How does one determine the $R$-symmetry group?

As far as I understand it, the $$R$$-symmetry group is just the largest subgroup of the automorphism group of the supersymmetry (SUSY) algebra which commutes with the Lorentz group. I know for $$\mathcal{N}=1$$ SUSY, the $$R$$-symmetry is $$U(1)$$, mainly due to there being only one supercharge. However, I was wondering: how does one find the $$R$$-symmetry group for an extended $$\mathcal{N}>1$$ supersymmetric theory?

Also, does the $$R$$-symmetry group depend on the dimension and/or geometry (e.g. if we had a compact spacetime manifold) of spacetime?