Hello, GAP-Forum,

in the online-manual of GAP 3.4.4 one can read

'ConjugacyClass( <G>, <g> )'

'ConjugacyClass' returns the conjugacy class of the element <g> in 
the group <G>. Signals an error if <g> is not an element in <G>.
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Let's try and see if this is the truth:

gap> G:=SymmetricGroup( 5 );; G.name:="S5";;
gap> (1,6) in Elements( G );
false
#
# Only to be sure; and now ...
#
gap> c := ConjugacyClass( G, (1,6) ); 
ConjugacyClass( S5, (1,6) )
gap> Elements( c );
[ (5,6), (4,6), (3,6), (2,6), (1,6) ]
#
# Oops! Looks like something went quite wrong here :-(
#

However, if you want to know in which conjugacy class of S5 the
"element" (1,6) lies GAP 3.4.4 tells you

gap> classes := ConjugacyClasses( G );
[ ConjugacyClass( S5, () ), ConjugacyClass( S5, (1,2) ), 
  ConjugacyClass( S5, (1,2)(3,4) ), ConjugacyClass( S5, (1,2,3) ), 
  ConjugacyClass( S5, (1,2,3)(4,5) ), ConjugacyClass( S5, (1,2,3,4) ), 
  ConjugacyClass( S5, (1,2,3,4,5) ) ]
gap> PositionProperty( classes, x->x=ConjugacyClass(G,(1,6)) ); 
false
#
# Probably because none of the objects in the list 'classes'  matches 
# the list [ (5,6), (4,6), (3,6), (2,6), (1,6) ], the conjugacy class
# of (1,6) in S5 ?
#

Very interested in an explanation for GAP's slightly strange behaviour
in the given example is

Mathias Kratzer