The degree of a class of minimal non-PS-groups

We show that the least n such that we can embed the minimal non-PS-group \(\,\,G ={\big <}a, b \,:\, a^{q} = b^{4} = 1, ab=ba^{q-1} {\big >}\) $G=〈a,b:a^q=b^4=1,ab=b{a}^{q-1}〉$ in the symmetric group \(\textrm{S}_{n}\) ${\text{S}}_n$ is \(q+4\) $q+4$ .