What physical quantity is spin a generator of?

Question

I know, we do not have an classical analog for the concept of spin in quantum mechanics. But, consider the following, Any infinitesimal operator we have: $$U_{\epsilon}=\mathbb{I}-i\hat{G}\epsilon$$ where, for the infinitesimal translation: $$\hat{G}\rightarrow\frac{\hat{p}}{\hbar}$$ Similarly, for an infinitesimal rotation, by analogy, we have the angular momentum operator. Now, for a spin system, what is it a generator of?