Systematic analysis of 3HDM symmetries

Symmetries play a central role in the structure of multi-Higgs-doublet models. While considerable progress has been made in classifying realisable symmetry groups in three-Higgs-doublet models, the completeness of existing classifications remains an open question. In this talk, I revisit conventional symmetry transformations from a new perspective, leading to a more systematic framework for identifying realisable symmetries. I then extend the analysis to the recently proposed GOOFy transformations, which act non-trivially on scalar doublets and their conjugates.