Order = 19958400 =
27.34.52.7.11.
Mult = 2.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of A11 are a, b where a is in class 3A, b has order 9 and ab has order 11.
Standard generators of 2.A11 are preimages A, B where A has order 3 and B has order 9.
Standard generators of S11 = A11.2 are c, d where c is in class 2C, d is in class 10D and cd has order 11.
Standard generators of 2.S11 are preimages C, D where CD has order 11.
Black box algorithms
Checking generators (semi-presentations)
| Group | Semi-presentation | File |
|---|---|---|
| A11 | 〈〈 a, b | some conditions 〉〉 | Download |
Representations
Representations of A11
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 11 Std Details 55 Std Details 165 Std Details 330 Std Details 462 Std Details 2520 a Std Details 2520 b Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 10 Std Details 0 Z 44 Std Details 0 Z 45 Std Details 0 Z 110 Std Details 0 Z 120 Std Details 0 C 126 a Std Details 0 C 126 b Std Details 0 Z 132 Std Details 0 Z 165 Std Details 0 Z 210 Std Details 0 Z 231 Std Details 0 Z 252 Std Details Char Ring Dimension ID Generators Description Link 2 GF(2) 10 Std Details 2 GF(4) 16 a Std Details 2 GF(4) 16 b Std Details 2 GF(2) 32 Std Details 2 GF(2) 44 Std Details 2 GF(2) 100 Std Details 2 GF(2) 144 Std Details 2 GF(2) 164 Std Details 2 GF(2) 186 Std Details 2 GF(2) 198 Std Details 2 GF(2) 416 Std Details 2 GF(4) 584 a Std Details 2 GF(2) 848 Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 10 Std Details 3 GF(3) 34 Std Details 3 GF(3) 45 Std Details 3 GF(3) 109 Std Details 3 GF(3) 120 Std Details 3 GF(3) 126 a Std Details 3 GF(3) 126 b Std Details 3 GF(3) 131 Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 10 Std Details 5 GF(5) 43 Std Details 5 GF(5) 45 Std Details 5 GF(5) 55 Std Details 5 GF(5) 89 Std Details 5 GF(5) 110 Std Details 5 GF(5) 120 Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 10 Std Details 7 GF(7) 44 Std Details 7 GF(7) 45 Std Details 7 GF(7) 66 Std Details Char Ring Dimension ID Generators Description Link 11 GF(11) 9 Std Details 11 GF(11) 36 Std Details 11 GF(11) 44 Std Details 11 GF(11) 84 Std Details
Representations of 2.A11
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 5040 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 16 a Std Details 3 GF(3) 16 b Std Details 3 GF(3) 144 Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 16 a Std Details 5 GF(5) 16 b Std Details 5 GF(5) 56 a Std Details 5 GF(5) 56 b Std Details Char Ring Dimension ID Generators Description Link 7 GF(49) 16 a Std Details 7 GF(49) 16 b Std Details 7 GF(7) 32 Std Details 7 GF(7) 144 Std Details Char Ring Dimension ID Generators Description Link 11 GF(11) 16 Std Details 11 GF(11) 128 Std Details
Representations of S11
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 11 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 32 Std Details
Representations of 2.S11
- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 32 Std Details 5 GF(5) 32 Std Details 7 GF(7) 32 Std Details 11 GF(11) 16 Std Details