About this representation
| Group
| M23
|
| Group generators
| Standard generators
|
| Number of points
| 23
|
| Primitivity information
| Primitive
|
| Transitivity degree
| 4
|
| Rank
| 2
|
| Suborbit lengths
| 1, 22
|
| Character
| 1 + 22
|
| Point stabiliser
| M22
|
| Notes
| This representation is 4-transitive, and acts on an S(4, 7, 23) Steiner system. There are 253 blocks, one of which is {1, 2, 3, 4, 5, 11, 17}. You can find the rest in GAP as follows:
G := Group(b11,b21);
B := [1, 2, 3, 4, 5, 11, 17];
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
| 23
|
|
| 2A
| 7
| 28
|
| 3A
| 5
| 36
|
| 4A
| 3
| 22, 44
|
| 5A
| 3
| 54
|
| 6A
| 1
| 22, 32, 62
|
| 7A
| 2
| 73
|
| 7B
| 2
| 73
|
| 8A
| 1
| 2, 4, 82
|
| 11A
| 1
| 112
|
| 11B
| 1
| 112
|
| 14A
| 0
| 2, 7, 14
|
| 14B
| 0
| 2, 7, 14
|
| 15A
| 0
| 3, 5, 15
|
| 15B
| 0
| 3, 5, 15
|
| 23A
| 0
| 23
|
| 23B
| 0
| 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
|