Many thanks for the quick reply, Martin.
Will the following work if I want a provably correct result
(when mylimit is a proven upper bound on the size of G)?
H:=ShallowCopy(G); StabChain(H,rec(random:=800; # or whatever limit:=mylimit); if Size(H) = mylimit then G := H; else StabChain(G); fi;
Does StabChain ever change an existing component of the group record;
that is, should I make a Copy instead of a ShallowCopy in the first