Haven't yet been assigned a tutor for an introduction to group theory course; but am working through and have found the following question, where I'm stuck as to the questions meaning!

Here's the question:

Determine all the elements of S5 that conjugate p to s.

p is a 3 cycle and a two cycle
s is also a 3 cycle and a two cycle.

So - do I just say

s = g o p o g^(-1)

and then work through the 12 available permutations of s; and list the ones that generate a 3 cycle and a two cycle? or is there something I'm clearly missing? (like a working brain!)

thanks for taking the time to read; and hoping you can throw some insight this way!