//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;
//four constituents interchanged by automorphisms

_LR`G :=
MatrixGroup<3, ext<K|Polynomial(K, [1, 1, 2, -1, 1])> where K is RationalField()
|
[[-5/2,-2,1,-3/2],[0,0,0,0],
[-1,-5,3,-2],[3/2,1,0,1/2],[
-1,0,0,0],[3/2,3,-2,3/2],[
3/2,-1,0,1/2],[0,0,0,0],[
5/2,2,-1,3/2]],
[[1/2,-1,1,-1/2],[1/2,-1,1,
-1/2],[0,0,0,0],[-2,-1,1,-1
],[0,1,-1,1],[-1/2,-4,2,-3/2
],[1/2,1,0,1/2],[0,0,-2,0],
[1/2,0,0,-1/2]]>;

return _LR;
