Dear Mr. Gomez,

this is really a bug that you have found in the conjugacy class
routines in GAP 3.4. It will be fixed in the next version, but you can
apply the following patch yourself and it should work then:

In file 'lib/ratclass.g', lines 2905--2911 read:

class := RationalClass( G, cl.representative ^ S1.bijection,
Image( S1.bijection, cl.centralizer ), cl.galoisGroup );
class.centralizer.size := Size( cl.centralizer );
class.power := RationalClass( G,
cl.power.representative ^ S1.bijection,
Image( S1.bijection, cl.power.centralizer ),
cl.power.galoisGroup );

Replace these seven lines by the following eight lines:

class := RationalClass( G, cl.representative ^ S1.bijection,
Image( S1.bijection, cl.centralizer ) );
class.galoisGroup := SylowSubgroup( cl.galoisGroup, p );
class.centralizer.size := Size( cl.centralizer );
class.power := RationalClass( G,
cl.power.representative ^ S1.bijection,
Image( S1.bijection, cl.power.centralizer ) );
class.power.galoisGroup := SylowSubgroup( cl.power.galoisGroup, p );

Sorry for any inconvenience,

Heiko Theissen