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Irreducible representations of the Point Group 6 (No. 22)

Table of characters

(1)
(2)
(3)
C1
C2
C3
C4
C5
C6
GM1
A'
GM1
1
1
1
1
1
1
GM4
A''
GM2
1
-1
1
-1
1
-1
GM2
2E'
GM3
1
-(1+i3)/2
-(1+i3)/2
-(1-i3)/2
-(1-i3)/2
1
GM5
2E''
GM4
1
(1+i3)/2
-(1+i3)/2
(1-i3)/2
-(1-i3)/2
-1
GM3
1E'
GM5
1
-(1-i3)/2
-(1-i3)/2
-(1+i3)/2
-(1+i3)/2
1
GM6
1E''
GM6
1
(1-i3)/2
-(1-i3)/2
(1+i3)/2
-(1+i3)/2
-1
(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: -6+001
C3: 3-001
C4: -6-001
C5: 3+001
C6: m001

Matrices of the representations of the group

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