I will start adding references on this topic here.
A recent comment on GAP system:
GAP implementation of LHS spectral sequence:
Case of 2D: 17 wallpaper groups, 13 arithmetic classes. There are many materials talking about them. First, a nice summary:
Then, an excellent outline of the proof by Michael Weiss (who is a distinguished professor in topology https://en.wikipedia.org/wiki/Michael_Weiss_(mathematician))：
And this note brings to the ultimate material that I was looking for — a book by Patrick Morandi (the original source, http://sierra.nmsu.edu/Morandi/notes/Wallpaper.pdf , is not working, but the following one is)
The paper “Cohomology for Anyone” by David A. Rabson, John F. Huesman,and Benji N. Fisher:
Several papers by Michel;
The book N-dimensional crystallography by R. L. E. Schwarzenberger
219 Space groups becomes 230 Space groups when resolving chirality (enantiomorphic).
The eleven enantiomorphic groups are listed here: