//Standard generators of L2(11) are a and b where a has order 2, b has order 3
//and ab has order 11.
//Standard generators of the double cover 2.L2(11) = SL2(11) are preimages A and
//B where B has order 3 and AB has order 11.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [a^-1, b^-1] ] where a is (_LR`F).1 where b is (_LR`F).2;
//one constituent, fixed by _LR`AI[1][1]
_LR`G :=
MatrixGroup<10, ext<K|Polynomial(K, [2, 0, 1])> where K is RationalField() |
[[1,-3],[0,-2],[
1,-2],[0,1],[
2,1],[4,1],[-2,2],[
0,-2],[0,1],[
1,1],[3,-1],[1,-1],[
1,0],[-2,1],[
1,0],[1,2],[-3,0],[
1,0],[-1,1],[
1,1],[1,2],[1,2],[
1,2],[-1,-1],[
-2,-1],[-4,0],[0,-2],[
1,2],[-1,-1],[
-1,0],[2,-1],[-1,-1],[
1,0],[1,1],[1,
1],[2,1],[-1,1],[
0,-1],[1,0],[
-1,0],[3,0],[1,-1],[
2,0],[-1,1],[
1,1],[0,2],[-2,0],[
1,-1],[-1,1],[
-1,1],[1,1],[1,2],[
1,1],[-1,-1],[
-2,-1],[-3,0],[0,-2],[
1,2],[-1,-1],[
0,0],[-2,-2],[-2,-1],[
-1,-1],[1,1],[
2,-1],[3,-2],[1,2],[
-2,-1],[1,1],[
2,0],[0,-2],[1,-2],[
1,-2],[1,2],[
1,2],[3,1],[-1,2],[
1,-3],[0,2],[
0,0],[0,1],[3,0],[
0,0],[-2,0],[
-1,1],[-2,1],[-1,-1],[
2,0],[-2,1],[
0,0],[1,1],[-1,-1],[
0,1],[1,0],[2,
1],[0,0],[0,0],[
-1,-1],[1,0],[
-2,0]],
[[0,-3],[2,0],[
2,-2],[-1,1],[-1,0],[
2,1],[-1,1],[
2,-1],[-2,1],[2,1],[
2,-1],[-2,3],[
1,1],[-1,-2],[0,-3],[
0,-1],[1,-1],[
-1,3],[-1,-2],[1,2],[
6,2],[0,2],[3,
3],[-2,-1],[-2,-1],[
-3,2],[-2,-2],[
2,3],[-1,-2],[-2,1],[
-1,-1],[1,-2],[
-1,-1],[-1,1],[2,1],[
2,0],[-1,1],[
0,-2],[0,2],[1,0],[
-1,0],[-2,1],[
-1,1],[1,-1],[1,-1],[
0,-2],[2,0],[
-2,1],[0,-1],[0,0],[
3,1],[0,1],[2,
1],[-1,-1],[0,0],[
-2,1],[-1,-1],[
1,1],[-1,-1],[-2,1],[
1,1],[3,2],[2,
1],[-2,-1],[-4,0],[
-3,1],[-1,-2],[
3,2],[-3,-1],[0,0],[
-3,1],[1,-1],[
-2,0],[0,0],[1,1],[
-1,-1],[1,0],[
-1,-1],[0,1],[0,-1],[
2,1],[-3,0],[
-1,1],[1,-1],[2,-1],[
1,0],[1,0],[
-3,1],[2,-1],[-1,1],[
2,1],[-2,0],[
0,2],[0,0],[1,-1],[
0,0],[0,0],[
-1,1],[1,-1],[-1,0]]>;

return _LR;
