Field
How it is known
A crystal's structure is read from the pattern it scatters. The reciprocal lattice, systematic absences, and what an experiment can and cannot see.
The reciprocal lattice
Nobody has seen a space group. Crystals are read from where they scatter, and where they scatter is a second lattice in which long has become short and short has become long.
Systematic absences
The most informative part of a diffraction pattern is the part that is not there. A glide plane cancels alternate reflections along a row, exactly, and those missing spots are how a symmetry nobody can see is identified.