//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<6, ext<K|Polynomial(K, [1, 1, 1])> where K is RationalField() |
[[1,-1],[0,1],[
0,-2],[0,0],[-1,0],[
2,2],[0,0],[0,
0],[1,1],[-1,-1],[
-1,-1],[0,1],[
-2,-1],[1,0],[-1,0],[
-1,0],[1,1],[
0,-1],[-1,-1],[0,0],[
0,0],[0,0],[0,
0],[1,0],[0,0],[
0,1],[-1,-1],[
0,-1],[0,0],[0,-1],[
1,0],[0,1],[1,
0],[-1,-1],[-1,0],[
0,1]],
[[0,0],[0,0],[
1,1],[-1,-1],[-1,-1],[
0,1],[0,1],[0,
-1],[0,1],[0,0],[
1,0],[-1,-1],[
1,1],[0,0],[1,0],[
0,0],[0,0],[0,
0],[0,1],[0,-1],[
0,1],[0,0],[0,
0],[-1,-1],[1,1],[
-1,-1],[2,1],[
0,1],[0,0],[0,2],[
1,1],[-1,0],[
1,1],[1,0],[0,-1],[
0,1]]>;

return _LR;
