1. The problem statement, all variables and given/known data I would like to find the number of distinct elements in S17 that are made up of two 4-cycles and three 3-cycles. 2. Relevant equations 3. The attempt at a solution This seems like a very simple question but since the group is so huge it's hard to figure out. I have been trying to look at the problem from the point of view of group actions but that has not gotten me anywhere yet.