Past exam of the lie Groups and Differentiable Manifolds course of the University of Oxford / 2008 / A / 3 / b / i

A finite discrete group has trivial identity component, so its only torus is $T=\{1\}$. Thus $N_G(T)=G$ and, under the definition $N_G(T)/T$,The alternative quotient by the centralizer would give a different answer for a disconnected group; it is not the convention used here.