//Standard generators of L3(3) are a and b where a has order 2, b is in class 3B
//and ab is in class 13A/B. The last condition is equivalent to: ab has order 13
//and ababb has order 4.

_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;
//Irreducible, fixed by _LR`AI[1]

_LR`G := sub<GL(12,Integers()) |
\[ 0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1 ],
\[ 1,0,0,0,0,0,0,0,0,0,-1,0,0,0,1,0,0,0,0,0,0,0,-1,0,
0,0,0,0,1,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,-1,0,0,
1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,1,0,0,-1,0,0,0,
0,0,0,0,0,0,1,0,-1,0,0,0,0,1,0,0,0,0,0,0,-1,0,0,0,0,
0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,1,0,0,0,-1,0,0,0,0,0,
0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,-1,0 ] >;

return _LR;
