//Standard generators of G2(3) are a and b where a has order 2, b is in class 3C
//and ab has order 13.
//Standard generators of the triple cover 3.G2(3) are preimages A and B where A
//has order 2 and AB has order 13.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [ a, (a*b^2)^-3*b*(a*b^2)^3 ] ]
                     where a is (_LR`F).1 where b is (_LR`F).2;
//irreducible fixed by auto

_LR`G := sub< GL(14,Integers()) |
[0,1,0,0,0,0,0,0,0,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,
-1,0,-1,1,0,0,0,0,0,0,0,0,0,0,
-1,1,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,0,
0,0,0,0,-1,-1,0,0,0,0,0,0,0,-1],

[0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,
1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,
-1,0,-1,0,-1,0,0,-1,0,-1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,
1,0,1,0,1,0,0,0,0,0,-1,0,-1,0,
-1,0,-1,0,-1,-1,-1,0,-1,0,0,-1,0,-1]>;

return _LR;
