  Neutrino mass matrix via a seesaw mechanism is constructed by assuming that the underlying symmetry of both heavy Majorana and Dirac mass matrices is the discrete subgroup $\Delta(27)$ symmetry of SU(3). Using the experimental data of neutrino oscillation, the neutrino mass matrix exhibits maximal $\nu_{\mu}-\nu_{\tau}$ mixing and has a specific prediction on the effective neutrino mass in neutrinoless double beta decay which can be tested in future experiment. 
Neutrino Masses via a Seesaw with Heavy Majorana and Dirac Neutrino Mass   Matrices from Discrete Subgroup $\Delta (27)$ of SU(3)