P-4 is number 81 of the 230 space groups: a primitive tetragonal lattice carrying the point-group class -4. A general position in its cell is repeated 4 times.
It holds an improper operation, so a single enantiomer cannot crystallise in it. It is symmorphic: some origin removes every glide plane and screw axis.
A diffraction pattern from a crystal in it shows the Laue symmetry 4/m, so that is the most the symmetry of the intensities can tell you before the structure is solved.
Molecular point groups with their operations and character tables, the 230 space groups with a cell builder, and the 17 wallpaper and 7 frieze groups drawn live. The tool needs JavaScript, and WebGL2 for the 3D views; these are the pages it offers: