Order = 4952179814400 = 212.312.52.7.13.
Mult = 2 × 2.
Out = S4.
Porting notes
Porting incomplete.Standard generators
Standard generators of O8+(3) are a, b where a is in class 2A, b is in class 5B, ab has order 13 and abb has order 14. Alternatively: a is in class 2A/B/C, b is in class 5A/B/C, ab has order 13 and abb has order 14.
Standard generators of 2.O8+(3) are preimages A, B where A has order 2, B has order 5 and AB has order 13.
Standard generators of 22.O8+(3) are preimages A, B where B has order 5 and AB has order 13.
Type II standard generators of O8+(3):S4 are x, y.
Type II standard generators of 22.O8+(3):S4 are X, Y.
Representations
Representations of O8+(3)
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- Permutation representations:
Number of points ID Generators Description Link 1080 a Std Details 1080 b Std Details 1080 c Std Details 1080 d Std Details 1080 e Std Details 1080 f Std Details 1120 a Std Details 1120 b Std Details 1120 c Std Details 28431 a Std Details 28431 b Std Details 28431 c Std Details 28431 d Std Details 36400 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 298 Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 28 Std Details 3 GF(3) 35 a Std Details 3 GF(3) 35 b Std Details 3 GF(3) 35 c Std Details 3 GF(3) 195 Std Details 3 GF(3) 322 Std Details 3 GF(3) 518 a Std Details 3 GF(3) 518 b Std Details 3 GF(3) 518 c Std Details 3 GF(3) 567 a Std Details 3 GF(3) 567 b Std Details 3 GF(3) 567 c Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 300 Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 299 Std Details Char Ring Dimension ID Generators Description Link 13 GF(13) 300 Std Details
Representations of 2.O8+(3)
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- Permutation representations:
Number of points ID Generators Description Link 2160 a Std Details 2160 b Std Details 2240 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 8 Std Details 3 GF(3) 56 Std Details 3 GF(3) 104 Std Details 3 GF(3) 224 a Std Details 3 GF(3) 224 b Std Details 3 GF(3) 384 Std Details
Representations of O8+(3):S4
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- Permutation representations:
Number of points ID Generators Description Link 3360 Type II Details 6480 Type II Details
Representations of 22.O8+(3):S4
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- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 24 Type II Details