About this representation
Group
| M24
|
Group generators
| Standard generators
|
Number of points
| 24
|
Primitivity information
| Primitive
|
Transitivity degree
| 5
|
Rank
| 2
|
Suborbit lengths
| 1, 23
|
Character
| 1 + 23
|
Point stabiliser
| M23
|
Notes
| This representation is 5-transitive, acting on a S(5, 8, 24) Steiner system. There are 759 blocks, one of which is {1, 2, 3, 4, 5, 11, 17, 24}. You can find the others in GAP with the command:
B := [1, 2, 3, 4, 5, 11, 17, 24];
G := Group(b11, b21);
O := Orbit(G, B, OnSets);
|
Contributed by
| Not recorded
|
Download
This representation is available in the following formats:
On conjugacy classes
Conjugacy class |
Fixed points |
Cycle type |
1A
| 24
|
|
2A
| 8
| 28
|
2B
| 0
| 212
|
3A
| 6
| 36
|
3B
| 0
| 38
|
4A
| 0
| 24, 44
|
4B
| 4
| 22, 44
|
4C
| 0
| 46
|
5A
| 4
| 54
|
6A
| 2
| 22, 32, 62
|
6B
| 0
| 64
|
7A
| 3
| 73
|
7B
| 3
| 73
|
8A
| 2
| 2, 4, 82
|
10A
| 0
| 22, 102
|
11A
| 2
| 112
|
12A
| 0
| 2, 4, 6, 12
|
12B
| 0
| 122
|
14A
| 1
| 2, 7, 14
|
14B
| 1
| 2, 7, 14
|
15A
| 1
| 3, 5, 15
|
15B
| 1
| 3, 5, 15
|
21A
| 0
| 3, 21
|
21B
| 0
| 3, 21
|
23A
| 1
| 23
|
23B
| 1
| 23
|
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
|