[GAP Forum] groups of order p^3*q^3

[Alexander Konovalov]

Dear Walter,

> On 25 Jul 2016, at 14:45, Walter Becker <w_becker at hotmail.com> wrote:
> 
> The question is how many groups are there for these
> 
> orders.  Note here that the Group Constructions program
> 
> of  Besche and Eick give for the case of p=3 and q=7 the
> 
> number 215 (and actually constructs them). The Thesis of
> 
> of R. Laue (see page 226) seems to give 229 (plus the
> 
> 25 direct product cases of the groups of order 27 and 343 ?).
> 
> 
> The compiled list of groups available on the internet does
> 
> not contain an entry for the groups of order 9261.

The Group Numbers reproducibility project 
(https://github.com/alex-konovalov/gnu)
actually has an entry for gnu(9261): see

https://github.com/alex-konovalov/gnu/pull/43

and it is 215. Same number obtained by using the
latest GrpConst package both in GAP 4.8.3 and master
branch of the development version of GAP at the
time of submission.

I don't have Laue's thesis so I can not comment more
on the reasons for the discrepancies, but hopefully
some one else could add more.

Best wishes
Alexander