Quiz:Element structure of alternating group:A4

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

Element order and conjugacy class structure
Review the conjugacy class structure:

{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
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{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
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 * This equals its own inverse, hence is conjugate to its inverse
 * This is not in the alternating group, because it is an odd permutation
 * This equals its own inverse, hence is conjugate to its inverse
 * This is not in the alternating group, because it is an odd permutation

{How many conjugacy classes of elements are there in the alternating group of degree four? - 1 - 2 - 3 + 4 - 5 - 6 - 7
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{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
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