Order = 10151968619520 =
210.312.5.7.13.41.
Mult = 2.
Out = 2 × 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of O8−(3) are a, b where a is in class 2A, b is in class 4F, ab has order 41, abb has order 6 and ababb has order 41.
Standard generators of 2.O8−(3) are preimages A, B where AB has order 41 and ABABB has order 41.
Standard generators of O8−(3):21 are c, d where c is in class 2D/E, d is in class 8F, cd has order 41, cdd has order 12 and cdcdd has order 18.
Standard generators of 2.O8−(3):21 are preimages C, D where C has order 2 and CD has order 41.
Type I standard generators of O8−(3).23 are g, h where g is in class 3A, h is in class 8VW, gh has order 56 and ghh has order 36.
Type II standard generators of O8−(3).23 are g, h where g is in class 2A, h is in class 8XY, gh has order 24, ghh has order 7, ghhh has order 56 and ghhhh has order 3.
Standard generators of O8−(3).22 are i, j where i is in class 2DE, j is in class 8B1, ij has order 82 and ijj has order 8.
Representations
Representations of O8−(3)
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- Permutation representations:
Number of points ID Generators Description Link 1066 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 246 Std Details 3 GF(3) 8 Std Details
Representations of 2.O8−(3)
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- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(9) 8 a Std Details 3 GF(9) 8 b Std Details 3 GF(3) 16 Std Details
Representations of O8−(3):21
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- Permutation representations:
Number of points ID Generators Description Link 1066 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 8 Std Details
Representations of 2.O8−(3):21
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- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 16 Std Details
Representations of O8−(3).23
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- Permutation representations:
Number of points ID Generators Description Link 1066 Type I Details 1066 Type II Details - Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 8 a Type I Details
Representations of O8−(3).22
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- Permutation representations:
Number of points ID Generators Description Link 1066 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 16 Std Details
Representations of O8−(3).D8
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- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 8 Details