  We have used the SmallGroups library of groups, together with the computer
algebra systems GAP and Mathematica, to search for groups with a
three-dimensional irreducible representation in which one of the group
generators has a twice-degenerate eigenvalue while another generator has
non-degenerate eigenvalues. By assuming one of these group generators to
commute with the charged-lepton mass matrix and the other one to commute with
the neutrino (Dirac) mass matrix, one derives group-theoretical predictions for
the moduli of the matrix elements of either a row or a column of the lepton
mixing matrix. Our search has produced several realistic predictions for either
the second row, or the third row, or for any of the columns of that matrix.
