A new family of locally 5-arc transitive graphs of pushing up type with respect to the prime 3

Let $q$ be a power of the prime 3. For each value of $q$ we construct an amalgam ${\mathfrak A}=(G_1,G_2;G_{1,2})$ together with a completion $G$, such that the associated coset $\Delta$ is a locally $5$-arc transitive $G$-graph of pushing up type. For $q=3$, the amalgam is of shape ${\cal E}_1$ in the sense of \cite{b1}. For the other values of $q$, the amalgam is of a previously unknown shape. The resulting family of graphs is the first infinite family of locally 5-arc transitive graphs containing a vertex $z$ for which the group that fixes all 3-arcs originating at $z$ is non-trivial. Furthermore, we give conditions on $q$ for which the amalgam ${\mathfrak A}$ admits subamalgams whose associated coset graphs are also locally 5-arc transitive and of pushing up type too. Thereby providing further examples of vertex stabilizer amalgams that can arise in locally 5-arc transitive graphs of pushing up type.