List of Small Groups - Small Groups Library

Small Groups Library

The group theoretical computer algebra system GAP contains the "Small Groups library" which provides access to descriptions of small order groups. The groups are listed up to isomorphism. At present, the library contains the following groups:

• those of order at most 2000, except for order 1024 (423164062 groups in the library; the ones of order 1024 had to be skipped, as there are an additional 49487365422 nonisomorphic 2-groups of order 1024.);
• those of cubefree order at most 50000 (395 703 groups);
• those of squarefree order;
• those of order for n at most 6 and p prime;
• those of order for p = 3,5,7,11 (907 489 groups);
• those of order qn×p where qn divides 28, 36, 55 or 74 and p is an arbitrary prime which differs from q;
• those whose orders factorise into at most 3 primes.

It contains explicit descriptions of the available groups in computer readable format.