Permutation Groups [HB 17]

New Features:

• 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.

• A new FPGroupStrong algorithm has been implemented, a combination of STCS, BCS verification and results of Volker Gebhardt.
• The range of groups that MaximalSubgroups and AutomorphismGroup may be applied to is increased. 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 prime) may be found as if they were in the database. Functions MaximalSubgroups and AutomorphismGroup may be applied to any permutation group with all non-abelian composition factors in the database or listed above.
• A function DoubleCosetRepresentatives, computing a set of representatives of the double cosets of subgroups H and K of a permutation group G has been provided.

Bug fixes:

• A bug in computing an EARNS for a primitive group has been fixed.
• Several memory leaks, particularly associated with computing socle quotients and socle factors, have been stopped.
• Fixed user reported bug in ReduceGenerators.