  We study a continuum model of the weakly interacting Bose gas in the presence
of an external field with minima forming a triangular lattice. The second
lowest band of the single-particle spectrum ($p$-band) has three minima at
non-zero momenta. We consider a metastable Bose condensate at these momenta and
find that, in the presence of interactions that vary slowly over the lattice
spacing, the order parameter space is isomorphic to $S^{5}$. We show that the
enlarged symmetry leads to the loss of topologically stable vortices, as well
as two extra gapless modes with quadratic dispersion. The former feature
implies that this non-Abelian condensate is a "failed superfluid" that does not
undergo a Berezinskii-Kosterlitz-Thouless (BKT) transition. Order-by-disorder
splitting appears suppressed, implying that signatures of the $S^5$ manifold
ought to be observable at low temperatures.
