 Thus the number of elements in the conjugacy class of is the index of the centralizer in  ; hence the size of each conjugacy class divides the order of the group.Furthermore, if we choose a single representative element from every conjugacy class, we infer from the disjointness of the conjugacy classes that , where is the centralizer of the element .Observing that each element of the center forms a conjugacy class containing just itself gives rise to the class equation