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,