//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;
//one constituent, fixed by _LR`AI[1], mapped to inequivalent rep by AutIms[2].

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

return _LR;
