Dear Thomas,
Thank you for your explanation of my perceived problem with the
TableAutomorphism function. I should have slept on it before seeking
help, as I did eventually figure out my difficulty. My mind quite
stubbornly insisted in viewing the situation incorrectly. Anyway I
did see the problem by making use of one of my favorite features
of GAP, namely access to the libraries. It was a simple matter to

i). Make a temporary copy of the library file containing the
TableAutomorphisms function.

ii). Locate the code which checks that a proposed permutation
respects the powermaps.

iii). Insert a statement to print out the proposed permutations
just before and after checking them.

Being able to examine the calculations in this way allowed me to
see my error immediatly.

One can also use access to the library files to customize some
functions. For example, one may want to insert statements printing
out data which will help determine whether a calculation is going to
take 2 minutes or 2 years!

Anyway thanks again for you response.
Thanks also to all the GAP folks for their wonderful work.

Peter Blanchard