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Irreducible representations of the Point Group 6/m (No. 23)

Table of characters

(1)
(2)
(3)
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
C12
GM1+
Ag
GM1+
1
1
1
1
1
1
1
1
1
1
1
1
GM1-
Au
GM1-
1
1
1
1
1
1
-1
-1
-1
-1
-1
-1
GM4+
Bg
GM2+
1
-1
1
1
-1
-1
1
-1
1
1
-1
-1
GM4-
Bu
GM2-
1
-1
1
1
-1
-1
-1
1
-1
-1
1
1
GM5+
2E1g
GM3+
1
1
-(1+i3)/2
-(1-i3)/2
-(1-i3)/2
-(1+i3)/2
1
1
-(1+i3)/2
-(1-i3)/2
-(1-i3)/2
-(1+i3)/2
GM5-
2E1u
GM3-
1
1
-(1+i3)/2
-(1-i3)/2
-(1-i3)/2
-(1+i3)/2
-1
-1
(1+i3)/2
(1-i3)/2
(1-i3)/2
(1+i3)/2
GM2+
2E2g
GM4+
1
-1
-(1+i3)/2
-(1-i3)/2
(1-i3)/2
(1+i3)/2
1
-1
-(1+i3)/2
-(1-i3)/2
(1-i3)/2
(1+i3)/2
GM2-
2E2u
GM4-
1
-1
-(1+i3)/2
-(1-i3)/2
(1-i3)/2
(1+i3)/2
-1
1
(1+i3)/2
(1-i3)/2
-(1-i3)/2
-(1+i3)/2
GM6+
1E1g
GM5+
1
1
-(1-i3)/2
-(1+i3)/2
-(1+i3)/2
-(1-i3)/2
1
1
-(1-i3)/2
-(1+i3)/2
-(1+i3)/2
-(1-i3)/2
GM6-
1E1u
GM5-
1
1
-(1-i3)/2
-(1+i3)/2
-(1+i3)/2
-(1-i3)/2
-1
-1
(1-i3)/2
(1+i3)/2
(1+i3)/2
(1-i3)/2
GM3+
1E2g
GM6+
1
-1
-(1-i3)/2
-(1+i3)/2
(1+i3)/2
(1-i3)/2
1
-1
-(1-i3)/2
-(1+i3)/2
(1+i3)/2
(1-i3)/2
GM3-
1E2u
GM6-
1
-1
-(1-i3)/2
-(1+i3)/2
(1+i3)/2
(1-i3)/2
-1
1
(1-i3)/2
(1+i3)/2
-(1+i3)/2
-(1-i3)/2
(1): Notation of the irreps according to Koster GF, Dimmok JO, Wheeler RG and Statz H, (1963) Properties of the thirty-two point groups, M.I.T. Press, Cambridge, Mass.
(2): Notation of the irreps according to Mulliken RS (1933) Phys. Rev. 43, 279-302.
(3): Notation of the irreps according to H. T. Stokes, B. J. Campbell, and R. Cordes (2013) Acta Cryst. A. 69, 388-395 for the GM point.

Lists of symmetry operations in the conjugacy classes

C1: 1
C2: 2001
C3: 3-001
C4: 3+001
C5: 6-001
C6: 6+001
C7: -1
C8: m001
C9: -3-001
C10: -3+001
C11: -6-001
C12: -6+001

Matrices of the representations of the group

N
General position
Seitz Symbol
GM1+(1)
GM1-(1)
GM2+(1)
GM2-(1)
GM3+(0)
GM3-(0)
GM4+(0)
GM4-(0)
GM5+(0)
GM5-(0)
GM6+(0)
GM6-(0)
1
(
1 0 0
0 1 0
0 0 1
)
1
1
1
1
1
1
1
1
1
1
1
1
1
2
(
0 -1 0
1 -1 0
0 0 1
)
3+001
1
1
1
1
ei2π/3
ei2π/3
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
e-i2π/3
e-i2π/3
3
(
-1 1 0
-1 0 0
0 0 1
)
3-001
1
1
1
1
e-i2π/3
e-i2π/3
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
ei2π/3
ei2π/3
4
(
-1 0 0
0 -1 0
0 0 1
)
2001
1
1
-1
-1
1
1
-1
-1
1
1
-1
-1
5
(
0 1 0
-1 1 0
0 0 1
)
6-001
1
1
-1
-1
ei2π/3
ei2π/3
e-iπ/3
e-iπ/3
e-i2π/3
e-i2π/3
eiπ/3
eiπ/3
6
(
1 -1 0
1 0 0
0 0 1
)
6+001
1
1
-1
-1
e-i2π/3
e-i2π/3
eiπ/3
eiπ/3
ei2π/3
ei2π/3
e-iπ/3
e-iπ/3
7
(
-1 0 0
0 -1 0
0 0 -1
)
1
1
-1
1
-1
1
-1
1
-1
1
-1
1
-1
8
(
0 1 0
-1 1 0
0 0 -1
)
3+001
1
-1
1
-1
ei2π/3
e-iπ/3
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
e-i2π/3
eiπ/3
9
(
1 -1 0
1 0 0
0 0 -1
)
3-001
1
-1
1
-1
e-i2π/3
eiπ/3
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
ei2π/3
e-iπ/3
10
(
1 0 0
0 1 0
0 0 -1
)
m001
1
-1
-1
1
1
-1
-1
1
1
-1
-1
1
11
(
0 -1 0
1 -1 0
0 0 -1
)
6-001
1
-1
-1
1
ei2π/3
e-iπ/3
e-iπ/3
ei2π/3
e-i2π/3
eiπ/3
eiπ/3
e-i2π/3
12
(
-1 1 0
-1 0 0
0 0 -1
)
6+001
1
-1
-1
1
e-i2π/3
eiπ/3
eiπ/3
e-i2π/3
ei2π/3
e-iπ/3
e-iπ/3
ei2π/3
k-Subgroupsmag
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