Quiz:Element structure of alternating group:A4

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See element structure of alternating group:A4 for background information.

Element order and conjugacy class structure

Review the conjugacy class structure: [SHOW MORE]

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

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

2 Which of the following elements is in the alternating group on the set \{ 1,2,3,4 \} and is not conjugate to its inverse in the alternating group?

() -- the identity element
(1,2) -- a 2-transposition
(1,2)(3,4) -- a double transposition
(1,2,3) -- a 3-cycle
(1,2,3,4) -- a 4-cycle

3 How many conjugacy classes of elements are there in the alternating group of degree four?

1
2
3
4
5
6
7

4 How many orbits are there in the alternating group of degree four under the action of its automorphism group?

1
2
3
4
5
6
7