Tim Hsu asked in the forum:

I've been trying to set up a calculation using AugmentedCosetTableRrs.
Now, when you have the statement

aug := AugmentedCosetTableRrs(G,ct,2,"_q");

(ct is the coset table for a subgroup S in G),
aug.primaryGeneratorWords contains descriptions of the primary
generators of S in terms of words in the generators of G. According
to the GAP manual, aug.tree, (in some form) contains a description of
the secondary generators of S in terms of the primary relators, so in
theory, you should be able to obtain the secondary generators of S in
terms of words in G. Could someone tell me how to get this from the
tree?

My next question is, do RewriteSubgroupRelators,
PresentationAugmentedCosetTable, TzGo, or FpGroupPresentation change
the ordering of the generators in any way, other than eliminating
generators? Thanks very much.

I just want to acknowledge that the message has been read. The person
who has implemented these routines, and therefore probably can best
answer these questions, is Volkmar Felsch, who at present is on
holidays. We will come back to the question whatever the exact answer
will be, please excuse the delay. Joachim Neubueser