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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 C. J. Bradley, A. P. Cracknell, The Mathematical Theory of Symmetry in Solids (Clarendon Press, Oxford, 1972) 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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