  We study a five dimensional SU(3) nonsupersymmetric gauge theory compactified
on $M^4\times S^1/Z_2$ and discuss the gauge hierarchy in the scenario of the
gauge-Higgs unification. Making use of calculability of the Higgs potential and
a curious feature that coefficients in the potential are given by discrete
values, we find two models, in which the large gauge hierarchy is realized,
that is, the weak scale is naturally obtained from an unique large scale such
as a grand unified theory scale or the Planck scale. The size of the Higgs mass
is also discussed in each model. One of the models we find realizes both large
gauge hierarchy and consistent Higgs mass, and shows that the Higgs mass
becomes heavier as the compactified scale becomes smaller.
