Painting a Cube

You have six different colors to paint a cube. Each face of the cube should be painted. You can use every color to paint as many faces of the cube as you like (0, 1, 2, 3, 4, 5, 6); but you cannot use more than one color on a single face. How many different painting patterns can be formed on this cube?

Note: If a pattern can be formed by rotating another pattern any number of times, these two patterns are not considered as different.

answers: # 81     popularity: 92.3 %     difficulty: 73.1 %