Group Theory - Conjugacy
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!