[GAP Forum] How to identify a group

[Mikhail Klin]

Dear Michael,
GAP may identify your group 
or as a group of order 432,
or as a transitive group of degree 9,
however it does not have requested catalogues
of symmetries of geometrical 
or combinatorial structures.

In fact, your group is the automorphism group 
of the affine plane of order 3.
Moreover, this plane has is in a sense 
most famous labelling.

Best regards,
Mikhail

********************************************************************

Dr. Mikhail Klin
Department of Mathematics 
Ben-Gurion University of the Negev
P.O.Box 653, Beer Sheva 84105, Israel
Tel: (0)8/6477-802  (office)
     (0)8/641-37-15 (home)
Fax: +972-(0)8/6477-648
e-mail: klin at cs.bgu.ac.il

On Thu, 26 Jan 2006, Michael Schweitzer wrote:

> Dear forum members,
> 
> given a group G of order n (given by generators). Is GAP
> able to identify the group by name or as the
> group of symmetries of some geometric object?
> 
> For example: I define G suchthat G is isomorphic to A5. Can I ask GAP: 
> which group is G? And GAP answers: A5- which is,for example,
> the symmetry group of the icosahedron.
> 
> That is, does GAP contain a database of finite groups of
> small orders ( < several hundrets, say) which includes
> information about the transformation group aspect: this
> group, among other things, is the symmetry group of X or
> operates in a natural manner on X (I know that GAP
> does contain a database of small groups - but is this kind
> of information stored there?).
> 
> The group in question is of order 432 with generators
> 
> g1 := (4,6,5)(7,8,9) andg2 := (1,7,2,4,6,9,5,3)
> 
> 
> Regards,
> Michael Schweitzer
> 
> 
> Michael Schweitzer
> Alt-Heiligensee 51 A
> 13503 Berlin
> email: ms-swissoft at arcor.de
> 
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