  M(atrix) theory on an orbifold and classical two-branes therein are studied
with particular emphasis to heterotic M(atrix) theory on $S_1/Z_2$ relevant to
strongly coupled heterotic and dual Type IA string theories. By analyzing
orbifold condition on Chan-Paton factors, we show that three choice of gauge
group are possible for heterotic M(atrix) theory: SO(2N), SO(2N+1) or USp(2N).
By examining area-preserving diffeomorphism that underlies the M(atrix) theory,
we find that each choices of gauge group restricts possible topologies of
two-branes. The result suggests that only the choice of SO(2N) or SO(2N+1)
groups allows open two-branes, hence, relevant to heterotic M(atrix) theory. We
show that requirement of both local vacuum energy cancellation and of
worldsheet anomaly cancellation of resulting heterotic string identifies
supersymmetric twisted sector spectra with sixteen fundamental representation
spinors from each of the two fixed points. Twisted open and closed two-brane
configurations are obtained in the large N limit.
