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Now the elements of correspond to the list in the given order. We can find the elements corresponding to the permutations and by looking up their positions in , in order to construct the symmetric group on 3 letters as a subgroup .
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Since is itself a Cayley table group, it is most useful to inspect the images of the elements under the Embedding.
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| (7) |
is the direct product of and the 2-element subgroup generated by the transposition .