Sets of Operations on Set of 3 Elements

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

Let $\AA$, $\BB$, $\CC_1$, $\CC_2$, $\CC_3$ and $\DD$ be respectively the set of all operations $\circ$ on $S$ such that the groups of automorphisms of $\struct {S, \circ}$ are as follows:

Let $\CC := \CC_1 \cup \CC_2 \cup \CC_3$.

The following results can be deduced:

Also see

 * Count of Binary Operations on Set
 * Count of Binary Operations with Identity
 * Count of Commutative Binary Operations on Set