//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;
//four constituents, interchanbged in pairs by _LR`AI[1]
_LR`G :=
MatrixGroup<6, ext<K|Polynomial(K, [4, 0, 2, 0, 1])> where K is RationalField() 
|
[[-1,3,3/2,3/2],[0,-2,-1,-1
],[-2,1,3/2,1/2],[-2,-2,-1,0
],[1,1,-1/2,-1],[0,-1,-1,0],
[-1,2,2,3/2],[1,-2,-1,-1],[
-1,2,1/2,3/2],[-2,-2,-1,0],[
3,0,1/2,-1],[-1,-1,-1,-1/2],[
3,2,3/2,-1/2],[-2,-2,-1,0],[
3,1,3/2,0],[0,1,1,1],[
-2,-2,-3/2,-1],[-1,0,-1/2,1/2
],[-4,2,1/2,2],[2,-1,-1,-3/2
],[-3,-1,1,1/2],[-2,-2,-3/2,
-1/2],[3,2,1/2,-1/2],[1,-1,
-1/2,-1/2],[0,0,0,0],[1,0,0,
0],[0,0,0,0],[0,0,0,0],[
0,0,0,0],[0,0,0,0],[
2,0,1,0],[0,-1,-1/2,0],[
-1,2,-1/2,1/2],[0,1,0,1/2],[
0,-1,0,-1/2],[-1,0,-1/2,0]],
[[3,2,2,-1],[-2,-3,-1/2,1/2
],[6,2,2,1],[2,0,3/2,3/2],[
-2,-2,-1,-3/2],[-2,-1,-1/2,1/2
],[2,0,3/2,0],[-1,-1,-1,0],
[1,2,0,1],[-1,1,-1/2,1/2],[
1,-1,1/2,-1/2],[-2,0,-1,0],[
1,-2,-1/2,-3/2],[0,1,1,1],[
3,0,-1/2,0],[2,1,1/2,1/2],[
-2,-1,0,0],[0,1,1/2,1/2],[
-2,1,-1/2,0],[0,-1,0,-1/2],[
1,-1,3/2,0],[1,-1,1/2,0],[
-1,1,-1/2,0],[1,-1,0,0],[
0,-1,-2,-2],[-2,2,3/2,1],[
5,-3,3/2,-3/2],[2,1,3/2,0],[
-4,0,-3/2,1/2],[1,1,1,1],[
4,1,1/2,-1],[-2,0,0,1],[
3,1,1,-1/2],[0,1,1,1],[
-2,-2,-3/2,-1/2],[-1,0,1/2,1/2]]>;

return _LR;
