On this page you can see the character tables of most of the groups we use. I will try to update the list as soon as I can. You choose a group from the menu and click on Another Group. You can also reduce your own representation G of the group into the irreducible ones for the group by clicking on Reduce. It handles fine the groups with real characters but the ones with complex characters are not developed yet, nor the Cinf, Dinf. you may input your character as numbers or in a form acosb without parenthesis and multiplication sign, where b is in degrees. Please let me know if you find any mistakes. Enjoy ;-)

I don't have that group yet. Try later

All the character tables are presented in the same way: The notation for the symmetry operations is as follows:
E The identity transformation (E coming from the German Einheit, meaning unity).
Cn Rotation (clockwise) through an angle of 2p/n radians, where n is an integer. The axis for which n is greatest is termed the principal axis.
Cnk Rotation (clockwise) through an angle of 2kp/n radians. Both n and k are integers.
Sn An improper rotation (clockwise) through an angle of 2p/n radians. Improper rotations are regular rotations followed by a reflection in the plane perpendicular to the axis of rotation. Also known as alternating axis of symmetry and rotation-reflection axis because Sn= sh Cn= Cnsh
i The inversion operator (the same as S2). In Cartesian coordinates, (x, y, z) --> (-x, -y, -z). Irreducible representations that are even under this symmetry operation are usually denoted with the subscript g for gerade (german=even), and those that are odd are denoted with the subscript u for ungerade (german=odd).
s A mirror plane (from the German word for mirror - Spiegel).
sh Horizontal reflection plane - passing through the origin and perpendicular to the axis with the highest symmetry.
sv Vertical reflection plane - passing through the origin and the axis with the highest symmetry.
sd Diagonal or dihedral reflection in a plane through the origin and the axis with the highest symmetry, but also bisecting the angle between the twofold axes perpendicular to the symmetry axis. This is actually a special case of sv.