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Scott Murray asked

Is their a command to tell if two character tables

are the same, without computing the entire group

of transforming permutations (section 65.18 of the

manual)?

It depends on what ``the same'' means.

If one is interested in equality of the lists of irreducible

characters (and power maps) then it is sufficient to

compare these bits of information for the two tables.

If one is interested in equality up to permutations of

rows and columns then the only GAP command for comparing

character tables is `TransformingPermutationsCharacterTables'.

If transforming permutations exist then they are encoded

via one transformation of columns and rows plus the

group of table automorphisms of the second argument;

this automorphism group is computed as a byproduct of the

current implementation, it does not cause extra work.

In particular, there is no non-constructive algorithm in GAP

for deciding the equality of character tables up to permutations

of columns and rows.

Kind regards,

Thomas

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