1. The problem statement, all variables and given/known data D4 acts on the vertices of the square. Labeling them counterclockwise starting from the top left as 1, 2, 3, 4, find the corresponding homomorphism to S4. 2. Relevant equations 3. The attempt at a solution I am not completely sure what the question is asking. It's pretty clear to see which elements of D4 would correspond to which permutations of S4, so am I being asked to just list which elements of D4 correspond to which permutations of S4? How would I prove the the resulting map is a homomorphism? It seems like it would be tedious to check all values to see if the homomorphism property is always satisfied.