Dear GAP-Forum,

Graham Sharp from Oxford reminded us of a problem in the unpatched 3.4.3 (the
old version) of the primitive groups library. This had been fixed in Patch
#10, but as we did not explicitely note this in the upgrade information, I
enclose my response to him as a remainder.

gap> list := AllPrimitiveGroups(DegreeOperation,27,Transitivity, [2..27]);
[ AGL(1,27), AYL(1,27), ASL(3,3), AZL(3,3), A(27), S(27) ]
gap> List(list, Size);
[ 702, 2106, 151632, 303264, 5444434725209176080384000000, 
  10888869450418352160768000000 ]

I would have thought that ASL(3,3) aqnd AZL(3,3) (which I understand is
code for A\Sigma{}L(3,3), ie ASL(3,3) with field automorphisms adjoined)
are the same, but that AGL(3,3) is distinct from both, and indeed has the
size indicated for AZL(3,3), and so should be in the list returned by the
above code

Is this an error or am I confused?

You are right. This is an Error. The names of primitive groups have been
fixed for the last release, using the names by Buekenhout & Leemans,
JSymbComp. They give the following names for these groups

[ AGL(1,27), AYL(1,27), ASL(3,3), AGL(3,3), A(27), S(27) ]

which agrees with your observation.

> (possibly it has been returned, but under the name AZL(3,3) ).
Indeed this has happened as the list of names had been corrupt.

As there were a couple of other problems with names of primitive groups,
I strongly suggest you persuade your system administrator to obtain the
latest version which incidentally has been released just this week. You can
find it under the URL:
http://www-groups.dcs.st-and.ac.uk/~gap/Info/distrib.html

Best regards and many thanks for the reminder,

Alexander Hulpke