  We discussed the scenario that a discrete flavor group combined with CP
symmetry is broken to $Z_2\times CP$ in both neutrino and charged lepton
sectors. All lepton mixing angles and CP violation phases are predicted to
depend on two free parameters $\theta_{l}$ and $\theta_{\nu}$ varying in the
range of $[0, \pi)$. As an example, we comprehensively study the lepton mixing
patterns which can be derived from the flavor group $\Delta(6n^2)$ and CP
symmetry. Three kinds of phenomenologically viable lepton mixing matrices are
obtained up to row and column permutations. We further extend this approach to
the quark sector. The precisely measured quark mixing angles and CP invariant
can be accommodated for certain values of the free parameters $\theta_{u}$ and
$\theta_{d}$. A simultaneous description of quark and lepton flavor mixing
structures can be achieved from a common flavor group $\Delta(6n^2)$ and CP,
and accordingly the smallest value of the group index $n$ is $n=7$.
