Number of conjugacy classes in the group of all symmetries of the square. [closed]

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

a)$4$

b)$5$

c)$6$

d)$7$

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

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