Eclectic flavor group Δ(27) (sic) S3 and lepton model building

We have performed a systematical study of the eclectic flavor group Delta(27) (sic) S-3 which is the extension of the traditional flavor symmetry Delta(27) by the finite modular symmetry S-3. Consistency between Delta(27) and S-3 requires that the eight nontrivial singlet representations of Delta(27) should be arranged into four reducible doublets. The modular transformation matrices are determined for various Delta(27) multiplets, and the CP-like symmetry compatible with Delta(27) (sic)S-3 are discussed. We study the general form of the Kahler potential and superpotential invariant under Delta(27) (sic) S-3, and the corresponding fermion mass matrices are presented. We propose a bottom-up model for lepton masses and mixing based on Delta(27) (sic) S-3, a numerical analysis is performed and the experimental data can be accommodated.