Alexander Moreto wrote:
Computing the character table of a large group may, of course, take a very
long time. But if I'm just interested in a few characters (like, for
instance, the irreducible characters of degree n for some fixed n or the
faithful irreducible characters), if there some faster way to compute
them than computing the whole character table?
There are methods that compute new characters from old, but often it is not
guaranteed that thay will obtain all characters. What you can try is to run
the Dixon-Schneider Algorithm for a few sets (see section `Advanced Methods
for the Dixon-Schneider algorithm' of the reference manual:
and then try toi obtain the remaining characters by working with them as
class functions (see chapter ``Class functions'' in the manual), however it
is perceivable that this process will not find all characters you are
interested in, but only a subset. In particular it is hard to guarantee that
one has found all characters of a given degree, or all faithful characters,
unless the whole table has been determined.