Order = 23499295948800 = 220.35.52.7.17.31.
Mult = 1.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of O10+(2) are a, b where a is in class 2A, b is in class 20A and ab has order 21.
Standard generators of O10+(2):2 are c, d where c is in class 2E, d has order 16 and cd has order 45.
Presentations
| Group | Presentation | Link |
|---|---|---|
| O10+(2):2 | 〈 c, d | c2 = d16 = (cd)45 = [c,d]3 = [c,d2]2 = [c,d3]3 = [c,d4]2 = [c,d5]2 = [c,d6]2 = [c,d7]2 = (cd8)4 = (cd2cd2cd−1)9 = 1 〉 | Details |
Representations
Representations of O10+(2)
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 496 Std Details 527 Std Details 2295 a Std Details 2295 b Std Details 19840 Std Details 23715 Std Details 39680 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 155 Std Details 0 Z 186 Std Details Char Ring Dimension ID Generators Description Link 2 GF(2) 10 Std The natural representation. Details 2 GF(2) 16 a Std A ½-spin representation. Details 2 GF(2) 16 b Std The other ½-spin representation. Details 2 GF(2) 44 Std Details 2 GF(2) 100 Std Details 2 GF(2) 144 a Std Details 2 GF(2) 144 b Std Details 2 GF(2) 164 Std Details 2 GF(2) 320 Std Details 2 GF(2) 416 a Std Details 2 GF(2) 416 b Std Details 2 GF(2) 670 Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 155 Std Details 3 GF(3) 185 Std Details 3 GF(3) 868 Std Details
Representations of O10+(2):2
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 496 Std Details 527 Std Details 4590 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) 288 Std Details 2 GF(2) 320 Std Details 2 GF(2) 670 Std Details 2 GF(2) 832 Std Details
Maximal subgroups
Maximal subgroups of O10+(2)
| Subgroup | Order | Index | Programs/reps |
|---|---|---|---|
| S8(2) | Program: Generators | ||
| 28:O8+(2) | Program: Generators | ||
| 210:L5(2) | Program: Generators | ||
| 210:L5(2) | Program: Generators | ||
| (3 × O8-(2)):2 | |||
| 21+12:(S3 × A8) | |||
| 23+12:(S3 × S3 × L3(2)) | |||
| (A5 × U4(2)):2 | |||
| (S3 × S3 × A8):2 |
Maximal subgroups of O10+(2):2
| Subgroup | Order | Index | Programs/reps |
|---|---|---|---|
| O10+(2) | |||
| S8(2) × 2 | |||
| 28:O8+(2):2 | |||
| S3 × O8-(2):2 | |||
| 21+12:(S3 × S8) | |||
| [215]:A8 | |||
| 23+12:(32:D8 × L3(2)) | |||
| L5(2):2 | |||
| S5 × U4(2):2 | |||
| (S3 × S3):2 × S8 |