Databases of Groups [HB 24]

Changes:

• The database of primitive groups has been extended to degree 999 by Colva Roney-Dougal and Bill Unger. We believe the list to be complete. Numbering from Sims' list of degree up to 50 is changed. There are also added access functions, but the basic functions PrimitiveGroup(d,n) and NumberOfPrimitiveGroups(d) will work as before. A new function, which has been added, is PrimitiveGroupIdentification.
• The almost simple groups database now includes HS and L(6, 2). Derek Holt and Colva Roney-Dougal have also supplied routines so that the maximal subgroups and automorphism groups of the groups Alt(d ) (d < 1000), L(2, p), L(2, p²), L(2, p³), L(3, p), L(3, 8), L(3, 9), S(4, p), and U(3, p) (p a prime) may be found as if they were in the database.

Bug Fixes:

• A bug in the identification of groups in the small groups database has been fixed.