192
A Character Tables
A.1 Finite Point Groups
C 1 and the Binary Groups C s ,C i ,C 2
C 1
ˆ
E
A
1
C s
ˆ
E
ˆ
σ h
A ′
11
x,y,R z
x 2 ,y 2 ,z 2 ,xy
A ′′
1
−1
z, R x ,R y
yz,xz
C i
ˆ
E
ˆ
ı
A g
11
R x ,R y ,R z
x 2 ,y 2 ,z 2 ,yz,xz,xy
A u
1
−1
x,y,z
C 2
ˆ
E
ˆ
C
z
2
A
11
z, R z
x 2 ,y 2 ,z 2 ,xy
B
1
−1
x,y,R x ,R y
yz,xz
The Cyclic Groups C n (n = 3, 4, 5, 6, 7, 8)
C 3
ˆ
E
ˆ
C 3
ˆ
C 2
3
ǫ = exp(2πi/3)
A
11
1
z, R z
x 2 + y 2 ,z 2
E
1
ǫ
¯
ǫ
(x, y)(R x ,R y )
(x 2 − y 2 , xy)(yz, xz)
1
¯
ǫǫ
C 4
ˆ
E
ˆ
C 4
ˆ
C 2
ˆ
C 3
4
A
1
111
z, R z
x 2 + y 2 ,z 2
B
1
−11
−1
x 2 − y 2 ,xy
E
1
i
−1
−i
(x, y)(R x ,R y )( y z , x z )
1
−i
−1
i