Let be a rotation and be a reflection. What are the relationships? Is it and ? Also, has elements that are neither reflections nor rotations, but products of both. Perhaps define so that for any word , if contains an even number of reflections and if contains an odd number of reflections. Now, you need some form of parity function to check that this is well defined. If there exists any two words, equal in G, with one word containing an even number of reflections and one word containing an odd number, then f is not a homomorphism (and is not even well-defined).