  We study $SU(8)$ symmetry breaking induced by minimizing the Coleman-Weinberg
effective potential for a third rank antisymmetric tensor scalar field in the
56 representation. Instead of breaking $SU(8) \supset SU(3) \times SU(5)$, we
find that the stable minimum of the potential breaks the original symmetry
according to $SU(8) \supset SU(3) \times Sp(4)$. Using both numerical and
analytical methods, we present results for the potential minimum, the
corresponding Goldstone boson structure and BEH mechanism, and the
group-theoretic classification of the residual states after symmetry breaking.
