  In order to induce a family of mixing patterns of leptons which accommodate
the experimental data with a simple mathematical construct, we construct a
novel object from the hybrid of two elements of a finite group with a parameter
$\theta$. This construct is an element of a mathematical structure called
group-algebra. It could reduce to a generator of a cyclic group if
$\theta/2\pi$ is a rational number. We discuss a specific example on the base
of the group $S_{4}$. This example shows that infinite cyclic groups could give
the viable mixing patterns for Dirac neutrinos.
