  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.
