I just have a small question regarding the conjugation of permutation groups.
Two permutations are conjugates iff they have the same cycle structure.
However the conjugation permutation, which i'll call s can be any cycle structure. (s-1 a s = b) where a, b and conjugate permutations
My question is, how can you find out how many conjugation permutations (s) are within a group which also conjugate a and b.
So for example (1 4 2)(3 5) conjugates to (1 2 4)(3 5) under s = (2 4), how could you find the number of alternate s's in the group of permutations with 5 objects?
Thanks in advance