Order = 163849992929280 = 221.34.5.72.31.127.
Mult = 1.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of L7(2) are a, b where a is in class 2A, b has order 7 (necessarily in class 7E), ab has order 127 and ababababb has order 7.
Type I standard generators of L7(2):2 are c, d where c is in class 2A, d is in class 12H (centralizer order 144), cd has order 14 and cdcdd has order 12.
Type II standard generators of L7(2):2 are e, f where e is in class 2D, f is in class 8E/F (centralizer order 92160), ef has order ?? and efeff has order ??.
Black box algorithms
Checking generators (semi-presentations)
| Group | Semi-presentation | File |
|---|---|---|
| L7(2) | 〈〈 a, b | some conditions 〉〉 | Download |
Representations
Representations of L7(2)
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 127 a Std Details 127 b Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 126 Std Details Char Ring Dimension ID Generators Description Link 2 GF(2) 7 a Std Natural representation Details 2 GF(2) 7 b Std Dual of the natural representation Details 2 GF(2) 21 a Std Details 2 GF(2) 21 b Std Details 2 GF(2) 35 a Std Details 2 GF(2) 35 b Std Details 2 GF(2) 48 Std The adjoint representation Details 2 GF(2) 112 a Std Details 2 GF(2) 112 b Std Details 2 GF(2) 133 a Std Details 2 GF(2) 133 b Std Details 2 GF(2) 175 a Std Details 2 GF(2) 175 b Std Details 2 GF(2) 224 a Std Details 2 GF(2) 224 b Std Details 2 GF(2) 392 a Std Details 2 GF(2) 448 a Std Details 2 GF(2) 448 b Std Details 2 GF(2) 469 a Std Details 2 GF(2) 469 b Std Details 2 GF(2) 707 a Std Details 2 GF(2) 707 b Std Details 2 GF(2) 736 a Std Details
Representations of L7(2):2
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 254 Type II Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 14 Type II Details 2 GF(2) 42 Type II Details 2 GF(2) 48 Type II Details 2 GF(2) 70 Type II Details 2 GF(2) 224 Type II Details 2 GF(2) 266 Type II Details 2 GF(2) 350 Type II Details 2 GF(2) 392 Type II Details 2 GF(2) 448 Type II Details 2 GF(2) 736 Type II Details 2 GF(2) 896 Type II Details 2 GF(2) 938 Type II Details
Maximal subgroups
Maximal subgroups of L7(2)
| Subgroup | Order | Index | Programs/reps |
|---|---|---|---|
| 26:L6(2) | |||
| 26:L6(2) | |||
| 210:(S3 × L5(2)) | |||
| 210:(S3 × L5(2)) | |||
| 212:(L3(2) × A8) | |||
| 212:(L3(2) × A8) | |||
| 127:7 = F889. |
Maximal subgroups of L7(2):2
| Subgroup | Order | Index | Programs/reps |
|---|---|---|---|
| L7(2) | |||
| 21+10:L5(2):2 | |||
| L6(2):2 | |||
| 24+4:(S3 × S3):2 | |||
| S3 × L3(2):2 | |||
| 127:14 = F1778 |