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Irreducible representations of the Point Group 4/m (No. 11)

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-
Au
GM1-
1
1
1
1
-1
-1
-1
-1
GM2+
Bg
GM2+
1
1
-1
-1
1
1
-1
-1
GM2-
Bu
GM2-
1
1
-1
-1
-1
-1
1
1
GM3+
2Eg
GM3+
1
-1
i
-i
1
-1
i
-i
GM3-
2Eu
GM3-
1
-1
i
-i
-1
1
-i
i
GM4+
1Eg
GM4+
1
-1
-i
i
1
-1
-i
i
GM4-
1Eu
GM4-
1
-1
-i
i
-1
1
i
-i
(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: 4+001
C4: 4-001
C5: -1
C6: m001
C7: -4+001
C8: -4-001

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)
1
(
1 0 0
0 1 0
0 0 1
)
1
1
1
1
1
1
1
1
1
2
(
-1 0 0
0 -1 0
0 0 1
)
2001
1
1
1
1
-1
-1
-1
-1
3
(
0 -1 0
1 0 0
0 0 1
)
4+001
1
1
-1
-1
i
i
-i
-i
4
(
0 1 0
-1 0 0
0 0 1
)
4-001
1
1
-1
-1
-i
-i
i
i
5
(
-1 0 0
0 -1 0
0 0 -1
)
1
1
-1
1
-1
1
-1
1
-1
6
(
1 0 0
0 1 0
0 0 -1
)
m001
1
-1
1
-1
-1
1
-1
1
7
(
0 1 0
-1 0 0
0 0 -1
)
4+001
1
-1
-1
1
i
-i
-i
i
8
(
0 -1 0
1 0 0
0 0 -1
)
4-001
1
-1
-1
1
-i
i
i
-i
k-Subgroupsmag
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