Title: The Hurwitz Subgroups of $E_6(2)$,
Abstract: We prove that the exceptional group $E_6(2)$ is not a Hurwitz group. In the
course of proving this, we complete the classification up to conjugacy of all
Hurwitz subgroups of $E_6(2)$, in particular, those isomorphic to $L_2(8)$ and
$L_3(2)$.