//Standard generators of L2(19) are a and b where a has order 2, b has order 3 
//and ab has order 19.
//Standard generators of the double cover 2.L2(19) = SL2(19) are preimages A 
//and B where B has order 3 and AB has order 19.
_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 := sub<GL(18,Integers()) |
\[ 0,-1,0,0,1,0,0,0,0,0,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,-1,0,0,1,-1,0,0,1,1,0,0,-1,0,1,0,0,0,0,
0,0,0,0,0,0,1,0,0,1,0,1,0,-1,0,0,-1,0,0,0,0,-1,1,0,
0,1,0,0,-1,-1,0,1,0,0,0,1,0,0,1,1,0,0,0,1,0,0,-1,0,
0,1,0,0,0,1,-1,0,0,1,-1,0,0,-1,0,0,0,0,0,-1,-1,0,0,
-1,0,1,-1,0,0,1,0,0,0,0,-1,1,0,0,-1,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,1,0,-1,0,0,-1,0,-1,0,-1,0,-1,1,1,0,-1,1,
0,1,-1,0,1,-1,0,1,0,-1,2,-1,1,-1,1,-1,0,0,0,1,0,-1,1,
0,-1,-1,-1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,
0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,-1,0,-1,0,-1,2,0,
0,-1,0,1,1,-1,0,0,2,-1,0,0,1,-2,0,0,1,0,0,0,-1,0,1,0,
0,1,1,0,0,1,0,0,-1,0,1,0,0,0,-1,0,1,0,0,0,0,0,0,0,1,
0,0,0,0,0,0,-1,0,0,0,0,0,-1,0,-1,0,0,1,0,1,1,-1,0,0,
0,1,0,-1,1,0,-1,0,-1,0,0,0,0,1 ],
\[ 0,1,0,0,-1,1,0,0,0,0,-1,1,-1,-1,1,0,0,0,0,1,-1,0,
-1,1,0,1,0,-1,-1,2,0,-1,2,0,0,0,0,0,0,0,1,-1,0,0,1,0,
0,-1,0,0,0,0,0,0,0,-1,0,0,1,-1,-1,0,1,0,1,-2,1,0,0,0,
1,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,
1,0,0,0,0,-1,1,0,0,0,0,0,0,1,-1,-1,1,0,1,-1,-1,0,0,0,
0,1,0,0,-1,2,-1,0,0,0,0,-1,1,0,0,-1,1,-1,1,0,0,-1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,-1,1,0,0,-1,
0,0,1,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,
1,0,0,0,1,0,0,0,0,0,1,-1,0,0,0,0,1,-1,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,-1,0,-1,1,0,1,
1,0,-1,2,-1,-1,1,1,-1,0,0,0,0,0,0,0,0,0,1,0,0,0,-1,0,
0,0,0,0,0,-1,-1,0,1,0,0,-1,1,0,0,-1,0,0,0,0,0,0,0,0,
-1,0,0,0,0,0,-1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
-1,0,0,0,1,0,0,0,0,1 ] >;

return _LR;
