Sets of Operations on Set of 3 Elements/Automorphism Group of D/Isomorphism Classes

Theorem
Let $S = \set {a, b, c}$ be a set with $3$ elements.

Let $\DD$ be the set of all operations $\circ$ on $S$ such that the group of automorphisms of $\struct {S, \circ}$ forms the set $\set {I_S}$, where $I_S$ is the identity mapping on $S$.

Let $\oplus \in \DD$.

Then the isomorphism class of $\oplus$ consists of $6$ elements, all of which are in $\DD$.