About this representation
| Group
| McL
|
| Group generators
| Standard generators
|
| Number of points
| 22275
|
| Distinguishing letter
| c
|
| Description
| Cosets of 24:A7
|
| Primitivity information
| Primitive
|
| Transitivity degree
| 1
|
| Rank
| 13
|
| Suborbit lengths
| 1, 112, 140, 210, 420, 672, 16802, 2240, 33603, 5040
|
| Character
| 1 + 22 + 2.252 + 2.1750 + 3520 + 5103 + 9625
|
| Point stabiliser
| 24:A7
|
| Contributed by
| Not recorded
|
Download
This representation is available in the following formats:
On conjugacy classes
| Conjugacy class |
Fixed points |
Cycle type |
| 1A
| 22275
|
|
| 2A
| 435
| 210920
|
| 3A
| 0
| 37425
|
| 3B
| 54
| 37407
|
| 4A
| 15
| 2210, 45460
|
| 5A
| 0
| 54455
|
| 5B
| 5
| 54454
|
| 6A
| 0
| 3145, 63640
|
| 6B
| 6
| 224, 3143, 63632
|
| 7A
| 1
| 73182
|
| 7B
| 1
| 73182
|
| 8A
| 1
| 27, 4105, 82730
|
| 9A
| 0
| 92475
|
| 9B
| 0
| 92475
|
| 10A
| 0
| 587, 102184
|
| 11A
| 0
| 112025
|
| 11B
| 0
| 112025
|
| 12A
| 0
| 35, 670, 121820
|
| 14A
| 1
| 762, 141560
|
| 14B
| 1
| 762, 141560
|
| 15A
| 0
| 151485
|
| 15B
| 0
| 151485
|
| 30A
| 0
| 1529, 30728
|
| 30B
| 0
| 1529, 30728
|
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
|