These problems are very computational. Post what you did so far. Do you know what to do here? Pick an element in G and conjugate it with other elements that will give you its conjugacy class. Now take a another element from G which is not in that conjugacy class and conjugate it with other elements of G that will give you a new conjugacy class. Keep on going until you exhaust all of G. Note, that elements in Z(G) will simply be conjugate to themselves only.