A little problem with permutations.

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Let A_n be a subgroup of S_n that includes all the even permutations. How many permutations of order 6 does A_6 include?
 
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What do you mean by "order of a permutation"?
 
The order of the permutation as an element of a group, of course.

Remember that if you decompose an element x of Sn as a product of disjoint cycles, then the order of x is equal to the lcm of the lengths of the cycles. You will find that if you decompose an element x of S6 of order 6 into disjoint cycles, then x must be odd.
 

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