Character table for point group S12

=exp(2i/12)
 S12 E S12 C6 S4 C3 (S12)5 C2 (S12)7 (C3)2 (S4)3 (C6)5 (S12)11 linear functions,rotations quadraticfunctions cubicfunctions A +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 Rz z2, x2+y2 - B +1 -1 +1 -1 +1 -1 +1 -1 +1 -1 +1 -1 z - z3, z(x2+y2) E1 +1+1 ++* +2+2* +i-i -2*-2 -*- -1-1 --* -2-2* -i+i +2*+2 +*+ x+iy x-iy - (xz2, yz2) [x(x2+y2), y(x2+y2)] E2 +1+1 +2+2* -2*+2 -1-1 -2-2* +2*+2 +1+1 +2+2* -2*-2 -1-1 -2-2* +2*+2 - (x2-y2, xy) - E3 +1+1 +i-i -1-1 -i+i +1+1 +i-i -1-1 -i+i +1+1 +i-i -1-1 -i+i - - [x(x2-3y2), y(3x2-y2)] E4 +1+1 -2*-2 -2-2* +1+1 -2*-2 -2-2* +1+1 -2*-2 -2-2* +1+1 -2*-2 -2-2* - - [xyz, z(x2-y2)] E5 +1+1 -*+ +2*+2 +i-i -2+2* ++* -1-1 +*+ -2*-2 -i+i +2+2* --* Rx-iRyRx+iRy (xz, yz) -

 C2 , C3 , C6 , S4 Number of symmetry elements h = 12 Number of irreducible representations n = 12 Number of real irreducible representations n = 7 Abelian group yes Number of subgroups 4 Subgroups Optical Isomerism (Chirality) no Polar no

Reduction formula for point group S12

Type of representation

Information for point groups with complex irreducible representations

general 3N vib

E S12 C6 S4 C3 (S12)5 C2 (S12)7 (C3)2 (S4)3 (C6)5 (S12)11

Multipoles

dipole (p) B+E1 A+E2+E5 B+E1+E3+E4 A+E2+E3+E4+E5 B+E1+E2+E3+E4+E5 A+2B+E1+E2+E3+E4+E5 2A+B+E1+E2+E3+E4+2E5 A+2B+2E1+E2+E3+2E4+E5 2A+B+E1+2E2+2E3+E4+2E5