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Irreducible representations of the Point Group 62m (No. 26)

Table of characters

(1)
(2)
(3)
C1
C2
C3
C4
C5
C6
GM1
A1'
GM1
1
1
1
1
1
1
GM2
A2'
GM2
1
1
-1
-1
1
-1
GM4
A2''
GM3
1
-1
1
-1
1
-1
GM3
A1''
GM4
1
-1
-1
1
1
1
GM6
E'
GM5
2
0
0
-1
-1
2
GM5
E''
GM6
2
0
0
1
-1
-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: 2010, 2110, 2100
C3: m210, m1-10, m120
C4: -6+001, -6-001
C5: 3-001, 3+001
C6: m001

Matrices of the representations of the group

N
General position
Seitz Symbol
GM1(1)
GM2(1)
GM3(1)
GM4(1)
GM5(1)
GM6(1)
1
(
1 0 0
0 1 0
0 0 1
)
1
1
1
1
1
(
1 0
0 1
)
(
1 0
0 1
)
2
(
0 -1 0
1 -1 0
0 0 1
)
3+001
1
1
1
1
(
ei2π/3 0
0 e-i2π/3
)
(
ei2π/3 0
0 e-i2π/3
)
3
(
-1 1 0
-1 0 0
0 0 1
)
3-001
1
1
1
1
(
e-i2π/3 0
0 ei2π/3
)
(
e-i2π/3 0
0 ei2π/3
)
4
(
1 0 0
0 1 0
0 0 -1
)
m001
1
-1
-1
1
(
1 0
0 1
)
(
-1 0
0 -1
)
5
(
0 -1 0
1 -1 0
0 0 -1
)
6-001
1
-1
-1
1
(
ei2π/3 0
0 e-i2π/3
)
(
e-iπ/3 0
0 eiπ/3
)
6
(
-1 1 0
-1 0 0
0 0 -1
)
6+001
1
-1
-1
1
(
e-i2π/3 0
0 ei2π/3
)
(
eiπ/3 0
0 e-iπ/3
)
7
(
0 1 0
1 0 0
0 0 -1
)
2110
1
1
-1
-1
(
0 1
1 0
)
(
0 1
1 0
)
8
(
1 -1 0
0 -1 0
0 0 -1
)
2100
1
1
-1
-1
(
0 e-i2π/3
ei2π/3 0
)
(
0 e-i2π/3
ei2π/3 0
)
9
(
-1 0 0
-1 1 0
0 0 -1
)
2010
1
1
-1
-1
(
0 ei2π/3
e-i2π/3 0
)
(
0 ei2π/3
e-i2π/3 0
)
10
(
0 1 0
1 0 0
0 0 1
)
m110
1
-1
1
-1
(
0 1
1 0
)
(
0 -1
-1 0
)
11
(
1 -1 0
0 -1 0
0 0 1
)
m120
1
-1
1
-1
(
0 e-i2π/3
ei2π/3 0
)
(
0 eiπ/3
e-iπ/3 0
)
12
(
-1 0 0
-1 1 0
0 0 1
)
m210
1
-1
1
-1
(
0 ei2π/3
e-i2π/3 0
)
(
0 e-iπ/3
eiπ/3 0
)
k-Subgroupsmag
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