A locally $5$-arc transitive graph related to ${\mathrm{P}\mathrm{S}\mathrm{U}}_3(8)$

We construct a locally 5-arc transitive $G$-graph $\mathrm{\Delta }$, where $G\in \{{\mathrm{P}\mathrm{S}\mathrm{U}}_3(8)⋊C_2,{\mathrm{P}\mathrm{S}\mathrm{U}}_3(8)⋊C_6\}$. The corresponding vertex stabilizer amalgams are of local characteristic $3$ but are not weak $(B,N)$-pairs. They are the first examples of this kind where there exists a vertex $z$ such that the extension of $G_z\mathrm{/}{O}_p(G_z^{[1]})$ over $O_p(G_z^{[1]})$ is non-split.