Dear Forum members,
The recent discussion of the question about subgroups of the symmetric
group S4 that are isomorphic to the direct product of two cyclic groups of
oder 2 prompts me to remind that for a detailed understanding of the
subgroup structure of smaller groups GAP provides the package XGAP which
allows a graphical depiction of the subgroup lattice or parts thereof
and the switching from the graphical description to further group
theoretical investigation of the subgroups displayed. The XGAP manual
gives several examples of the use of XGAP even in cases where the
complete subgroup lattice is far too big to be displayed.
In the case of S4 you can nicely see what John McKay pointed out and in
fact can get a good understanding of how this all works.
Have fun with XGAP! Joachim Neubüser
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