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Is there some easy way to identify from the character table record

which columns are inverses of which other columns? I'd like to be able

to do this to, say, compute class multiplication constants

automatically (by a pre-defined function) from the table. Everything

else needed seems to be readily available in the record.

One could figure this out from the power maps in the record, but that

might be messy to do in a function.

Alternatively, one could just use the complex conjugate of a column,

but I don't even see how to do that in a function. Presumably this is

somewhere in the automorphisms of the table, but how would I tell which

automorphism is complex conjugation? Or identify that the table is

real, so that complex conjugation does nothing, and is therefore not

among the listed automorphisms.

Is it efficient just to use column orthogonality? The one column not

orthogonal to a given one is its inverse.

Probably I'm just missing something obvious here.

David Sibley

sibley@math.psu.edu

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