The general formula for the anomalous dimension can be found in Martin΄s review article (hep-ph/9709356), on page 62 relation (6.5.4). In the case of $SU(5)$ and especially in the paper of Kobayashi, ...
While searching in the Internet, I came to know about Werner Heisenberg's attempt to obtain an Unified Field Theory (see the book Introduction to Unified Field Theory of Elementary Particles). But ...
I understand how the assignment works for a symmetry breaking like $$SO(10) \rightarrow SU(3)_C \times SU(2)_L \times SU(2)_R \times U(1)_X$$ The Hypercharge can then easily computed by $$ ...
I'm starting to get a little desperate, because I can't find any introductory treatments of Grand Unified Theories (GUT). So far the only books I found are Mohapatra Unification and Supersymmetry ...