Lepton Mixing Predictions from (Generalised) CP and Discrete Flavour Symmetry

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 $\mathrm{\Delta }(6n^2)$ series. The most well-known member is $\mathrm{\Delta }(24)=S_4$. I present results of several extensive studies of lepton mixing predictions obtained in models with a $\mathrm{\Delta }(6n^2)$ 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.