Does there exist an isomorphism between the semigroups $S(4)$ and $\mathbf Z_{256}$.
$S(4)$ is the set of all maps from the set $X$ to itself and $X = \{1, 2, 3, 4\}$. $S(4)$ is a semigroup under the composition of mappings and $\mathbf Z_{256} = {0, 1, 2, … , 255}$ is the semigroup under multiplication of integers modulo 256.