  We propose a neutrino model based on a $\Delta(54)$ flavor symmetry suitable
for explaining the current neutrino oscillation data. Neutrino masses arise
from the type II seesaw mechanism where the $\Delta(54)$ field assignments has
led to a simple neutrino mass matrix with one texture zero and which satisfies
the magic symmetry consistent with the well-known trimaximal mixing matrix. We
found interesting predictions concerning neutrino masses and mixing. In
particular, only the normal neutrino mass hierarchy and the lower octant of the
atmospheric angles are allowed in this model. The model predicts as well that
the $CP$ conserving values for the Dirac $CP$ phase $\delta _{CP}$ are not
allowed and thus, $CP$ is always violated in the neutrino sector. We have also
investigated the sum of absolute neutrino masses from cosmological
observations, the effective Majorana mass $m_{\beta \beta }$\ from neutrinoless
double beta decay experiments, and the electron neutrino mass $m_{\beta }$\
from beta decays where we found that the obtained range of $m_{\beta \beta }$\
can be tested by several experiments in the near future.
