1 Which of the following correctly describes the conjugacy class size statistics of symmetric group:S4 (see element structure of symmetric group:S4#Conjugacy class structure)?

2 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#Conjugacy class structure.

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.

4 What is the smallest value of such that the symmetric group of degree contains an element of order 6?

5 What is the maximum possible size of a conjugacy class in the symmetric group of degree , for ?