1. The problem statement, all variables and given/known data See image. 2. Relevant equations 3. The attempt at a solution I am finding the orders of permutations. I know that you first find the orbits or cycles I don't know the difference (but I should). This is what my professor said: If you have (1345)(897) the orders are 4 and 3 respectively. If 4 and 3 are relatively prime then you just multiply 4 and 3 to get 12. So the order of the both is 12. Now if you have (1345)(6,7,8,9,10,11) the orders are 4 and 6 respectively. So now you look at the Least Common Multiple 4, 8, 12 and 6, 12 and so the order is the least common multiple which is 12. But in my problem I have (135)(264)(7), 7 is fixed and I don't know what to do when I have 3 of them. The orders should be 3, 3, 1, but I don't know how to combine them to get the order of the entire thing.