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

return _LR;
