  It is explained that the Standard Model combined charge conjugation and
parity transformation (CP) is a simultaneous complex conjugation outer
automorphism transformation of gauge and space-time symmetries. Simple examples
are given for the general concept of outer automorphisms ("symmetries of
symmetries"), as well as for their possible actions on physical theories. It is
highlighted that complex conjugation outer automorphisms do not, in general,
exist for all symmetries. Examples are given for cases in which the physical CP
transformation is violated as a consequence of requiring another symmetry. A
toy model is illustrated in which CP is spontaneously violated in the broken
phase of a continuous gauge symmetry, while an unbroken outer automorphism
protects the topological vacuum angle at $\theta=0$.
