What are the elements of Alt_4 ?

[quasar987]

Homework Statement

This is not HW per say, I'm just wondering what the elements of Alt_4 are (the subgroup of S4 consisting of all even permutations). I know Alt_4 is of order 4!/2=12, and I have so far that

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

are in Alt_4 but what are the other four elements??

 

[Dick]

How about (1,3,2) for example?

 

[quasar987]

Right, I forgot those.

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

the inverses of the four elements I listed.