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Irreducible representations of the Point Group 6 (No. 21)

Table of characters

(1)
(2)
(3)
C1
C2
C3
C4
C5
C6
GM1
A
GM1
1
1
1
1
1
1
GM4
B
GM2
1
-1
1
1
-1
-1
GM5
2E1
GM3
1
1
-(1+i3)/2
-(1-i3)/2
-(1-i3)/2
-(1+i3)/2
GM2
2E2
GM4
1
-1
-(1+i3)/2
-(1-i3)/2
(1-i3)/2
(1+i3)/2
GM6
1E1
GM5
1
1
-(1-i3)/2
-(1+i3)/2
-(1+i3)/2
-(1-i3)/2
GM3
1E2
GM6
1
-1
-(1-i3)/2
-(1+i3)/2
(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: 2001
C3: 3-001
C4: 3+001
C5: 6-001
C6: 6+001

List of pairs of conjugated irreducible representations

(GM3,GM5)
(GM4,GM6)
Matrices of the representations of the group

N
General position
Seitz Symbol
GM1(1)
GM2(1)
GM3(0)
GM4(0)
GM5(0)
GM6(0)
1
(
1 0 0
0 1 0
0 0 1
)
1
1
1
1
1
1
1
2
(
0 -1 0
1 -1 0
0 0 1
)
3+001
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
3
(
-1 1 0
-1 0 0
0 0 1
)
3-001
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
4
(
-1 0 0
0 -1 0
0 0 1
)
2001
1
-1
1
-1
1
-1
5
(
0 1 0
-1 1 0
0 0 1
)
6-001
1
-1
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
6
(
1 -1 0
1 0 0
0 0 1
)
6+001
1
-1
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
k-Subgroupsmag
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