About this representation
| Group
| McL
|
| Group generators
| Standard generators
|
| Number of points
| 15400
|
| Distinguishing letter
| a
|
| Description
| Cosets of 31+42S5
|
| Primitivity information
| Primitive
|
| Transitivity degree
| 1
|
| Rank
| 5
|
| Suborbit lengths
| 1, 90, 1215, 2430, 11664
|
| Character
| 1 + 252 + 4500 + 5103 + 5544
|
| Point stabiliser
| 31+4:2.S5
|
| Contributed by
| Not recorded
|
Download
This representation is available in the following formats:
On conjugacy classes
| Conjugacy class |
Fixed points |
Cycle type |
| 1A
| 15400
|
|
| 2A
| 56
| 27672
|
| 3A
| 91
| 35103
|
| 3B
| 10
| 35130
|
| 4A
| 12
| 222, 43836
|
| 5A
| 25
| 53075
|
| 5B
| 0
| 53080
|
| 6A
| 11
| 240, 315, 62544
|
| 6B
| 2
| 24, 318, 62556
|
| 7A
| 0
| 72200
|
| 7B
| 0
| 72200
|
| 8A
| 2
| 25, 411, 81918
|
| 9A
| 1
| 330, 91701
|
| 9B
| 1
| 330, 91701
|
| 10A
| 1
| 212, 511, 101532
|
| 11A
| 0
| 111400
|
| 11B
| 0
| 111400
|
| 12A
| 3
| 24, 33, 420, 66, 121272
|
| 14A
| 0
| 78, 141096
|
| 14B
| 0
| 78, 141096
|
| 15A
| 1
| 38, 518, 151019
|
| 15B
| 1
| 38, 518, 151019
|
| 30A
| 1
| 52, 64, 108, 153, 30508
|
| 30B
| 1
| 52, 64, 108, 153, 30508
|
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
|