Order = 352440 = 2^{3}.3^{2}.5.11.89.
Mult = 2.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of L_{2}(89) are a, b where a has order 2, b has order 3 and ab has order 89.
Standard generators of 2.L_{2}(89) are preimages A, B where B has order 3 and AB has order 89.
Representations
Representations of L_{2}(89)
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- Permutation representations:
Number of points ID Generators Description Link 90 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 89 Std Details 0 Z[z_{44}] 90 a Std Details
Representations of 2.L_{2}(89)
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- Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z[z_{88}] 90 a Std Details
Maximal subgroups
Maximal subgroups of L_{2}(89)
Subgroup | Order | Index | Programs/reps |
---|---|---|---|
89:44 | Program: Generators | ||
D_{90} | Program: Generators | ||
D_{88} | Program: Generators | ||
A_{5} | Program: Generators | ||
A_{5} | Program: Generators | ||
S_{4} | Program: Generators | ||
S_{4} | Program: Generators |