Order = 960 = 26.3.5.
Mult = 42 × 2.
Out = S4.
Porting notes
Porting incomplete.Standard generators
Standard generators of M20 = 24:A5 are a, b where a has order 4, b has order 3 and ab has order 4.
Standard generators of 21.M20 = 21+4:A5 are preimages A, B where B has order 3, AB has order 5, ABB has order 10 and AAB has order 6.
Standard generators of 22.M20 = 24:SL2(5) are preimages A, B where B has order 3 and AB has order 5.
Standard generators of 23.M20 are A, B where B has order 3, AB has order 5, ABB has order 5 and AAB has order 3.
Standard generators of 41.M20 are preimages A, B where B has order 3, AB has order 5, A has order 4 and ABABAAABABB has order 2.
Standard generators of 42.M20 are preimages A, B where B has order 3, AB has order 5, A has order 4 and ABABAAABABB has order 2.
Notes
- (M20) Standard generators of M20 map to standard generators of A5.
- (41.M20) We haven't fully checked that the standard generators for 4.M20 are sufficient to define it up to automorphisms.
- (42.M20) We haven't fully checked that the standard generators for 4.M20 and are sufficient to define it up to automorphisms.
Presentations
| Group | Presentation | Link |
|---|---|---|
| M20 | 〈 a, b | a4 = b3 = (ab)5 = (ab−1)5 = (a2b)3 = (abab−1ab−1a−1b−1)2 = 1 〉 | Details |
Representations
Representations of M20
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 20 a Std Details 20 b Std Details 20 c Std Details 20 d Std Details
Representations of 21.M20
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- Permutation representations:
Number of points ID Generators Description Link 12 a Std Details 12 b Std Details 20 a Std Details 20 b Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 6 a Std Details 0 Z 6 b Std Details 0 Z 10 a Std Details 0 Z 10 b Std Details 0 Z[b5] 12 a Std Details 0 Z[b5] 12 b Std Basis 0. Details 0 Z[b5] 12 b Std Basis 1. Details 0 Z 20 Std Details 0 Z 24 Std Details
Representations of 22.M20
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- Permutation representations:
Number of points ID Generators Description Link 120 a Std Details
Representations of 23.M20
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- Permutation representations:
Number of points ID Generators Description Link 24 Std Details
Representations of 42.M20
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- Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z[i] 4 a Std Basis 0. Details 0 Z[i] 4 a Std Basis 1. Details 0 Z[i] 20 a Std Details