//Standard generators of U3(3) = G2(2)' are a, b where a has order 2,
//b has order 6 and ab has order 7.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [a, b^-1] ] where a is (_LR`F).1 where b is (_LR`F).2;

//two constituents, interchanged by _LR`AI[1]
_LR`G :=
MatrixGroup<7, ext<K|Polynomial(K, [1, 0, 1])> where K is RationalField() |
[[1,-2],[1,2],[
1,-1],[-1,-1],[1,1],[
-2,2],[0,-2],[
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],[0,0],[0,0],[
0,0],[1,0],[0,
0],[2,2],[-3,-1],[
0,2],[2,-1],[
-1,0],[0,-3],[2,2],[
0,0],[0,0],[0,
0],[1,0],[0,0],[
0,0],[0,0],[0,
2],[-1,-2],[-1,1],[
2,1],[-1,-1],[
1,-2],[1,2]],
[[-1,1],[0,-2],[
-1,1],[1,1],[
0,-1],[2,-1],[0,2],[
0,0],[0,0],[0,
0],[1,0],[0,0],[
0,0],[0,0],[1,
2],[-2,-1],[0,1],[
2,0],[-1,-1],[
0,-2],[2,2],[2,1],[
-3,1],[1,1],[
1,-1],[-1,0],[-2,-2],[
3,0],[1,0],[
-1,1],[0,0],[0,0],[
0,0],[-1,-1],[
1,0],[1,0],[-1,1],[
1,0],[0,0],[0,
0],[-1,-1],[2,0],[
1,0],[-1,1],[
1,0],[0,-1],[0,1],[
-1,-1],[1,0]]>;

return _LR;
