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Dear Mrs. and Mr. Forum,

Thierry Dana-Picard asks the following question.

Let <t> be the character table of a group <g>, given by GAP. Is there a

way to get the elements of the various conjugacy classes of <g> and the

correspondence between these classes and the columns of <t>?

If <t> has been computed from <g> using 'CharTable' then the conjugacy

classes of <g> are stored in the component '<g>.conjugacyClasses', and

their ordering is the same as that of the columns in <t>.

If <t> is a library table then there is no particular representation of

the underlying group <g> attached to <t>, so it is not clear what it means

to ``get the elements'' of a conjugacy class corresponding to a particular

column of <t>. So the problem might be to identify the columns of a

library table <t> with the conjugacy classes of a group <g> for which <t>

is the character table. Probably many of the classes of <g> will be easily

identified by their element and centralizer orders, and maybe other

invariants. If this is not sufficient, one can compute the character

table of <g>, and then find permutations of columns and rows that transform

this table into <t> (e.g. using 'TransformingPermutationsCharTables').

In some cases there is a generic description of conjugacy classes, e.g.,

the classes of symmetric groups are parametrized by partitions, and the

classes of general linear groups are parametrized by normal forms of

matrices. This may make it easier to identify the columns and the classes.

Kind regards

Thomas Breuer

(sam@ernie.math.rwth-aachen.de)

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