Informationally Complete Characters for Quark and Lepton Mixings

A popular account of the mixing patterns for the three generations of quarks and leptons is through the characters kappa of a finite groupG. Here, we introduce ad-dimensional Hilbert space withd=cc(G), the number of conjugacy classes ofG. Groups under consideration should follow two rules, (a) the character table contains both two- and three-dimensional representations with at least one of them faithful and (b) there are minimal informationally complete measurements under the action of ad-dimensional Pauli group over the characters of these representations. Groups with smalldthat satisfy these rules coincide in a large part with viable ones derived so far for reproducing simultaneously the CKM (quark) and PNMS (lepton) mixing matrices.