🚀 go-pugleaf

J. McKinney asked for a reference to a list of all groups up to a given
limit. This question has several answers:

Listing *all* groups of a given order can be very tedious since there might
be lots of abelian groups of a given order, that can be obtained easily via
the canonical decomposition in elementary divisors. Thus most references
leave out abelian groups.

A standard reference (that should be aviable easily) is
   Coxeter, Moser: Generators and relations for discrete groups, 
   Ergebnisse der Mathematik und ihrer Grenzgebiete Bd. 14, Springer
that contains for example a list of all non abelian groups up to order 32.

If you would like to set the upper bound higher I strongly recommend
obtaining the group theoretical program GAP (aviable via anonymous ftp from

  samson.math.rwth-aachen.de
  dimacs.rutgers.edu
  math.ucla.edu
  pell.anu.edu.au

and various other servers), that contains (among others) all groups up to
order 100 and all 2-groups of order dividing 256.

Included are also character tables of a wide range of groups, including all
tables from the Cambridge ATLAS. The manual contains a more complete
bibliography of group lists.

The soon to be released (hopefully) version 3.2 will also include facilities
for computing the character table of a given finite group, which would allow
for a complete list of character tables of the groups up to order 100.

--
Alexander Hulpke,   Alexander.Hulpke@Math.RWTH-Aachen.DE,  +49 241 804551
Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, D 51 Aachen, Germany