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)".

**Authors:**

**Knowl status:**

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

**Referred to by:**

- curve.highergenus.aut.conjugacyclasses
- dq.curve.highergenus.aut.label
- lmfdb/artin_representations/main.py (line 492)
- lmfdb/galois_groups/main.py (line 379)
- lmfdb/galois_groups/templates/gg-show-group.html (line 87)
- lmfdb/higher_genus_w_automorphisms/main.py (line 1258)
- lmfdb/higher_genus_w_automorphisms/templates/hgcwa-search.html (line 16)
- lmfdb/higher_genus_w_automorphisms/templates/hgcwa-show-family.html (lines 27-29)
- lmfdb/higher_genus_w_automorphisms/templates/hgcwa-show-passport.html (lines 13-15)
- lmfdb/higher_genus_w_automorphisms/templates/hgcwa-stats-groups-per-genus.html (line 10)
- lmfdb/local_fields/main.py (line 463)
- lmfdb/number_fields/number_field.py (line 1010)

**History:**(expand/hide all)

- 2019-05-05 17:03:59 by John Jones (Reviewed)
- 2018-07-02 01:26:51 by Andrew Sutherland (Reviewed)

**Differences**(show/hide)