Quiz:Symmetric group

Elements
{Which of the following correctly describes the conjugacy class size statistics of symmetric group:S4 (see element structure of symmetric group:S4)? - 1,1,2,3,3 - 1,3,4,4,12 + 1,3,6,6,8 - 1,1,4,4,4,4,6 - 1,2,2,2,3,4,4,6
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{Given an element picked uniformly at random from symmetric group:S4, what is the probability that the square of this element is the identity element? See element structure of symmetric group:S4. - 1/4 + 5/12 - 1/2 - 7/12 - 2/3
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 * The element must be either the identity element, or in the conjugacy class of $$(1,2)$$ (size 6) or in the conjugacy class of $$(1,2)(3,4)$$ (size 3).

{What is the probability that two elements of symmetric group:S3, picked uniformly at random and independently (so they may be equal) generate the whole group? See generating sets for subgroups of symmetric group:S3. + 1/2 - 2/3 - 3/4 - 5/6 - 1
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{What is the smallest value of $$n$$ such that the symmetric group of degree $$n$$ contains an element of order 6? - 3 - 4 + 5 - 6 - 7
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 * No element of order 6, see element structure of symmetric group:S3.
 * No element of order 6, see element structure of symmetric group:S4.
 * Consider the element $$(1,2,3)(4,5)$$. The order is the lcm of 3 and 2, which is 6. See order of permutation is lcm of cycle sizes. See also element structure of symmetric group:S5.

{What is the maximum possible size of a conjugacy class in the symmetric group $$S_n$$ of degree $$n$$, for $$n \ge 3$$? - $$n!$$ - $$(n - 1)!$$ - $$(n - 2)!$$ + $$n!/(n - 1)$$ - $$n!/(n - 2)$$
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 * This arises as the conjugacy class for the cycle type corresponding to the partition $$n = (n - 1) + 1$$.