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)!)) ?

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- February 1st 2010, 05:25 AMpoornaConjugates 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)!)) ? - February 1st 2010, 05:32 AMpoorna
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? - February 2nd 2010, 03:17 AMSwlabr