I will start adding references on this topic here.
https://gap-packages.github.io/hap/tutorial/chap11_mj.html#X7C0B125E7D5415B4
A recent comment on GAP system:
https://github.com/gap-packages/hap/issues/69
GAP implementation of LHS spectral sequence:
https://gap-packages.github.io/hap/www/SideLinks/About/aboutSpaceGroup.html
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))：
https://diagonalargument.com/2020/04/26/wallpaper-groups/#more-1426
Click to access wallpaper-notes.pdf
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)
Mathematical Notes
https://drive.google.com/file/d/12fti6FKkwqlCyntRGAkXtjbrfUyw3p-g/view
The paper “Cohomology for Anyone” by David A. Rabson, John F. Huesman,and Benji N. Fisher:
https://arxiv.org/abs/cond-mat/0301601
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:
http://aflowlib.org/prototype-encyclopedia/enantiomorph_info.html
chunxiaoliu 