About this representation
Group
| M24
|
Group generators
| Standard generators
|
Number of points
| 759
|
Primitivity information
| Primitive
|
Transitivity degree
| 1
|
Rank
| 4
|
Suborbit lengths
| 1, 30, 280, 448
|
Character
| 1 + 23 + 252 + 483
|
Point stabiliser
| 24:A8 = 24:L4(2)
|
Contributed by
| Not recorded
|
Download
This representation is available in the following formats:
On conjugacy classes
Conjugacy class |
Fixed points |
Cycle type |
1A
| 759
|
|
2A
| 71
| 2344
|
2B
| 15
| 2372
|
3A
| 21
| 3246
|
3B
| 0
| 3253
|
4A
| 7
| 232, 4172
|
4B
| 11
| 230, 4172
|
4C
| 3
| 26, 4186
|
5A
| 4
| 5151
|
6A
| 5
| 28, 322, 6112
|
6B
| 0
| 35, 6124
|
7A
| 3
| 7108
|
7B
| 3
| 7108
|
8A
| 1
| 25, 415, 886
|
10A
| 0
| 22, 53, 1074
|
11A
| 0
| 1169
|
12A
| 1
| 22, 32, 44, 610, 1256
|
12B
| 0
| 3, 62, 1262
|
14A
| 1
| 2, 710, 1449
|
14B
| 1
| 2, 710, 1449
|
15A
| 1
| 3, 54, 1549
|
15B
| 1
| 3, 54, 1549
|
21A
| 0
| 3, 2136
|
21B
| 0
| 3, 2136
|
23A
| 0
| 2333
|
23B
| 0
| 2333
|
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
|