The SmallGrp GAP package

The Small Groups Library is a catalogue of groups of “small” order. The groups are sorted by their orders and they are listed up to isomorphism; that is, for each of the available orders a complete and irredundant list of isomorphism type representatives of groups is given. Currently, the library contains the groups

• of order at most 2000 except 1024,
• of cubefree order at most 50 000,
• of order p^7 for the primes p = 3, 5, 7, 11,
• of order p^n for n <= 6 and all primes p,
• of order q^n * p for q^n dividing 2^8, 3^6, 5^5 or 7^4, and p a prime different from q,
• of squarefree order,
• whose order factorises into at most 3 primes.

The package provides access to the groups of these orders, and a method to identify the catalogue number of a given group for many of these orders.

Documentation

Full information and documentation can be found in the manual, available as PDF doc/manual.pdf or as HTML doc/chap0_mj.html, or on the package homepage at

https://gap-packages.github.io/smallgrp/

Besides describing the available functions, the manual also documents how the library is organised: how the groups were determined, how they are stored, and which algorithms the identification routines use.

Related packages

Groups of further orders are provided by other GAP packages:

• SglPPow provides the groups of order p^7 for primes p > 11 and those of order 3^8. It extends this library: once loaded, its groups are available via SmallGroup and friends.
• SOTGrps constructs and identifies the groups whose order factorises into at most 4 primes, and those of order p^4 * q. It uses its own functions and its own numbering, which in general differs from the one used here.

Bug reports and feature requests

Please submit bug reports and feature requests via our GitHub issue tracker:

https://github.com/gap-packages/smallgrp/issues

Authors

The Small Groups Library has been constructed by Hans Ulrich Besche, Bettina Eick and Eamonn O’Brien. It is maintained by Max Horn.

License

The Small Groups Library is free software distributed under the Artistic License 2.0.

For details see the files LICENSE and COPYRIGHT.md.