Order = 6048 = 25.33.7.
Mult = 1.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of U3(3) = G2(2)' are a, b where a has order 2, b has order 6 and ab has order 7.
Standard generators of U3(3):2 = G2(2) are c, d where c is in class 2B, d is in class 4D and cd has order 7.
Presentations
| Group | Presentation | Link |
|---|---|---|
| U3(3) | 〈 a, b | a2 = b6 = (ab)7 = [a, (ab2)3] = b3[b2, ab3a]2 = 1 〉 | Details |
| U3(3):2 | 〈 c, d | c2 = d4 = (cd)7 = [c, d]6 = (cd(cd2)3)2 = [d2, cdc]3 = 1 〉 | Details |
Representations
Representations of U3(3)
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 28 Std Details 36 Std Details 63 a Std Details 63 b Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z[i] 6 Std Details 0 Z 7 a Std Details 0 Z[i] 7 b Std Details 0 Z[i] 7 c Std Details 0 Z 14 a Std Details 0 Z 14 b Std Details 0 Z 21 a Std Details 0 Z[i] 21 b Std Details 0 Z[i] 21 c Std Details 0 Z 27 Std Details 0 Z[i] 28 a Std Details 0 Z[i] 28 b Std Details 0 C 32 a Std Details 0 C 32 b Std Details 0 Z 42 Std Details 0 Z 56 Std Details 0 Z 64 Std Details Char Ring Dimension ID Generators Description Link 2 GF(2) 6 Std Details 2 GF(2) 14 Std Details 2 GF(2) 32 a Std Details 2 GF(2) 32 b Std Details Char Ring Dimension ID Generators Description Link 3 GF(9) 3 b Std Details 3 GF(9) 6 b Std Details 3 GF(3) 7 Std Details 3 GF(9) 15 b Std Details 3 GF(3) 27 Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 6 Std Details 7 GF(7) 7 a Std Details 7 GF(49) 7 b Std Details 7 GF(7) 14 Std Details 7 GF(7) 21 a Std Details 7 GF(49) 21 b Std Details 7 GF(7) 26 Std Details 7 GF(49) 28 a Std Details
Representations of U3(3):2
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 63 b Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 6 Std Details 2 GF(2) 14 Std Details 2 GF(2) 64 Std Details 3 GF(3) 6 Std Details 3 GF(3) 7 Std Details 3 GF(3) 12 Std Details 3 GF(3) 27 Std Details 3 GF(3) 30 Std Details