a nonsymmorphic space group
A nonsymmorphic space group is one that ESSENTIALLY contains a screw axis or a glide plane — a symmetry that only works because a fractional lattice translation is baked into it. You cannot get rid of that translation by any clever choice of origin; it is intrinsic. Of the 230 space groups, 157 are nonsymmorphic (the other 73 are the simple, symmorphic ones).
Here is the precise test. In a symmorphic group there is an origin at which every symmetry operation becomes a pure point operation (rotation, mirror, inversion) with no translation attached. In a nonsymmorphic group there is no such origin: at least one operation stubbornly keeps a fractional translation no matter where you put the origin — that is the signature of an essential screw or glide. The symbol shows it plainly: subscripts like 2_1, 4_1 or 6_3, or glide letters a, b, c, n, d. Examples are P2_1/c, Pnma, P6_3/mmc and diamond's Fd-3m (whose d is a diamond glide).
Nonsymmorphic symmetry is not a mere bookkeeping detail — it has physical bite. It forces particular systematic absences in diffraction (the classic way to detect a screw or glide), and in the electronic structure it can force bands to stick together in unavoidable degeneracies at the Brillouin-zone boundary, a fact now central to the physics of topological materials. And it is common: P2_1/c, the most frequently observed space group for organic molecular crystals, is nonsymmorphic.
Diamond has space group Fd-3m, nonsymmorphic because of its d-glide. That glide is exactly what threads the two interpenetrating carbon sublattices together and gives diamond its distinctive systematic absences.
Nonsymmorphic: an essential screw or glide that no origin choice can remove.
A screw or glide in a symbol does not automatically make the group nonsymmorphic if a different setting could remove it — but for the standard-setting symbols in the International Tables, a visible subscript or glide letter does mean nonsymmorphic. The 73 versus 157 split is exact.