  Combining work of Peyre, Colliot-Th\'el\`ene and Voisin, we give the first
example of a finite group $G$ such that the motivic class of its classifying
stack $BG$ in Ekedahl's Grothendieck ring of stacks over $\mathbb{C}$ is
non-trivial and $BG$ has trivial unramified Brauer group.
