How do I list the conjugacy classes of $D_n$?

Asked Nov 27 '19 at 19:35

Active Nov 27 '19 at 19:39

Viewed 579 times

I know that a conjugacy class looks like this:

$C_y = \{x \mid x = g^{-1} y g \}$ where $g, y \in G$

I also know a dihedral group looks like this:

$D_n = \{e, b, b^{2}, ..., b^{n-1}, a, ab, ..., ab^{n-1}\}$

How can I therefore list all the conjugacy classes for the general case?

Naive me just wrote this down as the answer:

All distinct $C_y = \{x | x = g^{-1} y g \}$ where $g, y \in D_n$

Well... that's not very useful. I'm just not sure what I'm supposed to do to answer the question satisfiably.

Here's the original question:

edited Nov 27 '19 at 19:39

Bernard

asked Nov 27 '19 at 19:35

Threnody

1

This might help : https://math.stackexchange.com/questions/556508/conjugate-class-in-the-dihedral-group – NewBornMATH Nov 27 '19 at 19:42
1

See also the homework solution here. – Dietrich Burde Nov 27 '19 at 19:42
Thank you both. The hw solution was especially helpful. – Threnody Nov 27 '19 at 19:47

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