We construct a locally 5-arc transitive G-graph Δ, where G∈{PSU3(8)⋊C2,PSU3(8)⋊C6}. 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 Gz/Op(Gz[1]) over Op(Gz[1]) is non-split.
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John van Bon (2024) studied this question.
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