= Right conjugation reverses composition
{title2=$c_h(k)=h^{-1}kh,\quad c_{gh}=c_h\circ c_g$}
For a <normal subgroup> $K$ of $G$, each $c_h:k\mapsto h^{-1}kh$ is a <group automorphism> of $K$. Its inverse is $c_{h^{-1}}$, but the dependence on $h$ is a <group antihomomorphism> under ordinary <function composition>, because $(gh)^{-1}k(gh)=h^{-1}(g^{-1}kg)h$. The assignment $h\mapsto(k\mapsto hkh^{-1})$ instead is a <group homomorphism> to the <automorphism group>. Equivalently the first convention is a right <group action>, while the second is a left <group action>.
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