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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
GM3
A1''
GM2
1
1
-1
-1
1
-1
GM4
A2''
GM3
1
-1
1
-1
1
-1
GM2
A2'
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 Bradley CJ and Cracknell AP, (1972) The Mathematical Theory of Symmetry in Solids. Oxford: Clarendon Press.
(2): Notation of the irreps according to Bradley CJ and Cracknell AP, (1972) The Mathematical Theory of Symmetry in Solids. Oxford: Clarendon Press, based on Mulliken RS (1933) Phys. Rev. 43, 279-302.
(3): Notation of the irreps according to A. P. Cracknell, B. L. Davies, S. C. Miller and W. F. Love (1979) Kronecher Product Tables, 1, General Introduction and Tables of Irreducible Representations of Space groups. New York: IFI/Plenum, 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

The number in parentheses after the label of the irrep indicates the "reality" of the irrep: (1) for real, (-1) for pseudoreal and (0) for complex representations.

N
Matrix presentation
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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