Is x a Group? Testing the 4 Axioms and Multiplication Table Method

[Nosjack]

Hey guys, I'm having an issue with a question, namely

Let x be a subset of S₄. Is x a group?

x = {e, (123), (132), (12)(34)}

I don't really understand how I can test the 4 axioms of a group and how x being a subset of S₄ would help?

 

[vela]

You have only four elements. Why not just write out the entire multiplication table and see if you have a group on your hands?