Bilbao Crystallographic Server arrow COREPRESENTATIONS PG

Irreducible corepresentations of the Magnetic Point Group 622 (N. 24.1.87)


Table of characters of the unitary symmetry operations


(1)
(2)
(3)
C1
C2
C3
C4
C5
C6
C7
C8
C9
GM1
A1
GM1
1
1
1
1
1
1
1
1
1
GM2
A2
GM2
1
1
1
1
-1
-1
1
1
1
GM4
B2
GM3
1
1
-1
-1
1
-1
1
1
-1
GM3
B1
GM4
1
1
-1
-1
-1
1
1
1
-1
GM6
E2
GM5
2
-1
2
-1
0
0
2
-1
-1
GM5
E1
GM6
2
-1
-2
1
0
0
2
-1
1
GM9
E3
GM7
2
-2
0
0
0
0
-2
2
0
GM8
E2
GM8
2
1
0
-√3
0
0
-2
-1
√3
GM7
E1
GM9
2
1
0
√3
0
0
-2
-1
-√3
The notation used in this table is an extension to corepresentations of the following notations used for irreducible representations:
(1): Bradley CJ and Cracknell AP, (1972) The Mathematical Theory of Symmetry in Solids. Oxford: Clarendon Press.
(2): Bradley CJ and Cracknell AP, (1972) The Mathematical Theory of Symmetry in Solids. Oxford: Clarendon Press, based on Mulliken RS (1933) Phys. Rev. 43, 279-302.
(3): A. P. Cracknell, B. L. Davies, S. C. Miller and W. F. Love (1979) Kronecher Product Tables, 1, General Introduction and Tables of Irreducible Representations of Space groups. New York: IFI/Plenum, for the GM point.

Lists of unitary symmetry operations in the conjugacy classes

C1: 1
C2: 3+001, 3-001
C3: 2001, d2001
C4: 6-001, 6+001
C5: 2110, 2100, 2010, d2110, d2100, d2010
C6: 2110, 2120, 2210, d2110, d2120, d2210
C7: d1
C8: d3+001, d3-001
C9: d6-001, d6+001

