  In this work we discuss the neutrino phenomenology in a $\Delta(54)$ discrete
flavor symmetry and evaluate the relic abundance of dark matter (DM) and active
neutrino-DM mixing angle considering various cosmological constraints. We
introduced two Standard Model Higgs particles along with vector-like fermions
and a new particle (S) which is a gauge singlet in the Standard Model. This
modification leads to a mass matrix that diverges from the tribimaximal
neutrino mixing pattern resulting in a non-zero reactor angle ($\theta_{13}$).
We also incorporated a $ Z_2 \otimes Z_3 \otimes Z_4$ symmetry for the specific
interactions in our model. The additional particle S is a sterile neutrino
which is considered to be a probable dark matter candidate with mass in keV
range.
