//Standard generators of L2(16) are a and b where a has order 2, b has order 3
//and ab has order 15.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [a, b^-1*a*b^-1*a*b*a*b^-1*a*b*a],
            [a, b^-1*a*b^-1*a*b^-1*a*b*a*b*a*b^-1*a*b*a*b*a*b]]
                  where a is (_LR`F).1 where b is (_LR`F).2;
//second automorphism is square of first - must handle that somehow!
//eight constituents permuted in two orbits by automorphism of order 4
_LR`G := sub<GL(120,Integers()) |
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0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0]>;

return _LR;
