As mentioned above, conjugacy classes are domains, so all domain functions are applicable to conjugacy classes (see Domains). This section describes the functions that are implemented especially for conjugacy classes. Functions not mentioned here inherit the default functions mentioned in the respective sections.
In the following let C be the conjugacy class of the element g in the group G.
Elements( C )
The elements of the conjugacy class C are computed as the orbit of g under G, where G operates by conjugation.
Size( C )
The size of the conjugacy class C is computed as the index of the centralizer of g in G.
h in C
To test whether an element h lies in C, in tests whether there is
an element of G that takes h to g. This is done by calling
RepresentativeOperation(G,h,g) (see RepresentativeOperation).
Random( C )
A random element of the conjugacy class C is computed by conjugating g with a random element of G.
GAP 3.4.4