  Models of neutrino mass which attempt to describe the observed lepton mixing
pattern are typically based on discrete family symmetries with a non-Abelian
and one or more Abelian factors. The latter so-called shaping symmetries are
imposed in order to yield a realistic phenomenology by forbidding unwanted
operators. Here we propose a supersymmetric model of neutrino flavor which is
based on the group T7 and does not require extra Z_N or U(1) factors, which
makes it the smallest realistic family symmetry that has been considered so
far. At leading order, the model predicts tribimaximal mixing which arises
completely accidentally from a combination of the T7 Clebsch-Gordan
coefficients and suitable flavon alignments. Next-to-leading order (NLO)
operators break the simple tribimaximal structure and render the model
compatible with the recent results of the Daya Bay and Reno collaborations
which have measured a reactor angle of around 9 degrees. Problematic NLO
deviations of the other two mixing angles can be controlled in an ultraviolet
completion of the model.
