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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 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: m210, m1-10, m120
C3: 3-001, 3+001

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)
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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