[GAP Forum] What's the best way of finding the exact isomorphism type of a group?

[Will Chen]

Given a group G represented in GAP, the StructureDescription(G) tells you a
nice description of it, but of course it doesn't give you all the
information when G is a semidirect product or a nonsplit extension.

In these cases, if it's for example a semidirect product, is there a
built-in method of extracting the action of the quotient on the kernel?

For example, SmallGroup(96,202) has description "(C2 x SL(2,3)) : C2"

Its abelianization is C6 x C2. Is there an efficient way to determine which
of its C2 quotients gives the semidirect product decomposition, and to
determine the action of C2 on (C2 x SL(2,3))?

I mean I could always iterate over all the possible quotients and the
possible actions of C2 on the kernel and check to see which of them gives a
group isomorphic to the original one, but this seems kind of annoying to do
if I want to do this for many different groups.

-- 

William Chen
Member, School of Mathematics
Institute for Advanced Study,
Princeton, NJ, 08540
oxeimon at gmail.com