Lepton mixing predictions including Majorana phases from Δ(6n2)Δ(6n2) flavour symmetry and generalised CP

Generalised CP transformations are the only known framework which allows to predict Majorana phases in a flavour model purely from symmetry. For the first time generalised CP transformations are investigated for an infinite series of finite groups, Δ(6n2)=(Zn×Zn)⋊S3Δ(6n2)=(Zn×Zn)⋊S3. In direct models the mixing angles and Dirac CP phase are solely predicted from symmetry. The Δ(6n2)Δ(6n2) flavour symmetry provides many examples of viable predictions for mixing angles. For all groups the mixing matrix has a trimaximal middle column and the Dirac CP phase is 0 or π  . The Majorana phases are predicted from residual flavour and CP symmetries where α21α21 can take several discrete values for each n   and the Majorana phase α31α31 is a multiple of π. We discuss constraints on the groups and CP transformations from measurements of the neutrino mixing angles and from neutrinoless double-beta decay and find that predictions for mixing angles and all phases are accessible to experiments in the near future.