_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [ a^-1, b*a^-1*(a,b)^2 ] ]
                     where a is (_LR`F).1 where b is (_LR`F).2;
//Standard generators of A20 are a and b where a is in class 3A, b has order 19,
//ab has order 18 and [a,b] has order 2.

//Irreducible, fixed by _LR`AI[1].
_LR`G := sub< GL(19,Integers()) |
[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,-1,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,-1,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-1,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,-1,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1],

[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]>;

return _LR;
