New Models of $SU(6)$ Grand Gauge-Higgs Unification

A five dimensional $SU(6)$ grand gauge-Higgs unification compactified on $S^1\mathrm{/}{Z}_2$ is discussed. We propose new sets of the $SU(6)$ representations where the quarks and leptons in one generation are embedded and there is no extra massless exotic fermions absent in the Standard Model. The correct electroweak symmetry breaking pattern can be realized by introducing some adjoint fermions. We also analyze whether a viable Higgs mass can be obtained.