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Dear Mrs. and Mr. Forum,

Thomas Breuer already answered the question of Thierry Dana-Picard.

however, there are two minor comments, I'd like to add:

When the ``easy'' invariants (orders, centralizers, permutation

character etc.) are not sufficient, and one has to compute the character

table of <g>, it may be sufficient, to compute this table only

partially (especially, if the group is large, the computation of the

whole table is not feasible at all).

A lot of this identification process could be automized. The routine

would be given a group, a character table and (if possible) further

informations, as the type of the permutation character (when using

permutation representations of small degree, this character is sometimes

determined unique by the degree, even without knowing the values on the

conjugacy classes). The routine then would try to find a unique mapping

and compute further information (conjugacy classes, powermap, partial

character table) etc. itself until the correspondence is determined

completely (As the character table is known already, some of these

computations would be much more easy, then in the general case, as

sometimes the character table will give information, that can save

tedious computations, e.g. conjugacy tests).

Some time ago, I had considered writing a routine of this type, since I

needed something similar, but for the particular case, working ``by

hand'' had been faster. If there is sufficiently demand for that kind of

routine, I would reconsider my decision. (I can not promise anything

about availiability of a routine of this type yet.)

In case, you would be interested in such a routine please send me a

short eMail message (to the adress in the footer, not to the gap-forum

itself, as most readers won't be interested in particular answers).

Alexander Hulpke

(hulpke@bert.math.rwth-aachen.de)

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