About this representation
| Group
| HN
|
| Group generators
| Standard generators
|
| Number of points
| 1140000
|
| Primitivity information
| Primitive
|
| Transitivity degree
| 1
|
| Rank
| 12
|
| Suborbit lengths
| 1, 462, 25202, 10395, 16632, 30800, 69300, 1663202, 311850, 362880
|
| Character
| 1 + 133ab + 760 + 3344 + 8910 + 16929 + 35112ab + 267520 + 365750 + 406296
|
| Point stabiliser
| A12
|
| Notes
| This representation fails the automated semi-presentation test because our version of MeatAxe cannot cope with permutations on more than 1000000 points.
|
| Contributed by
| Not recorded
|
Download
This representation is available in the following formats:
On conjugacy classes
| Conjugacy class |
Fixed points |
Cycle type |
| 1A
| 1140000
|
|
| 2A
| 8800
| 2565600
|
| 2B
| 800
| 2569600
|
| 3A
| 645
| 3379785
|
| 3B
| 60
| 3379980
|
| 4A
| 160
| 2320, 4284800
|
| 4B
| 32
| 24384, 4282800
|
| 4C
| 0
| 2400, 4284800
|
| 5A
| 50
| 5227990
|
| 5B
| 0
| 5228000
|
| 5C
| 0
| 5228000
|
| 5D
| 0
| 5228000
|
| 5E
| 50
| 5227990
|
| 6A
| 61
| 2292, 32913, 6188436
|
| 6B
| 5
| 2320, 3265, 6189760
|
| 6C
| 20
| 220, 3260, 6189860
|
| 7A
| 1
| 7162857
|
| 8A
| 0
| 216, 42192, 8141400
|
| 8B
| 8
| 276, 4160, 8142400
|
| 9A
| 3
| 319, 9126660
|
| 10A
| 0
| 51760, 10113120
|
| 10B
| 10
| 220, 51758, 10113116
|
| 10C
| 0
| 5160, 10113920
|
| 10D
| 0
| 5160, 10113920
|
| 10E
| 0
| 5160, 10113920
|
| 10F
| 10
| 220, 51758, 10113116
|
| 10G
| 0
| 225, 5160, 10113915
|
| 10H
| 0
| 225, 5160, 10113915
|
| 11A
| 4
| 11103636
|
| 12A
| 5
| 228, 39, 4146, 61452, 1294218
|
| 12B
| 1
| 22, 353, 4160, 6106, 1294880
|
| 12C
| 0
| 210, 410, 6130, 1294930
|
| 14A
| 1
| 71257, 1480800
|
| 15A
| 5
| 315, 5128, 1575954
|
| 15B
| 0
| 512, 1575996
|
| 15C
| 0
| 512, 1575996
|
| 19A
| 0
| 1960000
|
| 19B
| 0
| 1960000
|
| 20A
| 0
| 532, 1064, 2056960
|
| 20B
| 0
| 532, 1064, 2056960
|
| 20C
| 2
| 24, 410, 56, 10876, 2056558
|
| 20D
| 0
| 1080, 2056960
|
| 20E
| 0
| 1080, 2056960
|
| 21A
| 1
| 792, 2154255
|
| 22A
| 0
| 22, 11800, 2251418
|
| 25A
| 0
| 2545600
|
| 25B
| 0
| 2545600
|
| 30A
| 1
| 22, 33, 512, 66, 1058, 15582, 3037686
|
| 30B
| 0
| 54, 104, 1552, 3037972
|
| 30C
| 0
| 54, 104, 1552, 3037972
|
| 35A
| 1
| 77, 3532570
|
| 35B
| 1
| 77, 3532570
|
| 40A
| 0
| 2, 42, 85, 103, 20438, 4028279
|
| 40B
| 0
| 2, 42, 85, 103, 20438, 4028279
|
Checks applied
| Check |
Description |
Date |
Checked by |
Result |
| Files exist
| Check whether files exist (where stated).
| Jul 4, 2006
| certify.pl version 0.05
| Pass
|