If is a finite group, then for any group element , the elements in the conjugacy class of are in one-to-one correspondence with cosets of the centralizer . This can be seen by observing that any two elements and belonging to the same coset (and hence, for some in the centralizer  ) give rise to the same element when conjugating : . That can also be seen from the orbit-stabilizer theorem, when considering the group as acting on itself through conjugation, so that orbits are conjugacy classes and stabilizer subgroups are centralizers. The converse holds as well.