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.

Tim Hsu