Word Count : 240

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Let ( G ) be a cyclic group of order 12, say ( G = \langle g \rangle = { e, g, g^2, \dots, g^{11} } ). By Cayley’s theorem, every group ( G ) is isomorphic to a subgroup of the symmetric group ( S_{|G|} ), the group of all permutations of ( |G| ) elements. Here, ( |G| _________ ______ _____ _____ ______ _________ _____ _____ ___.
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