About this representation
| Group
| HS
|
| Group generators
| Standard generators
|
| Number of points
| 15400
|
| Primitivity information
| Primitive
|
| Transitivity degree
| 1
|
| Rank
| 27
|
| Suborbit lengths
| 1, 24, 30, 362, 45, 1442, 1803, 3604, 72010, 28802
|
| 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
| 200
| 27600
|
| 2B
| 148
| 27626
|
| 3A
| 10
| 35130
|
| 4A
| 120
| 240, 43800
|
| 4B
| 8
| 296, 43800
|
| 4C
| 12
| 294, 43800
|
| 5A
| 0
| 53080
|
| 5B
| 15
| 53077
|
| 5C
| 0
| 53080
|
| 6A
| 4
| 23, 348, 62541
|
| 6B
| 2
| 24, 366, 62532
|
| 7A
| 0
| 72200
|
| 8A
| 0
| 24, 448, 81900
|
| 8B
| 2
| 25, 447, 81900
|
| 8C
| 2
| 25, 447, 81900
|
| 10A
| 0
| 540, 101520
|
| 10B
| 3
| 26, 529, 101524
|
| 11A
| 0
| 111400
|
| 11B
| 0
| 111400
|
| 12A
| 0
| 2, 340, 42, 613, 121266
|
| 15A
| 0
| 35, 52, 151025
|
| 20A
| 0
| 524, 108, 20760
|
| 20B
| 0
| 524, 108, 20760
|
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
|