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Irreducible representations of the Point Group 42m (No. 14)

Table of characters

(1)
(2)
(3)
C1
C2
C3
C4
C5
GM1
A1
GM1
1
1
1
1
1
GM3
B1
GM2
1
1
1
-1
-1
GM4
B2
GM3
1
1
-1
1
-1
GM2
A2
GM4
1
1
-1
-1
1
GM5
E
GM5
2
-2
0
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
C3: 2010, 2100
C4: m110, m1-10
C5: -4-001, -4+001

Matrices of the representations of the group

N
General position
Seitz Symbol
GM1(1)
GM2(1)
GM3(1)
GM4(1)
GM5(1)
1
(
1 0 0
0 1 0
0 0 1
)
1
1
1
1
1
(
1 0
0 1
)
2
(
-1 0 0
0 -1 0
0 0 1
)
2001
1
1
1
1
(
-1 0
0 -1
)
3
(
0 1 0
-1 0 0
0 0 -1
)
4+001
1
-1
-1
1
(
0 -1
1 0
)
4
(
0 -1 0
1 0 0
0 0 -1
)
4-001
1
-1
-1
1
(
0 1
-1 0
)
5
(
-1 0 0
0 1 0
0 0 -1
)
2010
1
1
-1
-1
(
0 1
1 0
)
6
(
1 0 0
0 -1 0
0 0 -1
)
2100
1
1
-1
-1
(
0 -1
-1 0
)
7
(
0 -1 0
-1 0 0
0 0 1
)
m110
1
-1
1
-1
(
1 0
0 -1
)
8
(
0 1 0
1 0 0
0 0 1
)
m110
1
-1
1
-1
(
-1 0
0 1
)
k-Subgroupsmag
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