//Standard generators of L2(27) are a and b where a has order 2, b has order 3
//and ab has order 7.
//Standard generators of the double cover 2.L2(27) = SL2(27) are preimages A and
//B where B has order 3 and AB has order 7.  

_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [a^-1, b^-1], //PSL(2,27).2 = PGL(2,27)
        [a, a^-1*b^-1*a*b*a*b^-1*a*b*a*b*a*b^-1*a*b*a*b^-1*a*b*a*b^-1*a*b]]
                 //PSL(2,27).3 = PSigmaL(2,27)
             where a is (_LR`F).1 where b is (_LR`F).2;
//six constituents (each twice), fixed by AI[1],interchanged in 3-cycle by AI[2]
_LR`G := sub<GL(312,Integers()) |
\[ -405,252,-145,851,405,362,458,82,170,-296,389,-93,256,172,
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6,26,0,0,0,0,-8,0,-22,23,27,0,7,0,7,9,-20,-5,-5,-9,-8,
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-2,-11,11,2,1,-2,0,0,44,9,1,54,0,-16 ] >;

return _LR;
