Order = 4585351680 = 29.39.5.7.13.
Mult = 6.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of O7(3) are a, b where a is in class 2A, b has order 7, ab has order 13 and abb has order 20.
Standard generators of 2.O7(3) are preimages A, B where B has order 7 and AB has order 13.
Standard generators of 3.O7(3) are preimages A, B where A has order 2 and B has order 7.
Standard generators of 6.O7(3) are preimages A, B where A has order 4, B has order 7 and AB has order 39.
Standard generators of O7(3):2 are c, d where c is in class 2D, d has order 7, cd has order 26 and cdcdd has order 14.
Standard generators of 2.O7(3):2 are preimages C, D where D has order 7.
Standard generators of 3O7(3):2 are preimages C, D where D has order 7.
Standard generators of 6.O7(3):2 are preimages C, D where D has order 7.
Representations
Representations of O7(3)
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- Permutation representations:
Number of points ID Generators Description Link 351 Std Details 364 Std Details 378 Std Details 1080 a Std Details 1080 b Std Details 1120 Std Details 3640 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 78 Std Details 0 Z 91 Std Details 0 Z 105 Std Details 0 Z 168 Std Details 0 Z 182 Std Details 0 Z 195 Std Details Char Ring Dimension ID Generators Description Link 2 GF(2) 78 Std Details 2 GF(2) 90 Std Details 2 GF(2) 104 Std Details 2 GF(2) 260 a Std Details 2 GF(2) 260 b Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 7 Std Details 3 GF(3) 21 Std Details 3 GF(3) 27 Std Details 3 GF(3) 35 Std Details 3 GF(3) 63 Std Details 3 GF(3) 189 a Std Details 3 GF(3) 309 Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 78 Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 78 Std Details Char Ring Dimension ID Generators Description Link 13 GF(13) 78 Std Details
Representations of 2.O7(3)
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- Permutation representations:
Number of points ID Generators Description Link 2160 a Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 8 Std Details
Representations of 3.O7(3)
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- Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(4) 27 a Std Details
Representations of O7(3):2
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- Permutation representations:
Number of points ID Generators Description Link 351 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 78 Std Details 3 GF(3) 7 Std Details
Representations of 2.O7(3):2
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- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 8 Std Details
Representations of 3O7(3):2
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- Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 54 Std Details