Group Theory Question, Dihedral Group
I've been asked to find all transitive actions up to similarity of the Dihedral Group of order 8. I'm not sure what exactly this is asking.
I know what a dihedral group is and I know what a transitive action is but how do you find out what the transitive actions for the group are? Does it not need a set X to act on? If so I'm assuming that set would be the set of edges of the regular polygon but I'm still a bit confused. I don't know where to go from there.
Can anyone help with this?
Thanks for your help,