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)$7$
Number of conjugacy classes in the group of all symmetries of the square.
2
$\begingroup$
group-theory
finite-groups
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0If you can see this group as a symmetric group $\;S_n\;$ with permutations, cycles and etc. it is pretty easy to answer this... – 2017-01-06
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3(e) $5\frac12$ (f) $-1$ (g) $3+4i$ (h) $\sqrt {-163} $ (i) $\varphi$ (j) all of the above – 2017-01-06
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0And, 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? – 2017-01-06
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0If you're just asking us without posting your attempt, you may aswell just [google it](https://www.google.be/search?q=conjugacy+classes+of+dihedral+group+d4). – 2017-01-06
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0Possible duplicate of [Conjugate class in the dihedral group](http://math.stackexchange.com/questions/556508/conjugate-class-in-the-dihedral-group) – 2017-01-06