Order = 239500800 =
29.35.52.7.11.
Mult = 2.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of A12 are a, b where a is in class 3A, b has order 11, ab has order 10 and abb has order 35.
Standard generators of 2.A12 are preimages A, B where A has order 3 and B has order 11.
Standard generators of S12 = A12:2 are c, d where c is in class 2D, d has order 11 and ab has order 12.
Standard generators of 2.S12 are preimages C, D where D has order 11.
Black box algorithms
Checking generators (semi-presentations)
| Group | Semi-presentation | File |
|---|---|---|
| A12 | 〈〈 a, b | some conditions 〉〉 | Download |
Representations
Representations of A12
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 12 Std Details 66 Std Details 220 Std Details 462 Std Details 495 Std Details 792 Std Details 2520 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 11 Std Details 0 Z 54 Std Details 0 Z 55 Std Details 0 Z 132 Std Details 0 Z 154 Std Details 0 Z 165 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) 44 Std Details 2 GF(2) 100 Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 10 Std Details 3 GF(3) 45 Std Details 3 GF(3) 54 Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 11 Std Details 5 GF(5) 43 Std Details 5 GF(5) 55 Std Details 5 GF(5) 89 Std Details
Representations of 2.A12
- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 16 a Std Details 3 GF(3) 16 b Std Details 5 GF(5) 32 Std Details 7 GF(7) 32 Std Details 11 GF(11) 32 Std Details