Dihedral group $D_4$ (symmetries of a square) is isomorphic to a subgroup of $S_4$ (permutation group) [duplicate]

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I have this problem that I have been stuck on for a while. I know that I can write the elements of $D_4$ as products of the identity, rotation by $90$ degrees and a vertical reflection and I have already written the $8$ elements of $D_4$ as their cycle notation is $S_4$ but have no idea what to do from there and would really appreciate the help!

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1 Answer

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Hint: Label the corners of a square. Permute them.

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