[GAP Forum] Group Actions In GAP

[Bill Allombert]

On Fri, Dec 13, 2013 at 11:31:30AM +0000, Michele Nardella wrote:
> Dear Subscribers to the GAP Forum,
> 
> I am an undergraduate student and taking my first class in Group Theory.
> I would like to obtain
> a) the permutation cycles of the faces of a truncated octahedron induced by
> the action of its rotation group (S_4); and
> b) the orbits of its faces;
> 
> To generate S_4 in GAP is the easiest part.
> By I do not know, how to specify the domain, \Omega, and \mu which is
> defined to be "a  function compatible with the group arithmetic." (
> http://www.gap-system.org/Manuals/doc/ref/chap41.html).

I really suggest you do the computation by hand, and then to do it using
GAP when you have a clear picture of the concept involved.
S_4 is a small group, so the computation is easy.

Cheers,
Bill.