[GAP Forum] how to compute all subgroups of order p up to conjugacy

Frank Lübeck frank.luebeck at math.rwth-aachen.de
Thu May 29 10:55:48 BST 2008

On Tue, May 27, 2008 at 09:56:14AM +0200, Frédéric Vanhove wrote:
> This is my problem : let G be a finite group, the order of which divisibly 
> by a prime p.  I would like to get a list of all subgroups of G of order p, 
> up to conjugacy.

Dear Frédéric Vanhove, dear Forum,

A subset of elements of a finite group which generate a conjugate of a fixed
cyclic subgroup, is called a "rational class".

With the GAP command RationalClasses you find representatives of all classes
of cyclic subgroups of a finite group. (There is also the undocumented function
RationalClassesPElements( group, prime).) These were used in former versions
of GAP as a step to find the conjugacy classes. 
For some groups it may be faster to compute all ConjugacyClasses(group) and
then check for repeated rational classes comparing RationalClass of
representatives of the conjugacy classes.

Best regards,


///  Dr. Frank Lübeck, Lehrstuhl D für Mathematik, Templergraben 64,  ///
\\\                    52062 Aachen, Germany                          \\\
///  E-mail: Frank.Luebeck at Math.RWTH-Aachen.De                        ///
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