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This is a page on GAP 3, which is still available, but no longer supported. The present version is GAP 4  (See  Status of GAP 3).

GAP 3 Data Library "Small Groups"


All groups of size up to 1000 (except 512 and 768).


Eamonn O'Brien, Bettina Eick, and Hans Ulrich Besche.

GAP 3 Manual section

A manual of the Small Groups Library is given as section 37.14 of the GAP 3 manual.

Corresponding GAP 4 data library

GAP 4 Package The SmallGroups Library

In GAP 4 the library has been extended. In release 3 of GAP 4 it contains the following groups:

  • those of order at most 2000 except 1024 (423 164 062 groups);
  • those of order 5^5 and 7^4 (92 groups);
  • those of order q^n * p where q^n divides 2^8, 3^6, 5^5 or 7^4 and p is an arbitrary prime different to q;
  • those whose order factorises into at most 3 primes.

Contact addresses

Eamonn O'Brien
Department of Mathematics
University of Auckland
Auckland, Private Bag 92019
New Zealand

Bettina Eick
Institut Computational Mathematics
TU Braunschweig
Pockelsstr. 14
D-38106 Braunschweig

Hans Ulrich Besche
Institut Computational Mathematics
Universitšt Braunschweig
Pockelsstr. 14
38106 Braunschweig