About this representation
| Group
| He
|
| Group generators
| Standard generators
|
| Number of points
| 244800
|
| Primitivity information
| Primitive
|
| Transitivity degree
| 1
|
| Rank
| 36
|
| Suborbit lengths
| 1, 16, 1122, 3432, 7844, 1029, 1372, 2352, 548813, 1646410
|
| Contributed by
| Not recorded
|
Download
This representation is available in the following formats:
On conjugacy classes
| Conjugacy class |
Fixed points |
Cycle type |
| 1A
| 244800
|
|
| 2A
| 0
| 2122400
|
| 2B
| 64
| 2122368
|
| 3A
| 0
| 381600
|
| 3B
| 84
| 381572
|
| 4A
| 0
| 461200
|
| 4B
| 0
| 232, 461184
|
| 4C
| 16
| 224, 461184
|
| 5A
| 0
| 548960
|
| 6A
| 0
| 640800
|
| 6B
| 4
| 240, 320, 640776
|
| 7A
| 24
| 734968
|
| 7B
| 24
| 734968
|
| 7C
| 45
| 734965
|
| 7D
| 3
| 734971
|
| 7E
| 3
| 734971
|
| 8A
| 4
| 26, 412, 830592
|
| 10A
| 0
| 1024480
|
| 12A
| 0
| 1220400
|
| 12B
| 0
| 22, 420, 610, 1220388
|
| 14A
| 0
| 212, 1417484
|
| 14B
| 0
| 212, 1417484
|
| 14C
| 1
| 2, 79, 1417481
|
| 14D
| 1
| 2, 79, 1417481
|
| 15A
| 0
| 1516320
|
| 17A
| 0
| 1714400
|
| 17B
| 0
| 1714400
|
| 21A
| 0
| 315, 2111655
|
| 21B
| 0
| 315, 2111655
|
| 21C
| 0
| 38, 712, 2111652
|
| 21D
| 0
| 38, 712, 2111652
|
| 28A
| 0
| 46, 288742
|
| 28B
| 0
| 46, 288742
|
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 20, 2006
| permanalyse version 0.03
| Check did not complete
|
| 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
|