About this representation
| Group
| M24
|
| Group generators
| Standard generators
|
| Number of points
| 1771
|
| Primitivity information
| Primitive
|
| Transitivity degree
| 1
|
| Rank
| 4
|
| Suborbit lengths
| 1, 90, 240, 1440
|
| Character
| 1 + 252 + 483 + 1035a
|
| Point stabiliser
| 26:3.S6
|
| Contributed by
| Not recorded
|
Download
This representation is available in the following formats:
On conjugacy classes
| Conjugacy class |
Fixed points |
Cycle type |
| 1A
| 1771
|
|
| 2A
| 91
| 2840
|
| 2B
| 51
| 2860
|
| 3A
| 16
| 3585
|
| 3B
| 7
| 3588
|
| 4A
| 11
| 240, 4420
|
| 4B
| 7
| 242, 4420
|
| 4C
| 7
| 222, 4430
|
| 5A
| 1
| 5354
|
| 6A
| 4
| 26, 329, 6278
|
| 6B
| 3
| 22, 316, 6286
|
| 7A
| 0
| 7253
|
| 7B
| 0
| 7253
|
| 8A
| 1
| 23, 421, 8210
|
| 10A
| 1
| 510, 10172
|
| 11A
| 0
| 11161
|
| 12A
| 2
| 2, 33, 43, 613, 12139
|
| 12B
| 1
| 2, 32, 4, 67, 12143
|
| 14A
| 0
| 713, 14120
|
| 14B
| 0
| 713, 14120
|
| 15A
| 1
| 53, 15117
|
| 15B
| 1
| 53, 15117
|
| 21A
| 0
| 7, 2184
|
| 21B
| 0
| 7, 2184
|
| 23A
| 0
| 2377
|
| 23B
| 0
| 2377
|
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 18, 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
|