//Standard generators of 3D4(2) are a, b where a is in class 2A,
//b has order 9, ab has order 13 and abb has order 8.
//Alternatively: a is in class 2A, b has order 9 and ab has order 13.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
             _LR`AI:=[[a,b^-2*a*b^3*a*b^-2*a]]
                     where a is (_LR`F).1 where b is (_LR`F).2;

_LR`G := sub< GL(26,Integers()) |
\[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,
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,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
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,
1,1,0,0,0,-1,0,-1,-1,-1,1,-1,-1,-1,0,0,1,-1,-1,0,0,0,0,0,0,0,
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,
-1,-1,-1,0,-1,1,0,0,0,1,0,0,0,0,1,1,0,0,0,-1,0,0,1,1,0,0,
1,1,0,0,0,-1,0,0,-2,-1,1,-1,0,-2,0,0,1,0,-1,0,-1,0,0,0,0,0,
0,0,1,0,1,-1,0,-1,0,-1,-1,0,-1,0,-2,-1,-1,0,0,0,0,-1,-2,-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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,-1,0,
-1,-1,0,0,0,1,0,0,2,1,-1,1,0,2,0,-1,-1,0,1,0,0,0,0,-1,0,-1],

\[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,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
-1,-1,0,0,-1,1,0,0,1,1,-1,0,0,1,0,0,0,0,1,-1,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
0,1,0,0,1,-1,0,-1,0,-1,1,0,-1,1,0,0,-1,-1,0,1,1,0,-1,-1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
0,0,0,0,-1,0,0,-1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,-1,1,-1,
0,0,-1,-1,-1,0,-1,0,-1,0,0,0,0,-1,0,1,0,0,-1,0,0,0,0,0,1,0,
-1,0,0,0,0,0,-1,-1,1,0,0,1,-1,2,-1,0,-2,-1,0,0,2,-1,-1,-1,0,0,
1,0,0,0,1,0,0,1,0,0,0,0,1,0,0,-1,0,0,0,1,-1,0,-1,0,-1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,-1,0,0,0,0,0,0,0,
-1,-2,-1,0,-2,2,-1,1,1,2,-1,1,1,1,1,1,0,1,1,-1,0,1,2,1,0,-1,
-1,-1,0,0,-2,2,0,1,2,2,-1,1,1,1,1,1,0,1,1,-1,0,1,2,0,0,-1,
0,-1,0,0,0,1,1,1,1,2,0,0,1,1,1,0,0,0,1,0,0,1,1,0,-1,0] >;

return _LR;
