Let $G=GL_3(\mathbb{C})$. Take the action of G on the set of its subgroups for conjugacy: $g \in G$, and H a subgroups of G $g.H=gHg^{-1}={ghg^{-1}, h \in H}$
a)Let T be the subgroup of G of the diagonal matrixes. Show that the stabilizator N of T respect this action is given by the invertible matrixes that has only one coefficient not equal to 0 in each row and each column.
b)Show that T is a normal subgroup of N
c)Show that, using ismorphism theorem, that $N/T~S_3$ the group of the permutations of 3 elements
d)Generalize to $GL_n(\mathbb{C})$