Minimal eclectic flavor group Q8 ⋊ S3 and neutrino mixing

A bstract We perform a comprehensive analysis of the minimal eclectic flavor group Q 8 ⋊ S 3 which is isomorphic to GL(2 , 3), and all its irreducible representations are induced from the irreducible representations of Q 8 and S 3 . The consistency conditions between EFG and generalized CP (gCP) symmetry are revisited, and we find the gCP symmetry compatible with the minimal EFG Q 8 ⋊ S 3 . The most general forms of Kähler potential and superpotential based on Q 8 ⋊ S 3 are discussed, and the corresponding fermion mass matrices are presented. A concrete lepton model invariant under Q 8 ⋊ S 3 and gCP is constructed, in which the experimental data of all six lepton masses and six mixing parameters can be successfully described through seven real input parameters. The model predicts a vanishing effective mass m ββ in neutrinoless double beta decay.