  In a classical, quartic field theory with $SU(N) \times Z_2$ symmetry, a
class of kink solutions can be found analytically for one special choice of
parameters. We construct these solutions and determine their energies. In the
limit $N\to \infty$, the energy of the kink is equal to that of a kink in a
$Z_2$ model with the same mass parameter and quartic coupling (coefficient of
${\rm Tr}(\Phi^4)$). We prove the stability of the solutions to small
perturbations but global stability remains unproven. We then argue that the
continuum of choices for the boundary conditions leads to a whole space of kink
solutions. The kinks in this space occur in classes that are determined by the
chosen boundary conditions. Each class is described by the coset space $H/I$
where $H$ is the unbroken symmetry group and $I$ is the symmetry group that
leaves the kink solution invariant.
