I want to know the answer to the following question:
What group can be the quotient of the free group over the generators of the group?
All the background I'm provided with is that "The dihedral group D4, for example, can be generated by two elements r and f (for example, r = r1, the right rotation and f = fv the vertical (or any other) reflection), which means that every symmetry of the square is a finite composition of these two symmetries or their inverses.". Is that enough to answer the question?
Answer: no