Are groups constructed using semidirect product always non-abelian? [duplicate]

When using semidirect product to construct new groups based on smaller groups, we have to define a group homomorphism from the non-normal subgroup to the group of automorphism of the normal one, i.e. if $$G = H \rtimes_{\phi} K$$, then $$\phi\colon K \to Aut(H)$$. Being $$\phi$$ non-trivial, can we ensure $$G$$ is non-abelian?
• If $\phi$ is non-trivial, it's easy to show that the group is non-abelian – Don Thousand Dec 21 '18 at 16:17