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AtlasRep Info for S4(7)

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Representations for G = S4(7): (all refer to std. generators 1)
1 G ≤ Sym(400a) rank 3, on cosets of 71+2+.(3 × SL(2, 7)) (1st max.)
2 G ≤ Sym(400b) rank 3, on cosets of 73:(3 × PGL(2, 7)) (2nd max.)
3 G ≤ Sym(1176) rank 5, on cosets of L2(49).22 (3rd max.)
4 G ≤ Sym(1225) rank 5, on cosets of 2.(L2(7) × L2(7)).2 (4th max.)
5 G ≤ GL(5,7)  
6 G ≤ GL(126,ℤ)  
7 G ≤ GL(175a,ℤ)  
8 G ≤ GL(175b,ℤ)  
9 G ≤ GL(224,ℤ)  
10 G ≤ GL(25a,Field([Sqrt(-7)]))  
11 G ≤ GL(25b,Field([Sqrt(-7)]))  
Programs for G = S4(7): (all refer to std. generators 1)

File created automatically by GAP on 22-Apr-2022.