What is the automorphism group of the compact symplectic group?

Question

I would like to know what the group of outer automorphisms of $Sp(2)$ is. I think this should be isomorphic to $\mathbb{Z}_2$, but I am not completely sure.

Answer 1

This is a compact semisimple Lie group whose Dynkin diagram is of type $B_2=C_2$ (one pair of vertices joined by an oriented double arrow), and has no nontrivial symmetry. So the outer automorphism group is trivial.