  We study the Wamsley group $\langle X,Y,Z\,|\, X^Z=X^\alpha, {}^Z Y=Y^\beta,
Z^\gamma=[X,Y]\rangle$ and its Sylow subgroups, where $\alpha^\gamma\neq 1\neq
\beta^\gamma$ and $\gamma>0$, obtaining the sharpest results when
$\alpha=\beta$.
