Order = 25015379558400 = 220.36.52.7.11.17.
Mult = 1.
Out = 2.
Porting notes
Fully copied from version 2. 30/7/06.Standard generators
Standard generators of O10−(2) are a, b where a is in class 2A, b is in class 5B, ab has order 33 and abababb has order 18. Alternatively: a is in class 2A, b is in class 5B, ab has order 33 and abab4 has order 3.
Standard generators of O10−(2):2 are c, d where c is in class 2E, d has order 11 and cd has order 36.
Representations
Representations of O10−(2)
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 495 Std Details 528 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 154 Std Details 0 Z 187 Std Details 2 GF(2) 10 Std Details 2 GF(4) 16 a Std Details 2 GF(4) 16 b Std Details 2 GF(2) 44 Std Details 2 GF(2) 100 Std Details 2 GF(2) 164 Std Details 2 GF(2) 670 Std Details
Representations of O10−(2):2
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 495 Std Details 528 Std Details 104448 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 10 Std Details 2 GF(2) 32 Std Details 2 GF(2) 44 Std Details 2 GF(2) 100 Std Details 2 GF(2) 164 Std Details 2 GF(2) 670 Std Details
Maximal subgroups
Maximal subgroups of O10−(2)
| Subgroup | Order | Index | Programs/reps |
|---|---|---|---|
| 28:O8−(2) | |||
| S8(2) | |||
| 21+12:(U4(2) × S3) | |||
| (3 × O8+(2)):2 | |||
| 26+8:(3 × A8) | |||
| 23+12:(L3(2) × A5) | |||
| A12 | |||
| 3 × U5(2) | |||
| (A5 × A8):2 | |||
| (S3 × S3 × U4(2)):2 |
Maximal subgroups of O10−(2):2
| Subgroup | Order | Index | Programs/reps |
|---|---|---|---|
| O10-(2) | |||
| 28:O8-(2):2 | |||
| S8(2) × 2 | |||
| 21+12:(U4(2):2 × S3) | |||
| S3 × O8+(2):2 | |||
| 26+8:(S3 × A8) | |||
| 23+12:(L3(2) × S5) | |||
| S12 | |||
| M12:2 | |||
| (3 × U5(2)):2 | |||
| S5 × S8 | |||
| (S3 × S3):2 × U4(2):2 |