Abstract
In this paper, we prove that the finite simple groups $\text{PSp}_{6}(q)$, ${\rm\Omega}_{7}(q)$ and $\text{PSU}_{7}(q^{2})$ are $(2,3)$-generated for all $q$. In particular, this result completes the classification of the $(2,3)$-generated finite classical simple groups up to dimension 7.
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