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Irreducible representations of the Point Group 3 (No. 17)

Table of characters

(1)
(2)
(3)
C1
C2
C3
C4
C5
C6
GM1+
A1g
GM1+
1
1
1
1
1
1
GM1-
A1u
GM1-
1
1
1
-1
-1
-1
GM2+
2Eg
GM2+
1
-(1+i3)/2
-(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
GM2-
2Eu
GM2-
1
-(1+i3)/2
-(1-i3)/2
-1
(1+i3)/2
(1-i3)/2
GM3+
1Eg
GM3+
1
-(1-i3)/2
-(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
GM3-
1Eu
GM3-
1
-(1-i3)/2
-(1+i3)/2
-1
(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: 3-001
C3: 3+001
C4: -1
C5: -3-001
C6: -3+001

Matrices of the representations of the group

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