//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<10, ext<K|Polynomial(K, [2, -1, 1])> where K is RationalField() |
[[2,0],[-1,0],[
2,0],[1,0],[-1,0],[
0,0],[-2,0],[
-2,1],[1,0],[-1,1],[
1,0],[0,0],[0,
0],[0,0],[0,0],[
0,0],[0,0],[0,
0],[0,0],[0,0],[
0,0],[1,0],[
-2,-1],[-4,1],[3,-1],[
0,0],[3,1],[4,
-1],[-1,2],[1,-2],[
-1,2],[1,-2],[
-3,3],[1,3],[0,-3],[
0,-1],[3,-4],[
0,-4],[1,0],[-4,0],[
-2,3],[1,-2],[
0,2],[0,2],[2,-3],[
1,-2],[1,-4],[
0,-3],[0,0],[-4,0],[
2,0],[-1,0],[
0,0],[2,0],[-3,0],[
-2,0],[-3,0],[
-3,0],[0,0],[-1,2],[
-1,3],[1,-2],[
-1,2],[-2,2],[2,-3],[
0,-1],[2,-3],[
1,-3],[-1,2],[-3,-1],[
0,0],[0,0],[1,
-1],[0,-1],[0,1],[
0,0],[-1,1],[
0,1],[-1,0],[1,0],[
1,0],[-1,0],[
1,1],[2,-1],[-2,1],[
-1,1],[-2,0],[
-3,1],[0,0],[0,1],[
7,0],[-4,0],[
2,-1],[1,1],[-4,-1],[
-4,1],[-6,2],[
-5,1],[1,2],[-2,3]],
[[-2,3],[1,-2],[
0,2],[0,2],[2,
-3],[1,-2],[1,-4],[
0,-3],[0,0],[
-4,0],[0,0],[-1,0],[
2,1],[4,-1],[
-3,1],[0,0],[-3,-1],[
-4,1],[1,-2],[
-1,2],[-2,0],[1,0],[
-3,1],[1,1],[
-1,1],[2,0],[1,-1],[
0,-1],[1,-2],[
0,0],[0,0],[0,0],[
0,1],[1,-1],[
0,1],[0,0],[-1,1],[
-1,1],[-1,0],[
1,0],[1,0],[0,0],[
0,0],[-1,0],[
0,0],[-1,0],[0,0],[
0,0],[-1,2],[
0,0],[-1,-1],[1,0],[
-1,0],[-1,0],[
1,1],[0,1],[1,1],[
1,1],[1,0],[2,
-1],[-3,0],[2,0],[
-3,1],[-2,1],[
2,1],[2,0],[4,-1],[
3,-1],[0,0],[
1,-2],[-1,0],[1,0],[
-1,-1],[-2,1],[
1,-1],[0,1],[2,0],[
3,-1],[1,0],[
0,-1],[-2,0],[1,0],[
0,0],[-2,0],[
3,0],[2,0],[3,0],[
3,0],[0,0],[1,
-2],[-5,2],[3,-2],[
-4,3],[-1,3],[
4,-1],[5,-1],[4,-4],[
3,-4],[3,-2],[
-2,-2]]>;

return _LR;
