Order = 227787103272960 =
221.38.5.7.11.43.
Mult = 1.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of U7(2) are a, b where a is in class 2A, b has order 7, ab has order 33 and abb has order 45.
Presentations
| Group | Presentation | Link |
|---|---|---|
| U7(2) | 〈 a, b | a2 = b7 = (ab)33 = [a, b]3 = [a, b2]3 = [a, b3]3 = [a, bab]2 = [a, b2ab2]2 = [a, bab2]3 = (abab−3ab−3)8 = 1 〉 | Details |
Representations
Representations of U7(2)
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 2709 Std Details 2752 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(4) 7 a Std Details 2 GF(4) 7 b Std Details
Maximal subgroups
Maximal subgroups of U7(2)
| Subgroup | Order | Index | Programs/reps |
|---|---|---|---|
| 21+10:(3 × U5(2)) | Program: Generators |
||
| 3.U6(2).3 | Program: Generators |
||
| 29+6:3.L3(4).3 | |||
| 24+12.(A5 × 31+2:2A4) | |||
| 3 × S3 × U5(2) | |||
| 31+2:2A4 × U4(2) | |||
| 36:S7 | Program: Generators |
||
| 43:7 = F301 |