Example of a finite, non-abelian group in which left invariant metric is also right invariant

Question

I need an example of a finite, non-abelian group $(G, \cdot)$ which satisfies the following condition:

If $d$ is a metric on $G$ such that $d(ax, ay)=d(x,y), \ \ \ \ \forall a,x,y \in G$,

then $d(xa, ya)=d(x,y), \ \ \ \ \forall a,x,y \in G$.

Could you help me find it or maybe tell me where to look for it?

Thank you.