Coupling Constant Unification

Currently I am working on gauge coupling unification in certain specific models. I studied basic renormalization in abelian gauge theory as well as scalar field theory during my MSc coursework but did not study renormalization group evolution properly. My supervisor advised me to look at Weinberg's QFT volumes, and believe me I liked the way this renormalization topic is written in that book and that has probably given me enough enthu to spend 3500 bucks to buy all the three volumes. The renormalization group evolution is given by $ \mu (d g/d \mu) = \beta(g) $, where g is the coupling constant and $ \mu $ is the mass scale. Thus this equation basically predicts the evolution of the gauge coupling constant with energy scale. I have not yet looked into the derivations of the beta functions for the most general case. I am just using the standard formula for one-loop beta function from text books and using it in my own model. The new thing I have learnt is that choosing a specific gauge group does not decide the beta function completely. Its the particle content of that group: the fermions, gauge bosons as well as Higgs scalars which decide the form of beta function. Thus for the same gauge group if we modify the particle content, the beta function will also change and accordingly the evolution of the coupling constants.