//Standard generators of S6(2) are a and b where a is in class 2A, b has order 7
//and ab has order 9.  Standard generators of the double cover 2.S6(2) are
//preimages A and B where B has order 7 and AB has order 9.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ ];
//irreducible

_LR`G := sub<GL(8,Integers()) |
\[ 1,1,2,2,2,2,1,0,-2,-3,-4,-6,-4,-3,-2,-1,0,1,1,2,2,1,
1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,-1,-1,-1,-2,-2,
-1,0,0,0,0,0,0,0,-1,-1,-1,1,1,1,2,2,2,2,1 ],
\[ -2,-2,-4,-5,-4,-3,-2,-1,-1,-2,-2,-4,-3,-2,-1,0,1,1,2,
2,2,2,1,0,1,2,2,4,3,2,1,1,-1,-2,-2,-3,-2,-2,-1,-1,0,1,
1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,2,2,2,2,1 ] >;

return _LR;
