D4d carries 16 symmetry operations in 7 classes, around a principal axis of order 4. A character table of the group therefore has 7 columns and as many irreducible representations.
It contains an improper operation, so no molecule in it is chiral. No direction is left invariant, so a molecule in it has no permanent dipole.
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: