Order = 20160 = 26.32.5.7.
Mult = 2.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of A8 = L4(2) are a, b where a is in class 3A, b has order 7, ab has order 6 and abb has order 15.
Standard generators of 2.A8 are preimages A, B where A has order 3 and B has order 7.
Standard generators of S8 = A8:2 are c, d where c is in class 2C, d has order 7 and cd has order 8.
Standard generators of 2.S8 are preimages C, D where D has order 7.
Standard generators of 2.S8 (isoclinic) are preimages C, D where D has order 7.
Black box algorithms
Checking generators (semi-presentations)
| Group | Semi-presentation | File |
|---|---|---|
| A8 | 〈〈 a, b | some conditions 〉〉 | Download |
Representations
Representations of A8
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 8 Std Details 15 a Std Details 15 b Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 7 Std Details 0 Z 14 Std Details 0 Z 20 Std Details 0 Z 21 a Std Details 0 C 21 b Std Details 0 C 21 c Std Details 0 Z 28 Std Details 0 Z 35 Std Details 0 Z 42 Std Details 0 C 45 a Std Details 0 C 45 b Std Details 0 Z 56 Std Details 0 Z 64 Std Details 0 Z 70 Std Details 0 Z 90 Std Details Char Ring Dimension ID Generators Description Link 2 GF(2) 4 a Std Details 2 GF(2) 4 b Std Details 2 GF(2) 6 Std Details 2 GF(2) 14 Std Details 2 GF(2) 20 a Std Details 2 GF(2) 20 b Std Details 2 GF(2) 64 Std Details
Representations of 2.A8
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 240 a Std Details 240 b Std Details 240 c Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link Undefined Z4 4 a Std Details Char Ring Dimension ID Generators Description Link 0 Z 8 Std Details 0 C 24 a Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 8 Std Details 3 GF(9) 24 a Std Details 3 GF(9) 24 b Std Details 3 GF(3) 48 a Std Details 3 GF(3) 48 b Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 8 Std Details 5 GF(25) 24 a Std Details 5 GF(25) 24 b Std Details 5 GF(25) 32 a Std Details 5 GF(25) 32 b Std Details 5 GF(5) 48 a Std Details 5 GF(5) 48 b Std Details 5 GF(5) 64 Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 8 Std Details 7 GF(7) 16 Std Details 7 GF(7) 48 Std Details 7 GF(7) 56 a Std Details 7 GF(7) 56 b Std Details 7 GF(49) 56 c Std Details 7 GF(49) 56 d Std Details 7 GF(7) 112 Std Details