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Irreducible representations of the Point Group 3m (No. 19)

Table of characters

(1)
(2)
(3)
C1
C2
C3
GM1
A1
GM1
1
1
1
GM2
A2
GM2
1
-1
1
GM3
E
GM3
2
0
-1
(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: m210, m1-10, m120
C3: 3-001, 3+001

Matrices of the representations of the group

N
General position
Seitz Symbol
GM1(1)
GM2(1)
GM3(1)
1
(
1 0 0
0 1 0
0 0 1
)
1
1
1
(
1 0
0 1
)
2
(
0 -1 0
1 -1 0
0 0 1
)
3+001
1
1
(
ei2π/3 0
0 e-i2π/3
)
3
(
-1 1 0
-1 0 0
0 0 1
)
3-001
1
1
(
e-i2π/3 0
0 ei2π/3
)
4
(
0 1 0
1 0 0
0 0 1
)
m110
1
-1
(
0 1
1 0
)
5
(
1 -1 0
0 -1 0
0 0 1
)
m120
1
-1
(
0 e-i2π/3
ei2π/3 0
)
6
(
-1 0 0
-1 1 0
0 0 1
)
m210
1
-1
(
0 ei2π/3
e-i2π/3 0
)
k-Subgroupsmag
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