group class

A complete set of mutually conjugate group elements. Each element in a group belongs to exactly one class, and the identity element (I = 1) is always in its own class. The conjugacy class orders of all classes must be integral factors of the group order of the group. From the last two statements, a group of prime order has one class for each element. More generally, in an Abelian group, each element is in a conjugacy class by itself. Two operations belong to the same class when one may be replaced by the other in a new coordinate system which is accessible by a symmetry operation. These sets correspond directly to the sets of equivalent operations.

graph cycle | subgroup