Order = 5663616 = 27.3.73.43.
Mult = 1.
Out = 2.
Porting notes
Porting incomplete. Type II generators not copied.Standard generators
Standard generators of U3(7) are a, b where a has order 2, b has order 3, ab has order 43 and ababb has order 4.
Standard generators of U3(7).2 are c, d where c is in class 7A, d is in class 4D and cd has order 6.
Presentations
| Group | Presentation | Link |
|---|---|---|
| U3(7) | 〈 a, b | a2 = b3 = (ab)43 = [a,b]4 = [a,bababab]3 = ab(ababab−1)2((ab)3(ab−1)3)3 = 1 〉 | Details |
Representations
Representations of U3(7)
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 344 Std Details 688 Std Details 1032 Std Details 1376 Std Details 2064 Std Details 2107 Std Details 14749 Std Details 16856 Std Details 43904 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 43 a Std Details 0 Q(i) 43 b Std Details 0 Q(i) 43 c Std Details Char Ring Dimension ID Generators Description Link 2 GF(2) 42 Std Details 2 GF(2) 258 Std Details 2 GF(2) 344 Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 42 Std Details 3 GF(3) 43 a Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 6 c Std Details 7 GF(7) 8 Std Details 7 GF(7) 12 Std Details 7 GF(7) 20 Std Details 7 GF(7) 27 Std Details 7 GF(7) 30 a Std Details 7 GF(7) 30 b Std Details 7 GF(7) 37 Std Details 7 GF(7) 42 c Std Details 7 GF(7) 48 Std Details Char Ring Dimension ID Generators Description Link 43 GF(43) 42 Std Details 43 GF(43) 43 a Std Details
Maximal subgroups
Maximal subgroups of U3(7)
| Subgroup | Order | Index | Programs/reps |
|---|---|---|---|
| 71+2:48 | Program: Generators | ||
| 2.(L2(7) × 4).2 | Program: Generators | ||
| 82:S3 | Program: Generators | ||
| L2(7):2 | Program: Generators | ||
| 43:3 = F129 | Program: Generators |