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What does the order of a class mean in a character table?

I am not from a chemistry background. I am trying to see how the symmetry operations affect the stiffness tensor which led me in the path of understanding character tables. I am looking at the character table for C6v group and I cannot understand what the factor 2 for C6(z) means. Is it representative of the fact that I can rotate in clockwise and anticlockwise direction?

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