[GAP Forum] Normalizing of Irr(G)

[Thomas Breuer]

Dear Forum,

Fatemeh Koorepazan-Moftakhar asked

> Suppose G is a group. Then we know Irr(G) is the set of all irreducible
> characters of G. In some example the principal character is not the first
> element of this list. Is there any command in GAP to normalize Irr(G)? By
> normalizing of Irr(G), I mean a reordering of Irr(G) in which the first
> element is principal character.

Called with a character table 't', say, of a finite group,
the function 'CharacterTableWithSortedCharacters'
returns a character table 's' which differs from 't'
only by the ordering of the irreducible characters.
The trivial character is guaranteed to be the first one
in the 'Irr' list of 's'.

If one starts from a group object 'G' then
'Irr( CharacterTableWithSortedCharacters( CharacterTable( G ) ) )'
is a list of the irreducible characters of 'G' with the property that
the trivial character is stored in the first position.

Note that the ordering of 'Irr( G )' is not affected by the
above commands.

See the entry about 'CharacterTableWithSortedCharacters'
in the GAP Reference Manual for more details.

All the best,
Thomas