type:="A1"; W:=CoxeterGroup(type); G,phi:=ReflectionGroup(W); R:=CharacterRing(G); G:=ReflectionGroup(CoxeterGroup("A1")); numberClassesDetectIrreducibles:=2; R:=CharacterRing(G); characterTable:=[ R![1,1], R![1,-1]]; A:=MatrixAlgebra(RationalField(), 1 ); conjugacyClasses:= [<1,1,A![1]>, <2,1,A![-1]>]; d:=rec;