//Standard generators of A6 are a and b where a has order 2, b has order 4 and
//ab has order 5.
//Standard generators of the double cover 2.A6 = SL2(9) are preimages A and B
//where AB has order 5 and ABB has order 5.
//Standard generators of the triple cover 3.A6 are preimages A and B where A has
//order 2 and B has order 4.
//Standard generators of the sixfold cover 6.A6 are preimages A and B where A
//has order 4, AB has order 15 and ABB has order 5.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [ a, b^-1*a*b^-1*a*b^-1*a*b^2*a^-1*b ], //A6.2_1 = S6
            [ a^-1, b^-1 ], //A6.2_2 = PGL(2,9)
            [ a^-1, b*a^-1*b*a^-1*b*a^-1*b^-2*a*b^-1]  ] //A6.2_3 = M_{10}
                  where a is (_LR`F).1 where b is (_LR`F).2;
//two constituents interchanged by _LR`AI[1], fixed by AutIms[2].

_LR`G :=
MatrixGroup<8,ext<K|Polynomial(K,[-1,-1,1])> where K is RationalField()|
[[-1,1],[0,0],[
-1,0],[0,1],[2,-1],[
1,-2],[0,0],[
-1,0],[1,-1],[1,0],[
0,0],[1,1],[
-1,1],[-1,0],[0,-1],[
0,-1],[1,1],[
0,-1],[-1,0],[0,-2],[
-1,0],[0,1],[
1,1],[1,1],[0,1],[
0,0],[0,1],[
-1,-3],[0,-1],[2,2],[
1,1],[1,2],[1,
1],[0,-1],[0,0],[
-1,-2],[-1,0],[
1,2],[1,1],[1,2],[
0,1],[0,0],[0,
2],[-2,-4],[0,-2],[
3,3],[1,2],[2,
3],[2,2],[0,-1],[
2,2],[-4,-8],[
-3,-2],[3,8],[2,4],[
4,6],[0,-2],[
1,0],[-1,-2],[4,5],[
-1,4],[-4,-4],[
-2,-3],[-2,-5]],
[[1,3],[-1,-1],[
3,3],[-7,-10],[
-2,-4],[6,10],[3,6],[
5,9],[-2,-3],[
0,1],[-2,-4],[6,12],[
3,4],[-6,-11],[
-4,-6],[-6,-9],[1,4],[
-1,-1],[3,5],[
-9,-14],[-2,-6],[9,13],[
4,8],[7,12],[
0,2],[0,0],[1,2],[
-3,-5],[-1,-2],[
3,5],[1,3],[3,4],[
-1,-1],[0,0],[
0,-1],[1,3],[1,1],[
-1,-2],[-1,-1],[
-1,-2],[0,1],[0,0],[
0,0],[0,-1],[
-1,0],[0,1],[0,1],[
0,1],[-2,0],[
0,1],[0,1],[0,1],[
3,-2],[2,-2],[
0,-1],[-1,0],[0,-2],[
1,0],[-1,-2],[
4,5],[-1,4],[-4,-4],[
-2,-3],[-2,-5]]>;

return _LR;
