C1 carries 1 symmetry operation in 1 class, and no axis of rotation above the identity. A character table of the group therefore has 1 column and as many irreducible representations.
It contains only proper rotations, so a molecule in it is chiral and optically active. It leaves a direction invariant, so a molecule in it may carry a permanent dipole.
In Hermann-Mauguin notation it is 1, and it is one of the crystal classes of the triclinic system. A diffraction pattern from a crystal in it shows the Laue symmetry -1.
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: