"Show that the C5 group is not a crystal point group."
2. Relevant information
1) "There exists another type of symmetry operation, called point symmetry, which leaves a point in the structure invariant"
2) "In crystallography, the angle of rotation cannot be arbitrary but can only take the following fractions of 2*pi: THETA= 2*pi/n where n = 1,2,3,4,6"
The Attempt at a Solution
So, the problem states that C5 is a group, mathematically, but just not a crystal point group. But obviously, C5 is also a point symmetry, since the point at the rotation axis is invariant. So the only thing I can think of is saying "by definition," because of the undemonstrated statement given by 2) above.
I have no idea how to proceed. I mean, it's a group. It's a point symmetry. If that's all I know, it should be a point group. Why isn't it a crystal point group? My book never explains what technical meaning modifying a phrase by "crystal" would yield.
Any hints would be greatly appreciated.