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The computer algebra systems GAP and Magma both include a database of small groups that includes all groups of order up to 2000, except for groups of order 1024. Groups in this database are identified by an ordered pair $[n,d]$ where $n$ is the order of the group and $d$ is a positive integer that distinguishes the group from others of the same order (the value of $d$ is the same in both GAP and Magma).

In both systems, the command "SmallGroup($n$,$d$)" will return an explicit representation of the group in terms of generators and relations.

Magma also associates a descriptive name to each small group. For example, the command "GroupName(SmallGroup(24,3))" returns the string "SL(2,3)".

Knowl status:
  • Review status: reviewed
  • Last edited by John Jones on 2019-05-05 17:03:59
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