Thread: simple question regarding orbits

This topic is giving me a hard time, I was thinking an example might help clear thing up.

Lets say I was given a group which consists of

and a set consisting of

and I was asked to find the respective orbits. Then would it simply be:

where 1 is a stabalizer

stabalizes 2




so the orbit of 2 is with order 3. And if I do the same procedure for 3 I would get the same elements with the same order so

Regarding 7 and 9, I'm thinking that all elements of stabalize 7 and 9, since they don't move, both with order 1 and and

is this correct?

And how would partition ?

consider the action of S_3 on X.