About this representation
| Group
| M12
|
| Group generators
| Standard generators
|
| Number of points
| 12
|
| Distinguishing letter
| b
|
| Primitivity information
| Primitive
|
| Transitivity degree
| 5
|
| Rank
| 2
|
| Suborbit lengths
| 1, 11
|
| Point stabiliser
| M11
|
| Notes
| This representation acts 5-transitively on the points of an S(5, 6, 12) Steiner system. One of the 132 blocks is {1, 2, 3, 4, 5, 6}, and the others can be found with the GAP commands:
G := Group(b11, b21);
B := [1, 2, 3, 4, 5, 6];
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
| 12
|
|
| 2A
| 0
| 26
|
| 2B
| 4
| 24
|
| 3A
| 3
| 33
|
| 3B
| 0
| 34
|
| 4A
| 4
| 42
|
| 4B
| 0
| 22, 42
|
| 5A
| 2
| 52
|
| 6A
| 0
| 62
|
| 6B
| 1
| 2, 3, 6
|
| 8A
| 2
| 2, 8
|
| 8B
| 0
| 4, 8
|
| 10A
| 0
| 2, 10
|
| 11A
| 1
| 11
|
| 11B
| 1
| 11
|
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
|