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

return _LR;
