So let's take a hexagonal crystal. The term: C_{6} then refers to the 6-fold rotation group. I litterarily have no idea about what a group is but still want to understand the basic things qualitatively. So what is meant by the 6-fold rotation group? Is it the set of 6 fold rotations leaving the crystal invariant. How many members are there in the case of the 2d and 3d hexagonal lattice? Combination of symmetry operations are also considered. For example: C_{6h} is the 6 fold rotation group plus the addition of a horizontal reflection plane. In this case, what specifies the position of this plane other than it being perpendicular to the rotation axis?