[GAP Forum] suggestion re S4 etc

[Joachim Neubüser]

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