Dear all,
I want to check whether two character tables are "equal" (in the sense
that their irreducible characters coincide and also the corresponding
power maps match, of course, everything up to permutation). According
to Thomas Breuer's answer from 2000
(http://www.gap-system.org/ForumArchive/Breuer.1/Thomas.1/Re__Comp.8/1.html)
there is no built in function to compare character tables in GAP, but
one has to do the checks manually. Is this still the case? What would
be the best way to do it? In particular, I want to recognize, for
example, the two character tables CharacterTable("A4") and
CharacterTable(AlternatingGroup(4)) as "equal". As I want to use this
in a function, I want to automatize it as far as possible.
In case only the "heads" of the character tables are known and I want
to avoid to calculate the irreducibles (as the groups might be very
large and the calculations needed can be done with induced characters),
there is probably no hope to see if two character tables are tables of
the same group, except if the attribute "UnderlyingGroup" is stored for
both tables?
Any help is greatly appreciated.
Best regards,
Andreas Bächle
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