//Standard generators of L2(37) are a and b where a has order 2, b has order 3
//and ab has order 37.
//Standard generators of the double cover 2.L2(37) = SL2(37) are preimages A and
//B where B has order 3 and AB has order 37.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI:=[[a^-1, a^-1*b*a*b^-1*a*b*a*b^-1*a^-1*b*a*b*a*b^-1*a^-1*b^-1*a*b^-1*a*
                             b*a*b^-1*a^-1*b*a*b*a*b^-1*a^-1*b*a^-1*b^-1*a*b]]
             where a is (_LR`F).1 where b is (_LR`F).2;
//18 constituents
_LR`G :=
/*
Original group: c9Group("sl237p")
Direct integral method
Schur index: 2
Character: ( 324, -324, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1,
1, 0, 0, 0, 0, 0, 0, -9, -9, -1, -1, -1, -1, -1, -1, -1, -1, -1, 9, 9 )
*/

MatrixGroup<648,IntegerRing() |
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97,-134,-353,-196,-480,0,682,-308,-44,-328,-55,0,0,0])>;

return _LR;
