Higgs boson from an extended symmetry

The variety of ideas put forward in the context of a composite picture for the Higgs boson calls for a simple and effective description of the related phenomenology. Such a description is given here by means of a minimal model and is explicitly applied to the example of a Higgs-top sector from an $SO(5)$ symmetry. We discuss the spectrum, the electroweak precision tests, B-physics, and naturalness. We show the difficulty in complying with the different constraints. The extended gauge sector relative to the standard $SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$, if there is any, has little or no impact on these considerations. We also discuss the relation of the minimal model with its ``little Higgs'' or holographic extensions based on the same symmetry.