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Dear Forum members,

Azmi Tamid had asked:

Dear GAP-forum,

Is there a way in GAP to compute the number of

non-isomorphic subgroups of a finite group G ?TIA,Azmi

There are several ways to determine all subgroups of a given group,

and they are described in detail in Chapter 37 (Groups) in the GAP

manual. To get just the number of non-isomorphic subgroups, you should

sort the representatives of the conjugacy classes of subgroups by some

invariants that you should choose according to the situation you are

in (order, some properties such as being abelian, solvable or

nilpotent, number of conjugacy classes of elements of given order,

order of some uniquely determined characteristic subgroups, such as

the commutatorgroup), and then apply isomorphism tests to those that

fall into the same class defined by these invariants.

Please do consult the manual first when you have a question which is

very likely answered using GAP. But next after that rather write to

the address 'gap-trouble' (which will be read by some helpful people)

than asking such a question in 'gap-forum' which will be read by

several hundred users of GAP. The Forum really should be reserved for

more subtle questions for which perhaps only a handful of experts, not

necessarily belonging to the GAP team, may have an answer, as well as

for bug fixes, general announcements and so on.

Kind regards Joachim Neubueser

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Prof. em. J. Neubueser

Lehrstuhl D fuer Mathematik

RWTH Aachen

Germany

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