A New Family Symmetry: Discrete Quaternion Group

We examine the structure of the quaternion group $Q_8$ and its possible application to the physics of flavor. We find that a $Q_8$ family symmetry is suitable to explain the difference between quark and lepton mixing patterns. Distinctive phenomenological predictions are derived for the neutrino sector and the electroweak Higgs sector. We also show how the $Q_8$ symmetry suppresses the effective operators which mediate proton decay.