Weak Cayley table groups of some crystallographic groups

For a group $G$, a weak Cayley isomorphism is a bijection $f:G\to G$ such that $f(g_1{g}_2)$ is conjugate to $f(g_1)f(g_2)$ for all $g_1,g_2\in G$. They form a group $\mathcal{W}(G)$ that is the group of symmetries of the weak Cayley table of $G$. We determine $\mathcal{W}(G)$ for each of the seventeen wallpaper groups $G$, and for some other crystallographic groups.