My Math Forum Permutation group conjugates

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 March 11th, 2012, 03:23 AM #1 Member   Joined: Nov 2011 Posts: 40 Thanks: 0 Permutation group conjugates Hey, 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

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