_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
//Standard generators of U5(2) are a and b where a is in class 2A, b has order 5
//and ab has order 11.

_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 := sub<GL(22,Integers()) |
\[ 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,-1,0,-1,0,0,0,0,0,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,-1,0,-1,0,0,0,0,0,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,-1,-1,-1,-1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
1,0,1,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,
-1,0,0,0,0,0,0,0,0,0,0,-1,0,-1,0,0,0,0,0,-1,-1,0,0,
-1,0,0,0,0,0,0,0,0,0,0,-1,0,-1,0,0,0,0,1,0,0,0,0,-1,
0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,
0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1,0,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1,0,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
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,-1,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,0,-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,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,0,1,
1,1,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,-1,0,-1,0,
0,0,0,0,0,0,-1,-1,0,0,0,0,0,0,1,1,0,1,-1,0,1,1,0,0,
1,0,0,0,0,0,-1,0,0,0,0,0,-1,0,-1,-1,0,-1,-1,0,0,0,0,
1,0,0,0,0,0,-1,0,0,0,0,-1,0,-1,0,0,0,0,0,-1,-1,1,0,0,
0,1,0,0,0,0,0,0,0,0,-1,0,-1,0,0,0,0,1,0,0,1,0,0,0,1,
0,0,1,1,0,1,0,0,0,0,1,0,0,0,0,0,-1,0,0,0,-1,0,0,-1,
-1,0,-1,-1,0,0,0,0,0,1,0,0,0,0,0,-1,0,0,0,-1,1,1,0,0,
0,0,1,1,0,1,0,0,1,1,0,0,0,-1,1,0,0,-1,0,0,0,0,0,0,
-1,0,-1,-1,0,0,-1,0,0,0,1,1,0,1,1,1,0,0 ]>;

return _LR;
