Order = 3311126603366400 = 224.36.52.72.13.17.
Mult = 2.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of F4(2) are a, b where a is in class 2C, b is in class 3C, ab is in class 17 and ababababbababbabb is in class 13.
Standard generators of 2.F4(2) are preimages A, B where B has order 3 and AB has order 17.
Standard generators of F4(2):2 are c, d where c is in class 2E, d is in class 3AB, cd has order 40 (necessarily in class 40B) and cdcdcdd has order 10.
Standard generators of 2.F4(2).2 are preimages C, D where D has order 3.
Standard generators of 2.F4(2).2 (isoclinic) are preimages C, D where D has order 3.
Representations
Representations of F4(2)
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- Permutation representations:
Number of points ID Generators Description Link 69888 a Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 26 a Std Details
Representations of 2.F4(2)
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- Permutation representations:
Number of points ID Generators Description Link 139776 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 52 Std Details 3 GF(3) 52 Std Details 3 GF(3) 2380 Std Details 5 GF(5) 52 Std Details 37 GF(37) 52 Std Details
Representations of F4(2):2
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- Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 52 Std Details
Representations of 2.F4(2).2
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- Matrix representations
Char Ring Dimension ID Generators Description Link 5 GF(25) 52 Std Details
Representations of 2.F4(2).4
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- Matrix representations
Char Ring Dimension ID Generators Description Link 5 GF(5) 52 Details
Maximal subgroups
Maximal subgroups of F4(2)
| Subgroup | Order | Index | Programs/reps |
|---|---|---|---|
| S8(2) | Program: Standard generators |