Let $G$ be the group of all symmetries of the square. Then the number of conjugacy classes in $G$ is






closed as off-topic by martini, Watson, TastyRomeo, MJD, Alex M. Jan 6 '17 at 12:26

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  • $\begingroup$ If you can see this group as a symmetric group $\;S_n\;$ with permutations, cycles and etc. it is pretty easy to answer this... $\endgroup$ – DonAntonio Jan 6 '17 at 12:18
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    $\begingroup$ (e) $5\frac12$ (f) $-1$ (g) $3+4i$ (h) $\sqrt {-163} $ (i) $\varphi$ (j) all of the above $\endgroup$ – MJD Jan 6 '17 at 12:21
  • $\begingroup$ And, if you are getting used to group theory, I recommend that you write down all elements of this group and its Cayley table. Have you tried that? $\endgroup$ – Alex Macedo Jan 6 '17 at 12:22
  • $\begingroup$ If you're just asking us without posting your attempt, you may aswell just google it. $\endgroup$ – TastyRomeo Jan 6 '17 at 12:23
  • $\begingroup$ Possible duplicate of Conjugate class in the dihedral group $\endgroup$ – Alex M. Jan 6 '17 at 12:26