  Let $p$ be an odd prime with $p\equiv1\bmod 4$. Then for any odd power $q$ of
$p$ and a positive integer $j$ we show that the groups
$\text{Sp}_{p^j+1}(q),\text{PSp}_{p^j+1}(q)$, and their Sylow $p$-subgroups are
non-$FSZ_{p^j}$.
