[GAP Forum] CharacterTable("SU3")

[Thomas Breuer]

Dear GAP Forum,

Stepan Orevkov had asked

> [...]
> 3). The following classtext for SU(3,q) looks strange:
>
> gap> LoadPackage("ctbllib");;
> gap> t:=CharacterTable("SU3");;
> gap> m:=t.classtext[8](3,3);;
> gap> m in GL(3,3^2);
> false
> gap> m in GL(3,3^6);
> true

The point is that the `classtext' values do not really give you
class representatives in the group in question,
so this is not a bug in the data but an inaccuracy in the documentation.
I will adjust the documentation for the next version of the character
table library.

What one gets in each case is an element that is conjugate
to a class representative but perhaps in a larger group.

As a simpler example, consider the generic character table of GL(2,q).
This group contains elements of order q^2-1 that are easiest
described as diagonalizable matrices with suitable eigenvalues in the
field with q^2 elements,
and the `classtext' values for these elements are in fact such
diagonal matrices.
However, the diagonal matrices are of course not contained in GL(2,q).
I hope this clarifies the situation.

All the best,
Thomas