  Gauge-Higgs grand unification theories are models of gauge-Higgs unification
that extend the electroweak group into a simple group that includes the color
symmetry. The minimal option is a gauge-Higgs grand unification based on the
SU(6) gauge group, mirroring SU(5) grand unification in 4D while providing a
solution to the hierarchy problem. We explore different minimal and realistic
novel incarnations of SU(6) gauge-Higgs grand unification. We submit the setup
to the various flavor hierarchies observed in nature and, utilizing the power
of the fifth dimension, identify an embedding that provides a compelling model
of quarks and leptons that naturally explains the mass hierarchies and the
CKM/PMNS structure. We perform a detailed study of quark - and lepton - flavor
constraints (which are intimately related due to the GUT nature) together with
an analysis of the Higgs potential which arises at the loop level. Electroweak
precision constraints on the model are discussed and the rich scalar sector is
analyzed. Future flavor constraints from upcoming experiments will provide a
stringent test for this class of models, while a scalar singlet and leptoquark
provide unique targets for current and future collider experiments to probe
this solution to various open questions in nature.
