I have been trying to work through some group theory questions but have no idea how to solve the ones iv been given. The question is for a tutorial but it is not assessed so I would appreciate any help i can get with it so i can ask my tutor better questions than were do i even start. Hopefully I should be able to solve the other questions on my own with the help i receive on this.
Fix a line L through opposite vertices of a cube. Consider the subgroup H of
the symmetries of the cube generated by g, where g is a rotation by 1/3 of a turn
about L. Then H acts on the set of vertices of the cube. Describe the orbits.