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Irreducible representations of the Point Group 3 (No. 16)

Table of characters

(1)
(2)
(3)
C1
C2
C3
GM1
A1
GM1
1
1
1
GM2
2E
GM2
1
-(1+i3)/2
-(1-i3)/2
GM3
1E
GM3
1
-(1-i3)/2
-(1+i3)/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: 3-001
C3: 3+001

List of pairs of conjugated irreducible representations

(GM2,GM3)
Matrices of the representations of the group

N
General position
Seitz Symbol
GM1(1)
GM2(0)
GM3(0)
1
(
1 0 0
0 1 0
0 0 1
)
1
1
1
1
2
(
0 -1 0
1 -1 0
0 0 1
)
3+001
1
ei2π/3
e-i2π/3
3
(
-1 1 0
-1 0 0
0 0 1
)
3-001
1
e-i2π/3
ei2π/3
k-Subgroupsmag
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