  In the context of $SU(3)_C \times SU(2)_L \times U(1)_Y \times U(1)_\chi$,
where $U(1)_\chi$ comes from $SO(10) \to SU(5) \times U(1)_\chi$, supplemented
by the non-Abelian discrete $\Delta(27)$ symmetry for three lepton families,
Dirac neutrino masses and their mixing are radiatively generated through dark
matter. The gauge $U(1)_\chi$ symmetry is broken spontaneously. The discrete
$\Delta(27)$ symmetry is broken softly and spontaneously. Together, they result
in two residual symmetries, a global $U(1)_L$ lepton number and a dark
symmetry, which may be $Z_2$, $Z_3$, or $U(1)_D$ depending on what scalar
breaks $U(1)_\chi$. Cobimaximal neutrino mixing, i.e. $\theta_{13} \neq 0$,
$\theta_{23} = \pi/4$, and $\delta_{CP} = \pm \pi/2$, may also be obtained.
