Dear gap-forum

On Fri, Mar 30, 2001 at 12:53:02PM -0500, Igor Schein wrote:
> On Wed, Mar 28, 2001 at 11:10:33AM +0200, Stefan Kohl wrote:
> > Dear gap-forum,
> >
> > Igor Schein wrote:
> >
> > > I'm far from being sophisticated in group theory and GAP, so please
> > > bear with me. In GAP 4.x I can access database of groups by using
> > > function SmallGroup, e.g. SmallGroup(32,1). What I need is to
> > > find out the number of quadratic residues for, say, the group above.
> > > Is it possible for arbitrary SmallGroup(n,k) as long as the group is
> > > in the database? Going further, I would like to construct a
> > > multiplication table for SmallGroup(32,k). Is it possible in GAP?
> >
> > You can get the number of quadratic residues in the group G
> > by using the function
> >
> > NumQuadRes := G -> Length(Set(List(AsList(G),g->g^2)));
> >
> > You can get a multiplication table of the group G by
> >
> > MultiplicationTable(AsList(G));

Thanks a lot, Stefan, this was very useful.

I have a somewhat related question. There're 51 groups of order 32, and
some of them are very hard to distinguish. For example,
SmallGroup(32,27) and SmallGroup(32,34). Are there standard methods (
preferable ones that can be done in GAP ) to determine whether or not 2
groups like above are isomorphic?

Thanks

Igor