Order = 3265920 = 27.36.5.7.
Mult = 3 × 3 × 4.
Out = D8.
Porting notes
Porting incomplete. This group has a lot of problems. Might have to copy over by hand.Standard generators
Standard generators of U4(3) are a, b where a has order 2, b is in class 6A, ab has order 7 and abababbababb has order 5.
Standard generators of U4(3).21 are c, d where c is in class 2B, d has order 9, cd has order 14 and cdcdd has order 9.
Standard generators of U4(3).4 are e, f where e is in class 4E/E', f has order 9, ef has order 28 and efeff has order 6.
Standard generators of U4(3).22 are g, h where g is in class 2D, h has order 7 and gh has order 8.
Standard generators of U4(3).23 are i, j where i is in class 2F, j has order 5, ij has order 8, ijj has order 8, ijijj has order 7 and ijijjijjj has order 10.
Standard generators of 32.U4(3).23 are preimages I, J where I has order 2 and J has order 5.
Standard generators of 32.U4(3).23' are preimages I, J where J has order 5.
Standard generators of U4(3):D8 are o, p where o is in class 2DD', p is in class 6NN' and op has order 20.
Standard generators of 2.U4(3).D8 are preimages O, P.
Representations
Representations of U4(3)
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- Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 21 Std Details 0 Z 35 a Std Details 0 Z 35 b Std Details 0 Z 90 Std Details 0 Z 140 Std Details 0 Z 189 Std Details 0 Z 210 Std Details
Representations of U4(3):D8
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- Permutation representations:
Number of points ID Generators Description Link 112 Std Details 252 Std Details 280 Std Details 324 Std Details 540 Std Details 1134 Std Details 2835 Std Details 4536 Std Details 5184 Std Details 8505 Std Details 9072 Std Details
Representations of 32.U4(3):D8
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- Permutation representations:
Number of points ID Generators Description Link 756 a Details 756 b Details 972 Details
Representations of 2.U4(3).D8
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- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 6 Std Details