  We construct a six-dimensional gauge-Higgs unification model with the
enlarged gauge group of $E_6$ on $S^2/Z_2$ orbifold compactification. The
standard model particle contents and gauge symmetry are obtained by utilizing a
monopole background field and imposing appropriate parity conditions on the
orbifold. In particular, a realistic Higgs potential suitable for breaking the
electroweak gauge symmetry is obtained without introducing extra matter or
assuming an additional symmetry relation between the SU(2) isometry
transformation on the $S^2$ and the gauge symmetry. The Higgs boson is a KK
mode associated with the extra-dimensional components of gauge field. Its odd
KK-parity makes it a stable particle, and thus a potential dark matter
candidate in the model. We also compute the KK masses of all fields at tree
level.
