  An important class of flavour groups, that are subgroups of $U(3)$ and that
predict experimentally viable lepton mixing parameters including Majorana
phases, is the $\Delta(6n^2)$ series. The most well-known member is
$\Delta(24)=S_4$. I present results of several extensive studies of lepton
mixing predictions obtained in models with a $\Delta(6n^2)$ flavour group that
preserve either the full residual $Z_2\times Z_2$ or a $Z_2$ subgroup for
neutrinos and can include a generalised CP symmetry. Predictions include mixing
angles and Dirac CP phase generally; and if invariance under a generalised CP
symmetry is included, also Majorana phases. For this, the interplay of flavour
group and generalised CP symmetry has to be studied carefully.
