Order = 74412 = 2^{2}.3^{3}.13.53.
Mult = 2.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of L_{2}(53) are a, b where a has order 2, b has order 3 and ab has order 53.
Standard generators of 2.L_{2}(53) are preimages A, B where B has order 3 and AB has order 53.
Representations
Representations of L_{2}(53)
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- Permutation representations:
Number of points ID Generators Description Link 54 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 53 Std Details 0 Z[z_{26}] 54 a Std Details
Representations of 2.L_{2}(53)
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- Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z[z_{52}] 54 a Std Details
Maximal subgroups
Maximal subgroups of L_{2}(53)
Subgroup | Order | Index | Programs/reps |
---|---|---|---|
53:26 | Program: Generators | ||
D_{54} | Program: Generators | ||
D_{52} | Program: Generators | ||
A_{4} | Program: Generators |