[GAP Forum] Comparing character tables in GAP

[Andreas Bächle]

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