A condensed set of information for each point group
The character tables present all of the symmetry operations and the irreducible representations, which form the basis vectors in the space of the point group. By decomposing a molecular basis into these irreducible representations one can determine which linear combinations are appropriate given the symmetry of the molecule. This can applied to linear combinations of atomic orbitals or linear combinations of bonds and angle bends etc. needed to make normal modes of vibration. The character tables also tell the user at a glance how various functional forms (including linear and quadratic transform in the point group.XXX
