I would point out that StructureDescription might not always return a group the way you'd like it. The manual explains a little more about how it picks a particular form for the structure.
That function also does not do anything with central products. Hence if I type: StructureDescription(SmallGroup(32,50)) I get: "(C2 x Q8) : C2" when it's also a central product of Q8 with D8. It returns some pretty awkward answers for other larger central products. It also will usually not let you know how the split or non-split extensions work, so you might get two non-isomorphic groups that return the same "StructureDescription". Also be forewarned that many times GAP will just compute the whole subgroup lattice to find a structure, so any group that would take a long time with LatticeByCyclicExtension or ConjugacyClassesSubgroups is likely to take a long time for StructureDescription. This would include, for instance, 2-groups of rank more than 5, groups with large permutation representations or large matrix representations and also finitely-presented groups. It does have a separate routine for any simple group that spits out the answer due to the classification in almost no time, however, while it could easily tell me a group is isomorphic to, say U4(3), it would take much longer (and probably use up all of your RAM) to say a group is isomorphic to U4(3):D8. On Thu, Dec 11, 2008 at 6:37 AM, Heiko Dietrich <h.dietr...@tu-bs.de> wrote: > Dear Paweł, > > you can use the command "StructureDescription": > > gap> for i in AllSmallGroups(1625) do Display(StructureDescription(i)); od; > C1625 > C325 x C5 > C13 x ((C5 x C5) : C5) > C13 x (C25 : C5) > C65 x C5 x C5 > > The output is explained in the manual: > > http://www.gap-system.org/Manuals/doc/htm/ref/CHAP037.htm#SECT006 > > Best, > Heiko > > > > On Tuesday 09 December 2008 20:56, Paweł Laskoś-Grabowski wrote: > > Hello, > > > > I have noticed that GAP Small Groups library provides useful information > > on the structure of groups belonging to the layer 1 of the library, but > > does not do so for (some) bit more complicated groups. I am rather > > dissatisfied by the output > > > > gap> SmallGroupsInformation(1625); > > > > There are 5 groups of order 1625. > > They are sorted by normal Sylow subgroups. > > 1 - 5 are the nilpotent groups. > > > > How can I obtain such a pleasant info like the following? > > > > gap> SmallGroupsInformation(125); > > > > There are 5 groups of order 125. > > 1 is of type c125. > > 2 is of type 5x25. > > 3 is of type 5^2:5. > > 4 is of type 25:5. > > 5 is of type 5^3. > > > > And, by the way, what does the colon stand for in the 125,3 and 125,4 > > type descriptions? I failed to find the explanation in the help pages. > > > > Regards, > > Paweł Laskoś-Grabowski > > > > _______________________________________________ > > Forum mailing list > > Forum@mail.gap-system.org > > http://mail.gap-system.org/mailman/listinfo/forum > > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum >
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