A Point Group Character Tables 483 Table A.19.Character table for group C6(hexagonal) C6(6) E Ce C3 C2 C ci x2+y2,22 R:,z A 1 1 1 1 1 1 B -1 -1 1 -1 1 w3 ws (x2,y2) (x,) E w3 (Rx,Ry)」 1 wi w3 w (x2-y2,xy) 1 3 1 3 w=e2mi/6 Table A.20.Character table for group Cev(hexagonal) C6e (6mm) E C2 2C3 2C6 30d 30u x2+y2,22 A 1 1 1 1 1 R A2 1 1 1 1 -1 -1 B1 1 -1 1 -1 -1 1 B2 1 -1 1 -1 1 -1 (xz,yz) (,y） E 2 -2 -1 1 0 (R=,Ru) 0 (x2-2,x) E2 2 2 -1 -1 0 Ceh =C6i (6/m)(hexagonal); S6=C3⑧i(③)(rhombohedral) Table A.21.Character table for group D6 (hexagonal) D6(622) E C2 2C3 2C6 3C%3C x2+2,2 A 1 1 1 1 1 R=,2 A2 1 1 1 1 -1 -1 B1 1 -1 -1 -1 B2 1 -1 -1 -1 1 (xz,yz) (x,） E 2 -2 -1 1 0 0 (Rx,Rg） (x2-y2,xy) E2 2 2 -1 -1 0 0 Deh =D6 i(6/mmm)(hexagonal) Table A.22.Character table for group Cs (icosahedral) C5(5) E Cs C号 c C x2+y2,z2 R=,z A 1 1 1 1 1 (xz,yz) (x,） E (1 w3 (Rz,Ru) w w3 w (x2-y2,x) Ew w2 1 w w=e2ri/5.Note group Csh =Cs h=S10(10)A Point Group Character Tables 483 Table A.19. Character table for group C6 (hexagonal) C6 (6) E C6 C3 C2 C2 3 C5 6 x2 + y2, z2 Rz, z A 111111 B 1 −1 1 −1 1 −1 (xz, yz) (x, y) (Rx, Ry) " E (1 1 ω ω5 ω2 ω4 ω3 ω3 ω4 ω2 ω5 ω (x2 − y2, xy) E (1 1 ω2 ω4 ω4 ω2 1 1 ω2 ω4 ω4 ω2 ω = e2πi/6 Table A.20. Character table for group C6v (hexagonal) C6v (6mm) E C2 2C3 2C6 3σd 3σv x2 + y2, z2 z A1 11 1 1 1 1 Rz A2 11 1 1 −1 −1 B1 1 −1 1 −1 −1 1 B2 1 −1 1 −1 1 –1 (xz, yz) (x, y) (Rx, Ry) " E1 2 −2 −1 100 (x2 − y2, xy) E2 2 2 −1 −100 C6h = C6 ⊗ i (6/m) (hexagonal); S6 = C3 ⊗ i (3) (rhombohedral) Table A.21. Character table for group D6 (hexagonal) D6 (622) E C2 2C3 2C6 3C 2 3C 2 x2 + y2, z2 A1 11 1 1 1 1 Rz, z A2 11 1 1 −1 −1 B1 1 −1 1 −1 1 −1 B2 1 −1 1 −1 −1 1 (xz, yz) (x, y) (Rx, Ry) " E1 2 −2 −110 0 (x2 − y2, xy) E2 2 2 −1 −10 0 D6h = D6 ⊗ i (6/mmm) (hexagonal) Table A.22. Character table for group C5 (icosahedral) C5 (5) E C5 C2 5 C3 5 C4 5 x2 + y2, z2 Rz, z A 11111 (xz, yz) (x, y) (Rx, Ry) " E ( 1 1 ω ω4 ω2 ω3 ω3 ω2 ω4 ω (x2 − y2, xy) E ( 1 1 ω2 ω3 ω4 ω ω ω4 ω3 ω2 ω = e2πi/5. Note group C5h = C5 ⊗ σh = S10(10)