  The statement of the lemma is true for $\epsilon =-$ since if $n$ is odd then $H$ is a subgroup of ${\mathrm{Sin}}_n^{+}(q^0) \rtimes  \langle \varphi \rangle$ (here $\varphi : g \mapsto g^{q^0}$), and if $n$ is even then it is sufficient to replace $q$ by $(-q)$ in the proof above.  \[