Franz Gaehler wrote in his email message of 1996/03/22
the GAP manual states that a Subgroup Conjugacy Class Record may
contain an optional field "conjugands". I have never ever been able
to make this field being bound, however. When computing the maximal
subgroups or minimal supergroups of a subgroup lattice, these
conjugands have to be computed, but apparently that information is
discarded afterwards. Which means that I have to recompute the
conjugands. After all, a minimal subgroup given in the form [n,m]
is of little value, if one does not know which conjugate of the
representative of class n carries number m! To find out you have
to recompute the conjugands...
We don't store the conjugands in the lattice or the subgroup conjugacy
class record, because it would require much too much storage (it would
make some of the lattice computations we did impossible with any
reasonable amount of memory).
Unfortunately it is impossible to recompute the conjugands afterwards.
This is because during the lattice computation the conjugands are
computed as the right transversal of the normalizer of the
representative. But 'RightTransversal' is not guaranteed to return the
same transversal if you call it after the lattice computation.
However, it is simple to modify 'MaximalSubgroups' and
'MinimalSupergroups' so that they not only give a subgroup in the form
'[<n>,<m>]' (which means <n>-th conjugacy class, <m>-th subgroup of that
class), but '[<n>,<m>,<c>]' where <c> is a conjugating element.
If you are interested, write me and I will send you the code.
-- .- .-. - .. -. .-.. --- ...- . ... .- -. -. .. -.- .- Martin Sch"onert, Martin.Schoenert@Math.RWTH-Aachen.DE, +49 241 804551 Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany