Thread: Conjugates of elements in a group

Hey, How do I find the conjugate classes of a dihedral group of order 2n?

And in Sn what is the number of r cycles? I thought it was nCr, but I have been asked to prove it is n!/(r((n-r)!)) ?

Oh wait, that r cycles question..

I can choose elements in nCr ways.
Out of these I fix the least element in the first place. So that there are (r-1) ways to fill the 2nd place and so on. i.e. the cycle say (5,2,7) is replaced by (2,7,5). So ther are (r-1)! ways of doing this. So the total no. of ways is nCr * (r-1)! which is the reqd. nswer.

Am I right?

Originally Posted by poorna

Hey, How do I find the conjugate classes of a dihedral group of order 2n?

What do elements of look like? So, take an arbitrary element in this form, and conjugate it by another arbitrary element, . What does this element look like?

Such elements form your conjugacy class.