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**aliceinwonderland** Let $\displaystyle G_{1} \times G_{2}=Z_{12} \times S_{24}$.

1. The commutator subgroup of $\displaystyle Z_{12} \times S_{24}$ I got is $\displaystyle e \times A_{24}$.

2. The quotient group of $\displaystyle \frac{Z_{12} \times S_{24}}{e \times A_{24}} = Z_{12} \times Z_{2}$.

Is above 1&2 correct?

Since the maximum order of elements in $\displaystyle Z_{12} \times Z_{2}$ is 12, the above 2 seems wrong. ((12 * 24!) / (0.5 *24!) = 24 ).

If 2 is wrong, what is the quotient group of 2?