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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)".
- Review status: reviewed
- Last edited by John Jones on 2019-05-05 17:03:59
Referred to by:History: (expand/hide all)
- lmfdb/artin_representations/main.py (line 543)
- lmfdb/galois_groups/main.py (line 481)
- lmfdb/galois_groups/templates/gg-show-group.html (line 100)
- lmfdb/higher_genus_w_automorphisms/main.py (line 601)
- lmfdb/higher_genus_w_automorphisms/main.py (line 1261)
- 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 11)
- lmfdb/higher_genus_w_automorphisms/templates/hgcwa-stats-groups-per-genus.html (line 44)
- lmfdb/sato_tate_groups/main.py (line 1130)
- 2019-05-05 17:03:59 by John Jones (Reviewed)
- 2018-07-02 01:26:51 by Andrew Sutherland (Reviewed)
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