About this representation
| Group
| McL
|
| Group generators
| Standard generators
|
| Number of points
| 22275
|
| Distinguishing letter
| b
|
| Description
| Cosets of 2A8
|
| Primitivity information
| Primitive
|
| Transitivity degree
| 1
|
| Rank
| 6
|
| Suborbit lengths
| 1, 210, 2240, 5040, 6720, 8064
|
| Character
| 1 + 252 + 1750 + 5103 + 5544 + 9625
|
| Point stabiliser
| 2.A8
|
| 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
| 211
| 211032
|
| 3A
| 81
| 37398
|
| 3B
| 27
| 37416
|
| 4A
| 7
| 2102, 45516
|
| 5A
| 25
| 54450
|
| 5B
| 0
| 54455
|
| 6A
| 1
| 240, 370, 63664
|
| 6B
| 7
| 210, 368, 63674
|
| 7A
| 1
| 73182
|
| 7B
| 1
| 73182
|
| 8A
| 1
| 23, 451, 82758
|
| 9A
| 0
| 327, 92466
|
| 9B
| 0
| 327, 92466
|
| 10A
| 1
| 212, 542, 102204
|
| 11A
| 0
| 112025
|
| 11B
| 0
| 112025
|
| 12A
| 1
| 32, 420, 634, 121832
|
| 14A
| 1
| 730, 141576
|
| 14B
| 1
| 730, 141576
|
| 15A
| 1
| 38, 516, 151478
|
| 15B
| 1
| 38, 516, 151478
|
| 30A
| 1
| 64, 108, 1514, 30732
|
| 30B
| 1
| 64, 108, 1514, 30732
|
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
|