Order = 3113510400 = 29.35.52.7.11.13.
Mult = 2.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of A13 are a, b where a is in class 3A, b has order 11 and ab has order 13.
Standard generators of 2.A13 are preimages A, B where A has order 3 and B has order 11.
Standard generators of S13 are c, d where c is in class 2D, d is in class 12M and cd has order 13.
Standard generators of 2.S13 are preimages C, D where CD has order 13.
Black box algorithms
Checking generators (semi-presentations)
| Group | Semi-presentation | File |
|---|---|---|
| A13 | 〈〈 a, b | some conditions 〉〉 | Download |
Representations
Representations of A13
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- Permutation representations:
Number of points ID Generators Description Link 13 Std Details 78 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 12 Std Details 0 Z 65 Std Details 0 Z 66 Std Details 0 Z 208 Std Details 0 Z 220 Std Details 2 GF(4) 32 a Std Details 2 GF(4) 32 b Std Details 2 GF(2) 64 Std Details
Representations of 2.A13
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- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 32 a Std Details 3 GF(3) 32 b Std Details Char Ring Dimension ID Generators Description Link 5 GF(25) 32 a Std Details 5 GF(25) 32 b Std Details 5 GF(5) 64 Std Details Char Ring Dimension ID Generators Description Link 7 GF(49) 32 a Std Details 7 GF(49) 32 b Std Details 7 GF(7) 64 Std Details Char Ring Dimension ID Generators Description Link 11 GF(121) 32 a Std Details 11 GF(121) 32 b Std Details 11 GF(11) 64 Std Details Char Ring Dimension ID Generators Description Link 13 GF(13) 32 Std Details
Representations of S13
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 13 Std Details 78 Std Details