From: Bettina Eick 
Subject: Re: kinship
Date: Thu, 31 Oct 1996 09:49:17 +0100 (MET)
 
In the current distribution of the computer algebra system GAP you can 
find a list of groups of order at most 100 (up to isomorphism). I used 
GAP and this list to count the groups of order at most 100 with two 
generators of which at least one is of order 2. There are 243 of them 
(including abelian groups). 
I would be happy to give you the numbers of these groups in the
GAP catalogue of groups of order at most 100. The groups in the 
catalogue are either given by power-commutator presentations (in
the soluble case) and by permatutations otherwise. I could also 
supply the GAP program to compute this list of groups which you might 
like to use to filter out the groups having further constraints. 
                               
Furthermore we just computed a list of all groups of order at most 1000 
without the groups of order 512 and 768. This list is not yet included
in the standard distribution of GAP, but I would be happy to give it
to you if it would be of any help. 
 
All of this implies that you would have to use GAP. However, it seems
to me that this would be the most suitable way to pass these groups to
you and maybe GAP would be of further help for your investigations.
I will send a mail directly to you with information on how to get
GAP (it is free of charge) and how to use it for your purposes.
 
Best wishes,
 
Bettina Eick