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Is the best way to do this just to write out each element's cycle decomposition, or is there a more efficient way?

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- Thread starter Mr Davis 97
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Is the best way to do this just to write out each element's cycle decomposition, or is there a more efficient way?

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fresh_42

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You can decompose the group:

Is the best way to do this just to write out each element's cycle decomposition, or is there a more efficient way?

$$S_4 \cong A_4 \rtimes \mathbb{Z}_2 \cong (V_4 \rtimes \mathbb{Z_3}) \rtimes \mathbb{Z}_2 \cong (\mathbb{Z}_2^2 \rtimes \mathbb{Z_3}) \rtimes \mathbb{Z}_2$$

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