# What does it mean to assign group operations to distinct sets for space groups?

I am trying to understand space groups in crystallography. In International tables for crystallography, for a nonsymmorphic space group, they list some symmetry operations. 8 of them are listed under the (0,0,0)+ set and 8 in the (1/2, 1/2, 1/2)+ set. What does this mean? Are there 16 operations in total? How do the sets differ?

Edit: I find similar notation for symmorphic space groups as well. There are some space groups with only one set and some with two or more, and I don't understand what determines the number of sets.

• +1. Welcome to the site and thank you for contributing your question here!!! We hope to see much more of you in the future! I pinged someone who often answers group theory questions, to draw their attention to this question, but they said the question is a bit too vague and they would be able to answer if you give a concrete example. Can you give a specific example and elaborate in more detail? Nov 27 '20 at 21:49
• Without the specific example and elaboration, we might have to close this question as needing more details. Dec 3 '20 at 21:57