Given a group G and a normal subgroup N there is a natural way to
associate elements of the group with the factor group in such a way as to
give a homomorphism. This mapping is 
and is called the
natural homomomorphism. It is of course onto and so an epimorphism.
The kernel of the map is N. Any two elements of G that are in the same
coset of N in G are mapped to the same element of the factor group.