Conjugate elements are in bijection with cosets of centralizer

Statement
Suppose $$g$$ is an element of a group $$G$$. Then, there is a natural bijection between the following two sets:


 * 1) The coset space of the centralizer of $$g$$ in G, i.e. the set $$G/C_G(g)$$
 * 2) The conjugacy class of $$g$$ in $$G$$, i.e., the set of elements of $$G$$ that are conjugate to $$g$$.