## Character table for point group C6h

=exp(2i/6)
 C6h E C6(z) C3 C2 (C3)2 (C6)5 i (S3)5 (S6)5 h S6 S3 linear functions,rotations quadraticfunctions cubicfunctions Ag +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 Rz x2+y2, z2 - Bg +1 -1 +1 -1 +1 -1 +1 -1 +1 -1 +1 -1 - - - E1g +1+1 ++* -*- -1-1 --* +*+ +1+1 ++* -*- -1-1 --* +*+ Rx+iRyRx-iRy (xz, yz) - E2g +1+1 -*- --* +1+1 -*- --* +1+1 -*- --* +1+1 -*- --* - (x2-y2, xy) - Au +1 +1 +1 +1 +1 +1 -1 -1 -1 -1 -1 -1 z - z3, z(x2+y2) Bu +1 -1 +1 -1 +1 -1 -1 +1 -1 +1 -1 +1 - - y(3x2-y2), x(x2-3y2) E1u +1+1 ++* -*- -1-1 --* +*+ -1-1 --* +*+ +1+1 ++* -*- x+iyx-iy - (xz2, yz2) [x(x2+y2), y(x2+y2)] E2u +1+1 -*- --* +1+1 -*- --* -1-1 +*+ ++* -1-1 +*+ ++* - - [xyz, z(x2-y2)]

 Cs , Ci , C2 , C3 , C6 , C2h , C3h , S6 Number of symmetry elements h = 12 Number of irreducible representations n = 12 Number of real irreducible representations n = 8 Abelian group yes Number of subgroups 8 Subgroups Optical Isomerism (Chirality) no Polar no

## Reduction formula for point group C6h

Type of representation

Information for point groups with complex irreducible representations

general 3N vib

E C6(z) C3 C2 (C3)2 (C6)5 i (S3)5 (S6)5 h S6 S3

## Multipoles

dipole (p) Au+E1u Ag+E1g+E2g Au+2Bu+E1u+E2u Ag+2Bg+E1g+2E2g Au+2Bu+2E1u+2E2u 3Ag+2Bg+2E1g+2E2g 3Au+2Bu+3E1u+2E2u 3Ag+2Bg+3E1g+3E2g 3Au+4Bu+3E1u+3E2u