  A natural question for groups $H$ is which data can be detected in its finite
quotients. A subset $X \subset H$ is called separable if for all $h\in H
\setminus X$, there exists an epimorphism $\varphi$ to a finite group $Q$ such
that $\varphi(h)\notin\varphi(X)$. More specifically, a group is said to be
conjugacy separable if every conjugacy class is separable. It is known that
many classes of groups are conjugacy separable, including virtually free and
polycyclic groups. The minimal order of the quotient $Q$, in terms of the
complexity of the conjugacy classes under consideration, is captured by the
conjugacy separability function $\mathrm{Conj}_H: \mathbb{N} \to \mathbb{N}$.
This function is in general ill understood, in fact the only large class of
groups for which it is known exactly are the abelian groups. Indeed, in this
case $\mathrm{Conj}_H$ is equal to the residual finiteness function, that is
the size of quotients needed to separate singletons, and thus logarithmic if
the group is infinite.
  Recent work has described the residual finiteness function for the class of
virtually abelian groups, which gives a lower bound for the conjugacy
separability function. The main result of this paper is a characterization of
$\mathrm{Conj}_H$ for every virtually abelian group $H$. If the corresponding
extension is associated with an irreducible representation over $\mathbb{Q}$,
we demonstrate that we obtain the same function as the residual finiteness
function. However, if the representation is not irreducible, we find an
expression that is in some cases strictly larger, which we illustrate with
several examples.
