Quotient map of groups ($\pi :G\to G/N,g\mapsto gN$)

The quotient map of groups sends each group element to its coset modulo a normal subgroup. It is a surjective group homomorphism, with group kernel exactly $N$. In the additive six-element example, it sends $0,3$ to $N$, $1,4$ to $1+N$, and $2,5$ to $2+N$. The quotient map of groups records the identification that produces the new group.