_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [ a^-1, b ] ]
                     where a is (_LR`F).1 where b is (_LR`F).2;
//Standard generators of A19 are a and b where a is in class 3A, b has order 19,
//ab has order 21.
//Irreducible, fixed by _LR`AI[1].

_LR`G := sub< GL(22,Integers()) |

return _LR;
