Quiz:Element structure of symmetric group:S4

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See element structure of symmetric group:S4 for full details.

Element orders and conjugacy class structure

Review the conjugacy class structure: [SHOW MORE]

1 What are the possible orders of elements of the symmetric group of degree four?

1,2,3,4 only
1,2,3,4,6 only
1,2,3,4,8 only
1,2,3,4,6,8 only
1,2,3,4,6,8,12 only

2 For which of the following orders of elements is there more than one conjugacy class of elements with that order in the symmetric group of degree four?

1
2
3
4
6
8
12

3 Which of the following is a representative of the conjugacy class in the symmetric group of degree four that has the largest size?

(1,2)
(1,2,3)
(1,2,3,4)
(1,2)(3,4)