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Irreducible representations of the Point Group m3 (No. 29)

Table of characters

(1)
(2)
(3)
C1
C2
C3
C4
C5
C6
C7
C8
GM1+
Ag
GM1+
1
1
1
1
1
1
1
1
GM1-
1Au
GM1-
1
1
1
1
-1
-1
-1
-1
GM2+
1Eg
GM2+
1
1
-(1+i3)/2
-(1-i3)/2
1
1
-(1+i3)/2
-(1-i3)/2
GM2-
1Eu
GM2-
1
1
-(1+i3)/2
-(1-i3)/2
-1
-1
(1+i3)/2
(1-i3)/2
GM3+
2Eg
GM3+
1
1
-(1-i3)/2
-(1+i3)/2
1
1
-(1-i3)/2
-(1+i3)/2
GM3-
2Eu
GM3-
1
1
-(1-i3)/2
-(1+i3)/2
-1
-1
(1-i3)/2
(1+i3)/2
GM4+
Tg
GM4+
3
-1
0
0
3
-1
0
0
GM4-
Tu
GM4-
3
-1
0
0
-3
1
0
0
(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, 2010, 2100
C3: 3--11-1, 3-1-1-1, 3--1-11, 3-111
C4: 3+1-1-1, 3+-1-11, 3+-11-1, 3+111
C5: -1
C6: m001, m010, m100
C7: -3--11-1, -3-1-1-1, -3--1-11, -3-111
C8: -3+1-1-1, -3+-1-11, -3+-11-1, -3+111

Matrices of the representations of the group

N
General position
Seitz Symbol
GM1+(1)
GM1-(1)
GM2+(0)
GM2-(0)
GM3+(0)
GM3-(0)
GM4+(1)
GM4-(1)
1
(
1 0 0
0 1 0
0 0 1
)
1
1
1
1
1
1
1
(
1 0 0
0 1 0
0 0 1
)
(
1 0 0
0 1 0
0 0 1
)
2
(
-1 0 0
0 -1 0
0 0 1
)
2001
1
1
1
1
1
1
(
1 0 0
0 -1 0
0 0 -1
)
(
1 0 0
0 -1 0
0 0 -1
)
3
(
-1 0 0
0 1 0
0 0 -1
)
2010
1
1
1
1
1
1
(
-1 0 0
0 -1 0
0 0 1
)
(
-1 0 0
0 -1 0
0 0 1
)
4
(
1 0 0
0 -1 0
0 0 -1
)
2100
1
1
1
1
1
1
(
-1 0 0
0 1 0
0 0 -1
)
(
-1 0 0
0 1 0
0 0 -1
)
5
(
0 0 1
1 0 0
0 1 0
)
3+111
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
(
0 0 1
1 0 0
0 1 0
)
(
0 0 1
1 0 0
0 1 0
)
6
(
0 0 1
-1 0 0
0 -1 0
)
3+111
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
(
0 0 -1
1 0 0
0 -1 0
)
(
0 0 -1
1 0 0
0 -1 0
)
7
(
0 0 -1
-1 0 0
0 1 0
)
3+111
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
(
0 0 1
-1 0 0
0 -1 0
)
(
0 0 1
-1 0 0
0 -1 0
)
8
(
0 0 -1
1 0 0
0 -1 0
)
3+111
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
(
0 0 -1
-1 0 0
0 1 0
)
(
0 0 -1
-1 0 0
0 1 0
)
9
(
0 1 0
0 0 1
1 0 0
)
3-111
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
(
0 1 0
0 0 1
1 0 0
)
(
0 1 0
0 0 1
1 0 0
)
10
(
0 -1 0
0 0 1
-1 0 0
)
3-111
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
(
0 -1 0
0 0 -1
1 0 0
)
(
0 -1 0
0 0 -1
1 0 0
)
11
(
0 1 0
0 0 -1
-1 0 0
)
3-111
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
(
0 -1 0
0 0 1
-1 0 0
)
(
0 -1 0
0 0 1
-1 0 0
)
12
(
0 -1 0
0 0 -1
1 0 0
)
3-111
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
(
0 1 0
0 0 -1
-1 0 0
)
(
0 1 0
0 0 -1
-1 0 0
)
13
(
-1 0 0
0 -1 0
0 0 -1
)
1
1
-1
1
-1
1
-1
(
1 0 0
0 1 0
0 0 1
)
(
-1 0 0
0 -1 0
0 0 -1
)
14
(
1 0 0
0 1 0
0 0 -1
)
m001
1
-1
1
-1
1
-1
(
1 0 0
0 -1 0
0 0 -1
)
(
-1 0 0
0 1 0
0 0 1
)
15
(
1 0 0
0 -1 0
0 0 1
)
m010
1
-1
1
-1
1
-1
(
-1 0 0
0 -1 0
0 0 1
)
(
1 0 0
0 1 0
0 0 -1
)
16
(
-1 0 0
0 1 0
0 0 1
)
m100
1
-1
1
-1
1
-1
(
-1 0 0
0 1 0
0 0 -1
)
(
1 0 0
0 -1 0
0 0 1
)
17
(
0 0 -1
-1 0 0
0 -1 0
)
3+111
1
-1
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
(
0 0 1
1 0 0
0 1 0
)
(
0 0 -1
-1 0 0
0 -1 0
)
18
(
0 0 -1
1 0 0
0 1 0
)
3+111
1
-1
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
(
0 0 -1
1 0 0
0 -1 0
)
(
0 0 1
-1 0 0
0 1 0
)
19
(
0 0 1
1 0 0
0 -1 0
)
3+111
1
-1
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
(
0 0 1
-1 0 0
0 -1 0
)
(
0 0 -1
1 0 0
0 1 0
)
20
(
0 0 1
-1 0 0
0 1 0
)
3+111
1
-1
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
(
0 0 -1
-1 0 0
0 1 0
)
(
0 0 1
1 0 0
0 -1 0
)
21
(
0 -1 0
0 0 -1
-1 0 0
)
3-111
1
-1
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
(
0 1 0
0 0 1
1 0 0
)
(
0 -1 0
0 0 -1
-1 0 0
)
22
(
0 1 0
0 0 -1
1 0 0
)
3-111
1
-1
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
(
0 -1 0
0 0 -1
1 0 0
)
(
0 1 0
0 0 1
-1 0 0
)
23
(
0 -1 0
0 0 1
1 0 0
)
3-111
1
-1
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
(
0 -1 0
0 0 1
-1 0 0
)
(
0 1 0
0 0 -1
1 0 0
)
24
(
0 1 0
0 0 1
-1 0 0
)
3-111
1
-1
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
(
0 1 0
0 0 -1
-1 0 0
)
(
0 -1 0
0 0 1
1 0 0
)
k-Subgroupsmag
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