Say that $G$ is a finitely generated group on $k \geq 2$ generators and $N$ is a normal subgroup of $G$.
I want to know if I can construct a $G$-action on $G/N$ such that the action is free. None of the usual actions such as left-multiplication, conjugation are going to work.
Are there any conditions that will allow me to construct a free $G$-action? Any help would be greatly appreciated.