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## Main Question or Discussion Point

I have a question regarding symmetry groups. I've often heard that the Standard Model is a SU(3) x SU(2) x U(1) theory. From what I understand these groups contain the symmetries under which the Lagrangian function is invariant. If so, what does every one of the 3 groups above contain (what symmetry do they correspond to) and does specifying the symmetry groups give a complete description of the Lagrangian ?