General Groups [HB 17]

Changes:

• The function FPGroup(G:StrongGenerators:=true) is replaced by FPGroupStrong(G). The former will be withdrawn in a future release, so change your code now!
• The function ExtraSpecialGroup has been extended to return both isomorphism types of extra-special group of order pⁿ.
• The process that produces pseudo-random elements of a group from its generators has been modified to use product replacement with an accumulator. This means two multiplications are required for each step, but results in elements that more closely approximate elements chosen uniformly at random.
• The IsConjugate function has been extended to sequences of group elements (thus giving another test for inner automorphisms).

New Features:

• The database of perfect groups compiled by Holt and Plesken has been converted into a new style database.
• A database containing almost simple groups with socle order up to 16 million is available. This database contains automorphism group and maximal subgroup information.