//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 both fixed by _LR`AI[1][1]
_LR`G := sub<GL(36,Integers()) |
\[ 10,-2,-2,-6,0,0,-1,-3,-9,-7,-3,-4,-4,-5,-1,0,-2,-7,-1,
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1,2,0,1,0,1,1,0,1,0,1,0,0,3,-1,-1,-2,-1,0,-1,-1,-2,-2,
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0,0,0,-1,-1,0,0,1,0,1 ],
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1,2,6,3,1,2,2,2,2,2,1,3,-1,0,1,2,1,1,3,2,5,3,2,0,-1,
1,2,4,2,2,-8,4,3,5,1,-1,2,3,7,7,2,3,2,4,2,0,3,6,0,3,
6,3,1,4,6,5,7,6,4,2,1,2,4,6,2,0,-1,1,0,0,1,-1,0,0,0,
1,0,1,1,1,0,-1,0,0,0,1,2,0,0,1,0,1,1,1,0,0,1,1,1,0,
0,-1,3,-2,-2,-2,-1,2,-1,-1,-2,-3,0,-2,0,-1,-1,1,-2,-2,0,
-2,-3,0,0,-2,-2,-3,-2,-2,-2,-1,0,-1,-2,-1,-1,1 ] >;

return _LR;
