type:="A2";
W:=CoxeterGroup(type);
G,phi:=ReflectionGroup(W);
R:=CharacterRing(G);
G:=ReflectionGroup(CoxeterGroup("A2"));
R:=CharacterRing(G);
characterTable:=[
R![1,1,1],
R![1,-1,1],
R![2,0,-1]];
A:=MatrixAlgebra(RationalField(), 2 );
conjugacyClasses:=
[<1,1,A![1,0,0,1]>,
<2,3,A![1,1,0,-1]>,
<3,2,A![0,1,-1,-1]>];

d:=rec<data|
        W:=W,
        G:=G,
        R:=GModule(G),
        T:=characterTable,
        C:=conjugacyClasses,
        phi:=phi,
        type:=type>;