Order = 43589145600 = 210.35.52.72.11.13.
Mult = 2.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of A14 are a, b where a is in class 3A, b has order 13, ab has order 12, abb has order 24 and ababb has order 20. Alternatively: a is in class 3A, b has order 13, ab has order 12 and [a,b] has order 2.
Standard generators of 2.A14 are preimages A, B where A has order 3 and B has order 13.
Standard generators of S14 = A14:2 are c, d where c is in class 2D, d has order 13 and ab has order 14.
Standard generators of 2.S14 are preimages C, D where D has order 13.
Standard generators of 2.S14 (isoclinic) are preimages C, D where D has order 13.
Black box algorithms
Checking generators (semi-presentations)
Group | Semi-presentation | File |
---|---|---|
A14 | 〈〈 a, b | some conditions 〉〉 | Download |
Presentations
Group | Presentation | Link |
---|---|---|
A14 | 〈 a, b | a3 = b13 = (ab)12 = [a,b]2 = (aabab)2 = [a,babab]2 = (aabababab)2 = (aabababababab)2 = [a,babababab]2 = 1 〉 | Details |
2.A14 | 〈 A, B | some relations 〉 | Details |
S14 | 〈 c, d | some relations 〉 | Details |
2.S14 | 〈 C, D | some relations 〉 | Details |
2.S14 (isoclinic) | 〈 C, D | some relations 〉 | Details |
Representations
Representations of A14
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- Permutation representations:
Number of points ID Generators Description Link 14 Std Details 91 Std Details 364 Std Details 1001 Std Details 1716 Std Details 2002 Std Details 3003 Std Details 135135 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 13 Std Details 0 Z 77 Std Details 0 Z 78 Std Details Char Ring Dimension ID Generators Description Link 2 GF(2) 12 Std Details 2 GF(2) 64 a Std Details 2 GF(2) 64 b Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 13 Std Details 3 GF(3) 64 Std Details 3 GF(3) 78 Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 13 Std Details 5 GF(5) 77 Std Details 5 GF(5) 78 Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 12 Std Details 7 GF(7) 66 Std Details 7 GF(7) 77 Std Details Char Ring Dimension ID Generators Description Link 11 GF(11) 13 Std Details 11 GF(11) 77 Std Details 11 GF(11) 78 Std Details Char Ring Dimension ID Generators Description Link 13 GF(13) 13 Std Details 13 GF(13) 76 Std Details 13 GF(13) 78 Std Details
Representations of 2.A14
- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 64 Std Details 5 GF(5) 64 Std Details 7 GF(49) 32 a Std Details 7 GF(49) 32 b Std Details 7 GF(7) 64 Std Details 11 GF(11) 64 Std Details 13 GF(13) 64 Std Details
Representations of S14
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 14 Std Details 91 Std Details 364 Std Details 1001 Std Details 1716 Std Details 2002 Std Details 3003 Std Details 135135 Std Details 39916800 Std Details 39916800 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 12 Std Details 2 GF(2) 64 a Std Details 2 GF(2) 64 b Std Details 7 GF(7) 12 Std Details
Representations of 2.S14
- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 7 GF(7) 64 Std Details
Representations of 2.S14 (isoclinic)
- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 7 GF(7) 64 Std Details