Conjugacy and the Class Equation · Medium problem

In $D_4 \times \mathbb Z_3$ (order $24$), let $a = (r, 1)$ where $r$ is the order-$4$ rotation of the square and $1$ generates $\mathbb Z_3$. If $b$ is any conjugate of $a$, what is (the order of $b$) plus (the size of $a$'s conjugacy class)?