//Standard generators of A7 are a and b where a is in class 3A, b has order 5
//and ab has order 7.
//Standard generators of the double cover 2.A7 are preimages A and B where A has
//order 3, B has order 5 and AB has order 7. Any two of these conditions implies
//the third.
//Standard generators of the triple cover 3.A7 are preimages A and B where B has
//order 5 and AB has order 7.
//Standard generators of the sextuple cover 6.A7 are preimages A and B where B
//has order 5 and AB has order 7.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [ a^-1, b ] ] where a is (_LR`F).1 where b is (_LR`F).2;
//two constituents interchanged by _LR`AI[1]

_LR`G :=
MatrixGroup<4, ext<K|Polynomial(K, [2, -1, 1])> where K is RationalField() |
[[0,1],[0,-2],[-2,-1],[-3,2],[0,1],[0,-2],[-1,-1],[-2,1],[0,-1],[-1,2],
[-1,2],[2,0],[-1,1],[2,-1],[2,-1],[-1,-1]],
[[-2,0],[3,0],[3,-1],[0,-2],[0,0],[0,-1],[-1,-1],[-2,1],[-1,0],[1,1],
[2,0],[1,-2],[0,0],[0,0],[-1,0],[-1,1]]>;

return _LR;
