About this representation
| Group
| Co3
|
| Group generators
| Standard generators
|
| Number of points
| 48600
|
| Primitivity information
| Primitive
|
| Transitivity degree
| 1
|
| Rank
| 8
|
| Suborbit lengths
| 1, 253, 506, 1771, 7590, 8855, 14168, 15456
|
| Character
| 1+23+253b+275+2024+5544+8855+31625c
|
| Point stabiliser
| M23
|
| Contributed by
| Not recorded
|
Download
This representation is available in the following formats:
On conjugacy classes
| Conjugacy class |
Fixed points |
Cycle type |
| 1A
| 48600
|
|
| 2A
| 1080
| 223760
|
| 2B
| 0
| 224300
|
| 3A
| 0
| 316200
|
| 3B
| 162
| 316146
|
| 3C
| 0
| 316200
|
| 4A
| 0
| 2540, 411880
|
| 4B
| 48
| 2516, 411880
|
| 5A
| 0
| 59720
|
| 5B
| 20
| 59716
|
| 6A
| 0
| 3360, 67920
|
| 6B
| 0
| 3360, 67920
|
| 6C
| 18
| 272, 3354, 67896
|
| 6D
| 0
| 281, 68073
|
| 6E
| 0
| 68100
|
| 7A
| 6
| 76942
|
| 8A
| 0
| 224, 4258, 85940
|
| 8B
| 0
| 224, 4258, 85940
|
| 8C
| 4
| 222, 4258, 85940
|
| 9A
| 0
| 95400
|
| 9B
| 0
| 95400
|
| 10A
| 0
| 5216, 104752
|
| 10B
| 0
| 210, 104858
|
| 11A
| 2
| 114418
|
| 11B
| 2
| 114418
|
| 12A
| 0
| 6180, 123960
|
| 12B
| 0
| 316, 6172, 123960
|
| 12C
| 0
| 29, 436, 6177, 123948
|
| 14A
| 2
| 22, 7154, 143394
|
| 15A
| 0
| 153240
|
| 15B
| 2
| 36, 532, 153228
|
| 18A
| 0
| 9120, 182640
|
| 20A
| 0
| 10108, 202376
|
| 20B
| 0
| 10108, 202376
|
| 21A
| 0
| 32, 212314
|
| 22A
| 0
| 2, 222209
|
| 22B
| 0
| 2, 222209
|
| 23A
| 1
| 232113
|
| 23B
| 1
| 232113
|
| 24A
| 0
| 68, 1286, 241980
|
| 24B
| 0
| 68, 1286, 241980
|
| 30A
| 0
| 1572, 301584
|
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
|