//Standard generators of Co3 are a, b where a is in class 3A,
//b is in class 4A and ab has order 14.

_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ ];
//irreducible
_LR`G := sub<GL(23,Integers()) |
\[0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,1,-1,1,-1,0,0,1,
1,0,0,0,0,0,0,-1,0,-1,1,0,0,0,0,0,0,0,-1,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
1,-1,1,-1,-1,0,-1,0,-1,1,1,-1,0,1,0,-1,0,0,0,0,-1,1,1,
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,-1,1,-1,1,0,0,0,0,0,-1,1,-1,1,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,-1,0,1,0,0,0,0,0,-1,0,0,-1,0,0,1,0,0,-1,0,-1,0,
1,-1,1,0,-1,1,0,0,-1,0,0,0,1,0,-1,-1,0,0,1,0,0,1,0,
0,-1,1,0,-1,0,0,0,0,0,0,0,1,1,0,0,-1,1,0,1,0,1,0,
1,-1,1,0,-1,1,-1,0,0,1,0,0,0,0,0,0,1,0,1,0,0,1,1,
1,-1,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,1,-1,0,0,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,1,0,1,1,0,1,0,0,-1,0,0,0,1,1,1,-1,0,-1,0,1,0,0,
0,0,0,0,0,-1,0,0,0,0,1,-1,0,1,1,0,-1,0,-1,1,-1,0,0,
-1,0,0,0,0,-1,0,1,0,0,0,-1,0,0,0,0,0,-1,0,0,-1,-1,0,
-1,1,0,1,0,0,1,0,0,-1,0,0,0,0,0,0,-1,-1,0,0,1,0,-1,
-1,1,0,0,0,0,1,0,-1,-1,-1,1,1,0,-1,0,-1,0,1,0,1,0,-1,
0,1,-1,0,1,0,0,0,1,0,0,0,-1,0,1,1,1,0,-1,-1,0,-1,0,
0,0,0,0,0,0,0,-1,0,0,0,0,0,-1,-1,-1,0,0,0,0,0,0,-1],
\[-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,-1,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,-1,0,-1,0,-1,0,0,0,0,-1,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
1,-1,1,0,0,0,0,0,0,-1,1,0,1,1,0,0,-1,1,-1,1,0,1,1,
1,0,1,-1,0,0,0,0,-1,-1,0,0,1,0,-1,-1,-1,0,0,0,0,0,0,
0,0,0,1,1,0,0,0,1,0,0,-1,-1,0,1,0,0,0,-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,
-1,0,-1,1,0,1,0,0,1,1,-1,0,-1,-1,1,0,1,-1,0,0,0,0,-1,
0,1,-1,0,0,0,0,-1,0,0,0,0,-1,0,0,0,0,0,0,-1,0,0,0,
0,0,0,-1,0,-1,0,1,-1,0,0,0,1,1,0,0,-1,1,0,0,0,0,1,
-1,0,0,1,-1,1,0,0,0,1,-1,0,0,0,0,0,0,-1,1,0,0,0,-1,
0,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,1,-1,0,0,0,
0,1,-1,-1,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,
0,-1,0,0,-1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,
1,-1,1,0,-1,1,0,-1,0,-1,0,1,1,0,-1,0,-1,1,0,1,1,1,0,
-1,1,0,0,0,-1,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,-1,0,
1,-1,0,0,0,0,0,-1,1,0,1,0,0,0,0,0,0,1,-1,1,0,1,0]>;

return _LR;
