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## Main Question or Discussion Point

Okay, so I'm trying to understand the notion of group actions, and I'm having a little difficulty understanding how to work on this question:

Describe all the ways the group [tex]S_3[/tex] can act on a set [tex]X[/tex]with 4 elements.

I mean, an action assigns with every element in [tex]S_3[/tex] a permutation of the set X. The confusing thing for me now is that the group we

Describe all the ways the group [tex]S_3[/tex] can act on a set [tex]X[/tex]with 4 elements.

I mean, an action assigns with every element in [tex]S_3[/tex] a permutation of the set X. The confusing thing for me now is that the group we

*start*with is a permutation group itself, so it's like for every permutation in [tex]S_3[/tex], we assign a permutation of X. But how does that help me answer the question?