Order = 979200 =
28.32.52.17.
Mult = 1.
Out = 4.
Porting notes
Porting incomplete. Standard generators have some commentsStandard generators
Standard generators of S4(4) are a, b where a is in class 2A/2B, b is in class 5E, ab has order 17 and ababb has order 15.
Standard generators of S4(4):2 are c, d where c is in class 2D, d is in class 4C/4D, cd has order 17 and cdd has order 4.
Standard generators of S4(4):4 are e, f where e is in class 2AB, f is in class 4F/4F', ef has order 16, eff has order 6, efeff has order 8 and efeffefff has order 6.
Black box algorithms
Checking generators (semi-presentations)
| Group | Semi-presentation | File |
|---|---|---|
| S4(4) | 〈〈 a, b | some conditions 〉〉 | Download |
Representations
Representations of S4(4)
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 85 a Std Details 120 b Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 18 Std Details 0 Z 34 a Std Details 0 Z 34 b Std Details 0 Z 50 Std Details 0 Z 50 a Std Details 0 C 51 a Std Details 0 C 51 b Std Details 0 C 51 c Std Details 0 C 51 d Std Details 0 Z 85 Std Details 0 Z 85 a Std Details 0 Z 85 b Std Details 0 Z 102 Std Details 0 Z 102 a Std Details 0 Z 102 b Std Details 0 Z 153 Std Details 0 Z[b5] 204 a Std Details 0 C 204 b Std Details 0 C 204 c Std Details 0 C 204 d Std Details 0 Z 408 a Std Details 0 Z 408 b Std Details 0 Z 900 Std Details Char Ring Dimension ID Generators Description Link 2 GF(4) 4 c Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 18 Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 18 Std Details 5 GF(5) 33 b Std Details Char Ring Dimension ID Generators Description Link 17 GF(17) 18 Std Details
Representations of S4(4):2
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- Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 8 a Std Details
Representations of S4(4):4
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 170 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 16 Std Details
Maximal subgroups
Maximal subgroups of S4(4)
| Subgroup | Order | Index | Programs/reps |
|---|---|---|---|
| 26:(3 × A5) | Program: Generators |
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| 26:(3 × A5) | Program: Generators |
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| L2(16):2 | Program: Generators |
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| L2(16):2 | Program: Generators |
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| (A5 × A5):2 | Program: Generators |
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| (A5 × A5):2 | Program: Generators |
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| S6 = A6:2 | Program: Generators |