  The generalized CP transformations can only be consistently defined in the
context of $\Delta(3n^2)$ lepton symmetry if a certain subset of irreducible
representations are present in a model. We perform a comprehensive analysis of
the possible automorphisms and the corresponding CP transformations of the
$\Delta(3n^2)$ group. It is sufficient to only consider three automorphisms if
$n$ is not divisible by 3 while additional eight types of CP transformations
could be imposed for the case of $n$ divisible by 3. We study the lepton mixing
patterns which can be derived from the $\Delta(3n^2)$ family symmetry and
generalized CP in the semi-direct approach. The PMNS matrix is determined to be
the trimaximal pattern for all the possible CP transformations, and it can only
take two distinct forms.
