As mentioned above, conjugacy classes of subgroups are domains, so all set theoretic functions are also 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.
Elements( C )
The elements of the conjugacy class C with representative U in the group G are computed by first finding a right transversal of the normalizer of U in G and by computing the conjugates of U with the elements in the right transversal.
V in C
Membership of a group V is tested by comparing the set of contained cyclic subgroups of prime power order of V with those of the groups in C.
Size( C )
The size of the conjugacy class C with representative U in the group G is computed as the index of the normalizer of U in G.
GAP 3.4.4