26, 34, 424, 638, 121144
|
| 12J
| 1
| 35, 412, 640, 121148
|
| 12K
| 1
| 22, 35, 42, 618, 121162
|
| 13A
| 1
| 131083
|
| 13B
| 1
| 131083
|
| 14A
| 1
| 2, 7201, 14905
|
| 15A
| 2
| 3, 522, 15931
|
| 16A
| 0
| 832, 16864
|
| 16B
| 0
| 832, 16864
|
| 18A
| 1
| 3, 624, 9156, 18696
|
| 18B
| 1
| 3, 624, 9156, 18696
|
| 18C
| 1
| 23, 3, 623, 9156, 18696
|
| 18D
| 1
| 3, 624, 928, 18760
|
| 20A
| 1
| 4, 53, 1024, 20691
|
| 21A
| 0
| 3, 716, 21665
|
| 22A
| 0
| 11128, 22576
|
| 22B
| 0
| 11128, 22576
|
| 24A
| 0
| 44, 812, 1220, 24572
|
| 24B
| 0
| 44, 812, 1220, 24572
|
| 30A
| 0
| 2, 3, 58, 107, 1591, 30420
|
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
|