The 27-dimensional Hopf algebra A(F), defined by the exact sequence of
quantum groups A ((SL(S, C)) -->(Fr) A (SLq(2)) -->(pi F) A(F), q = e
(2 pi i/3) is studied as a finite quantum group symmetry of the matrix
algebra M(3, C), describing the color sector of Alain Connes' formula
tion of the Standard Model. The duality with the Hopf algebra H, inves
tigated in a recent work by Robert Coquereaux, is established and used
to define a representation of H on M(3, C) and two commuting represen
tations of H on A(F).