## Character table for point group S8

=exp(2i/8)
 S8 E S8 C4 (z) (S8)3 C2 (S8)5 (C4)3 (S8)7 linear functions,rotations quadraticfunctions cubicfunctions A +1 +1 +1 +1 +1 +1 +1 +1 Rz x2+y2, z2 - B +1 -1 +1 -1 +1 -1 +1 -1 z - z3, z(x2+y2) E1 +1+1 ++* +i-i -*- -1-1 --* -i+i +*+ x+iy x-iy - (xz2, yz2) [x(x2+y2), y(x2+y2)] E2 +1+1 +i-i -1-1 -i+i +1+1 +i-i -1-1 -i+i - (x2-y2, xy) [xyz, z(x2-y2)] E3 +1+1 --* +i-i +*+ -1-1 ++* -i+i -*- Rx+iRyRx-iRy (xz, yz) [y(3x2-y2), x(x2-3y2)]

 C2 , C4 Number of symmetry elements h = 8 Number of irreducible representations n = 8 Number of real irreducible representations n = 5 Abelian group yes Number of subgroups 2 Subgroups Optical Isomerism (Chirality) no Polar no

## Reduction formula for point group S8

Type of representation

Information for point groups with complex irreducible representations

general 3N vib

E S8 C4 (z) (S8)3 C2 (S8)5 (C4)3 (S8)7

## Multipoles

dipole (p) B+E1 A+E2+E3 B+E1+E2+E3 A+2B+E1+E2+E3 2A+B+E1+E2+2E3 A+2B+2E1+2E2+E3 2A+B+2E1+2E2+2E3 3A+2B+2E1+2E2+2E3 2A+3B+3E1+2E2+2E3