//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()) |
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6,0,0,0,-1,-1],

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0,0,0]>;

return _LR;
