type:="A4";
W:=CoxeterGroup(type);
G,phi:=ReflectionGroup(W);
R:=CharacterRing(G);
G:=ReflectionGroup(CoxeterGroup("A4"));
R:=CharacterRing(G);
characterTable:=[
R![1,1,1,1,1,1,1],
R![1,-1,1,1,-1,1,-1],
R![4,2,0,1,0,-1,-1],
R![4,-2,0,1,0,-1,1],
R![5,1,1,-1,-1,0,1],
R![5,-1,1,-1,1,0,-1],
R![6,0,-2,0,0,1,0]];
A:=MatrixAlgebra(RationalField(), 4 );
conjugacyClasses:=
[<1,1,A![1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1]>,
<2,10,A![1,1,0,0,0,-1,0,0,0,1,1,0,0,0,0,1]>,
<2,15,A![0,0,-1,0,0,-1,0,0,-1,0,0,0,1,1,1,1]>,
<3,20,A![0,1,0,0,-1,-1,0,0,1,1,1,0,0,0,0,1]>,
<4,30,A![0,1,1,0,-1,-1,-1,0,1,1,0,0,0,0,1,1]>,
<5,24,A![0,1,1,1,-1,-1,-1,-1,1,1,0,0,0,0,1,0]>,
<6,20,A![0,0,1,1,-1,-1,-1,-1,1,0,0,0,0,1,1,0]>];

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