//Standard generators of L2(13) are a and b where a has order 2, b has order 3
//and ab has order 13.
//Standard generators of the double cover 2.L2(13) = SL2(13) are pre-images A
//and B where B has order 3 and AB has order 13.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [a^-1, b^-1*a*(b*a)^5*b^-1*a] ]
             where a is (_LR`F).1 where b is (_LR`F).2;
//irreducible - fixed  by _LR`AI[1][1]
_LR`G := sub<GL(14,Integers()) |
\[ 0,0,0,0,1,1,2,0,1,0,0,0,1,-1,-1,1,1,0,0,0,1,0,1,0,
0,-2,1,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,-1,
-1,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,-1,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,-1,-1,0,0,0,0,0,
-1,1,0,0,0,-1,0,0,0,1,0,0,1,-1,0,0,1,0,-1,0,-1,0,0,0,
0,0,0,0,0,0,0,0,-1,-1,1,1,2,0,0,0,0,0,1,-1,0,0,1,1,
0,-1,-1,0,0,-1,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,
0,0,-1,0,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1 ],
\[ 1,-1,-1,0,0,0,-1,0,-1,0,0,2,-1,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,1,0,-1,0,0,0,-1,0,-1,0,0,1,-1,1,0,-1,0,0,0,
0,0,-1,0,0,-1,1,0,0,-1,0,1,0,0,-1,0,0,0,0,0,0,0,0,0,
1,1,0,0,-1,-1,0,0,-1,0,-1,0,1,1,-1,-1,0,0,1,0,0,0,1,
0,1,-1,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
0,0,0,0,0,1,-1,0,0,-1,0,1,0,0,0,-1,0,0,1,0,0,1,-1,-1,
-1,-1,0,0,0,0,0,0,0,0,0,1,0,-1,0,0,1,1,0,0,0,0,0,0,
0,1,0,-1,-1,0,0,0,0,-1,-1,0,0,0,0,1,0,0,-1,0,0,0,1,0,
-1,0,-1,0,0 ]>;

return _LR;
