[GAP Forum] CharacterTable and Irr

[Alexander Hulpke]

Dear Forum,

Krishna Mohan asked:

> I wanted to know if the ordering of conjugacy classes as obtained by using the commands CharacterTable and Irr are the same.
> I generally find it to be so. The gap manual is not very clear about this although the impression I got was that it is indeed the same.

It does not need to be (but often is, in particular if the table is computed from scratch for a given group the classes are just taken as given by the group). If the table was taken from a library of existing tables, for example by connecting a given table with a given group, however, it is possible that the arrangement will differ.

Because of this, the attribute
IdentificationOfClasses
for a character table holds the corresponding class numbers of the underlying group. See the manual chapter

The Interface between Character Tables and Groups
http://www.gap-system.org/Manuals/doc/htm/ref/CHAP069.htm#SECT006

for more details.

Best,

Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke