  Let $F$ be any non-Archimedean local field with residue field of cardinality
$q_F$. In this article, we obtain a classification of typical representations
for the Bernstein components associated to the inertial classes of the form
$[{\rm GL}_n(F)\times F^\times, \sigma\otimes\chi]$ with $q_F>2$, and for the
principal series components with $q_F>3$. With this we complete the
classification of typical representations for ${\rm GL}_3(F)$, for $q_F>2$.
