Attempt Constructing a Model of Grand Gauge-Higgs Unification with Family Unification

We discuss a possibility whether a model of grand gauge-Higgs unification incorporating family unification in higher dimensions can be constructed. We first extend a five dimensional SU (6) grand gauge-Higgs unification model to a five dimensional SU (7) grand gauge-Higgs unification model compactified on an orbifold S¹/Z₂ to obtain three generations of quarks and leptons after symmetrybreaking of the larger family unified gauge group. A prescription of constructing a six dimensional SU (N) grand gauge-Higgs unification model including a five dimensional SU (7) grand gauge-Higgs unification after compactifying the sixth dimension on an orbifold S¹/Z₂ is given. We find a six dimensional SU (14) grand gauge-Higgs unification model with a set of representations containing three generations of quarks and leptons.