Making my own thread and carrying on from the other one:By my thing I meant that permutation I put. Again, I multiplied the two permutations together and yes they commute.(Original post by Farhan.Hanif93)
Not sure what you mean by "using my thing". The thing you mentioned in your other post is indeed a permutation. As for this being the whole centraliser, what about (1 3 5 2 4)? [think about why this one is in the centraliser of (1 2 3 4 5)]
So is it any order of any number in the group that form the centraliser?
EDIT: And saying that makes sense to me as to calculate the number of elements in the centraliser, I would do 5! and so this is basically all the different orders of numbers you have in that permutation, right?
... and the ones that won't