Order = 4585351680 = 29.39.5.7.13.
Mult = 2.
Out = 2.
Porting notes
Porting complete except note about some representatios not necessarily in standard generators. Check your representation carefully!Standard generators
Standard generators of S6(3) are a, b where a is in class 2A, b has order 5, ab has order 13 and abb has order 14.
Standard generators of 2.S6(3) are preimages A, B where B has order 5 and AB has order 13.
Standard generators of S6(3):2 are c, d where c is in class 2A, d is in class 4F, cd has order 20 and cdd has order 8.
Standard generators of 2.S6(3).2 are preimages C, D where CDCDCDCDDCDDD has order 13.
Standard generators of 2.S6(3).2 (isoclinic) are preimages C, D where CDCDCDCDDCDDD has order 13.
Representations
Representations of S6(3)
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- Permutation representations:
Number of points ID Generators Description Link 364 Std Details 1120 Std Details 3640 Std Details 7371 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z[ω] 13 a Std Details 0 Z[ω] 13 b Std Details 0 Z[ω] 78 Std Details 0 Z[ω] 91 a Std Details 0 Z[ω] 91 b Std Details 0 Z 105 Std Details 0 Z 168 Std Details 0 Z 195 Std Details Char Ring Dimension ID Generators Description Link 2 GF(4) 13 a Std Details 2 GF(2) 78 Std Details Char Ring Dimension ID Generators Description Link 5 GF(25) 13 a Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 13 a Std Details
Representations of 2.S6(3)
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- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 6 Std Details
Representations of S6(3):2
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- Permutation representations:
Number of points ID Generators Description Link 364 Std Details 1120 Std Details 3640 Std Details 7371 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 26 Std Details 3 GF(3) 13 Std Details
Representations of 2.S6(3).2
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- Permutation representations:
Number of points ID Generators Description Link 728 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 6 Std Details
Maximal subgroups
Maximal subgroups of S6(3)
| Subgroup | Order | Index | Programs/reps |
|---|---|---|---|
| 31+4:2.U4(2) | Program: Generators | ||
| 36:L3(3) | Program: Generators | ||
| 2.(A4 × U4(2)) | Program: Generators | ||
| 22+6:33:S3 | Program: Generators | ||
| L2(27):3 | Program: Generators | ||
| U3(3):2 × 2 | Program: Generators | ||
| L3(3):2 | Program: Generators | ||
| L2(13) | Program: Generators | ||
| L2(13) | Program: Generators | ||
| A5 | Program: Generators | ||
| 31+4:2.(S4 × A4) |
Maximal subgroups of S6(3):2
| Subgroup | Order | Index | Programs/reps |
|---|---|---|---|
| 31+4:2.U4(2):2 | |||
| 36:(L3(3) × 2) | |||
| 31+4:2.(S4 × S4) | |||
| 2.(A4 × U4(2)).2 | |||
| 22+6:33:D12 | |||
| L2(27):6 | |||
| (U3(3) × 4):2 | |||
| L3(3):2 × 2 | |||
| S5 |