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbolGM1GM2GM3GM4GM5GM6GM7GM8GM9
1
(
 1 0 0
 0 1 0
 0 0 1
)
(
 1 0
 0 1
)
1
1
1
1
1
(
 1 0
 0 1
)
(
 1 0
 0 1
)
(
 1 0
 0 1
)
(
 1 0
 0 1
)
(
 1 0
 0 1
)
2
(
  0 -1  0
  1 -1  0
  0  0  1
)
(
 (1+i√3)/2  0
  0 (1-i√3)/2
)
3+001
1
1
1
1
(
  ei2π/3  0
  0 e-i2π/3
)
(
  ei2π/3  0
  0 e-i2π/3
)
(
 -1  0
  0 -1
)
(
 e-iπ/3  0
  0  eiπ/3
)
(
  eiπ/3  0
  0 e-iπ/3
)
3
(
 -1  1  0
 -1  0  0
  0  0  1
)
(
 (1-i√3)/2  0
  0 (1+i√3)/2
)
3-001
1
1
1
1
(
 e-i2π/3  0
  0  ei2π/3
)
(
 e-i2π/3  0
  0  ei2π/3
)
(
 -1  0
  0 -1
)
(
  eiπ/3  0
  0 e-iπ/3
)
(
 e-iπ/3  0
  0  eiπ/3
)
4
(
 -1  0  0
  0 -1  0
  0  0  1
)
(
 -i  0
  0  i
)
2001
1
1
-1
-1
(
 1 0
 0 1
)
(
 -1  0
  0 -1
)
(
 -i  0
  0  i
)
(
 -i  0
  0  i
)
(
 -i  0
  0  i
)
5
(
  0  1  0
 -1  1  0
  0  0  1
)
(
 (√3-i)/2  0
  0 (√3+i)/2
)
6-001
1
1
-1
-1
(
  ei2π/3  0
  0 e-i2π/3
)
(
 e-iπ/3  0
  0  eiπ/3
)
(
  i  0
  0 -i
)
(
 e-i5π/6  0
  0  ei5π/6
)
(
 e-iπ/6  0
  0  eiπ/6
)
6
(
  1 -1  0
  1  0  0
  0  0  1
)
(
 (√3+i)/2  0
  0 (√3-i)/2
)
6+001
1
1
-1
-1
(
 e-i2π/3  0
  0  ei2π/3
)
(
  eiπ/3  0
  0 e-iπ/3
)
(
 -i  0
  0  i
)
(
  ei5π/6  0
  0 e-i5π/6
)
(
  eiπ/6  0
  0 e-iπ/6
)
7
(
  0  1  0
  1  0  0
  0  0 -1
)
(
  0 -(1+i√3)/2
  (1-i√3)/2  0
)
2110
1
-1
1
-1
(
 0 1
 1 0
)
(
 0 1
 1 0
)
(
  0 -1
  1  0
)
(
  0 -1
  1  0
)
(
  0 -1
  1  0
)
8
(
  1 -1  0
  0 -1  0
  0  0 -1
)
(
  0 -1
  1  0
)
2100
1
-1
1
-1
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0  1
 -1  0
)
(
  0 e-i2π/3
  e-iπ/3  0
)
(
  0 ei2π/3
  eiπ/3  0
)
9
(
 -1  0  0
 -1  1  0
  0  0 -1
)
(
  0 -(1-i√3)/2
  (1+i√3)/2  0
)
2010
1
-1
1
-1
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0 -1
  1  0
)
(
  0  e-iπ/3
 e-i2π/3  0
)
(
  0  eiπ/3
 ei2π/3  0
)
10
(
  0 -1  0
 -1  0  0
  0  0 -1
)
(
  0 -(√3-i)/2
  (√3+i)/2  0
)
21-10
1
-1
-1
1
(
 0 1
 1 0
)
(
  0 -1
 -1  0
)
(
 0 i
 i 0
)
(
 0 i
 i 0
)
(
 0 i
 i 0
)
11
(
 -1  1  0
  0  1  0
  0  0 -1
)
(
  0 -i
 -i  0
)
2120
1
-1
-1
1
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0  eiπ/3
 e-iπ/3  0
)
(
 0 i
 i 0
)
(
  0  e-iπ/6
 e-i5π/6  0
)
(
  0 e-i5π/6
  e-iπ/6  0
)
12
(
  1  0  0
  1 -1  0
  0  0 -1
)
(
  0  (√3+i)/2
 -(√3-i)/2  0
)
2210
1
-1
-1
1
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0 e-iπ/3
  eiπ/3  0
)
(
 0 i
 i 0
)
(
  0 e-i5π/6
  e-iπ/6  0
)
(
  0  e-iπ/6
 e-i5π/6  0
)
13
(
 1 0 0
 0 1 0
 0 0 1
)
(
 -1  0
  0 -1
)
d1
1
1
1
1
(
 1 0
 0 1
)
(
 1 0
 0 1
)
(
 -1  0
  0 -1
)
(
 -1  0
  0 -1
)
(
 -1  0
  0 -1
)
14
(
  0 -1  0
  1 -1  0
  0  0  1
)
(
 -(1+i√3)/2  0
  0 -(1-i√3)/2
)
d3+001
1
1
1
1
(
  ei2π/3  0
  0 e-i2π/3
)
(
  ei2π/3  0
  0 e-i2π/3
)
(
 1 0
 0 1
)
(
  ei2π/3  0
  0 e-i2π/3
)
(
 e-i2π/3  0
  0  ei2π/3
)
15
(
 -1  1  0
 -1  0  0
  0  0  1
)
(
 -(1-i√3)/2  0
  0 -(1+i√3)/2
)
d3-001
1
1
1
1
(
 e-i2π/3  0
  0  ei2π/3
)
(
 e-i2π/3  0
  0  ei2π/3
)
(
 1 0
 0 1
)
(
 e-i2π/3  0
  0  ei2π/3
)
(
  ei2π/3  0
  0 e-i2π/3
)
16
(
 -1  0  0
  0 -1  0
  0  0  1
)
(
  i  0
  0 -i
)
d2001
1
1
-1
-1
(
 1 0
 0 1
)
(
 -1  0
  0 -1
)
(
  i  0
  0 -i
)
(
  i  0
  0 -i
)
(
  i  0
  0 -i
)
17
(
  0  1  0
 -1  1  0
  0  0  1
)
(
 -(√3-i)/2  0
  0 -(√3+i)/2
)
d6-001
1
1
-1
-1
(
  ei2π/3  0
  0 e-i2π/3
)
(
 e-iπ/3  0
  0  eiπ/3
)
(
 -i  0
  0  i
)
(
  eiπ/6  0
  0 e-iπ/6
)
(
  ei5π/6  0
  0 e-i5π/6
)
18
(
  1 -1  0
  1  0  0
  0  0  1
)
(
 -(√3+i)/2  0
  0 -(√3-i)/2
)
d6+001
1
1
-1
-1
(
 e-i2π/3  0
  0  ei2π/3
)
(
  eiπ/3  0
  0 e-iπ/3
)
(
  i  0
  0 -i
)
(
 e-iπ/6  0
  0  eiπ/6
)
(
 e-i5π/6  0
  0  ei5π/6
)
19
(
  0  1  0
  1  0  0
  0  0 -1
)
(
  0  (1+i√3)/2
 -(1-i√3)/2  0
)
d2110
1
-1
1
-1
(
 0 1
 1 0
)
(
 0 1
 1 0
)
(
  0  1
 -1  0
)
(
  0  1
 -1  0
)
(
  0  1
 -1  0
)
20
(
  1 -1  0
  0 -1  0
  0  0 -1
)
(
  0  1
 -1  0
)
d2100
1
-1
1
-1
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0 -1
  1  0
)
(
  0  eiπ/3
 ei2π/3  0
)
(
  0  e-iπ/3
 e-i2π/3  0
)
21
(
 -1  0  0
 -1  1  0
  0  0 -1
)
(
  0  (1-i√3)/2
 -(1+i√3)/2  0
)
d2010
1
-1
1
-1
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0  1
 -1  0
)
(
  0 ei2π/3
  eiπ/3  0
)
(
  0 e-i2π/3
  e-iπ/3  0
)
22
(
  0 -1  0
 -1  0  0
  0  0 -1
)
(
  0  (√3-i)/2
 -(√3+i)/2  0
)
d21-10
1
-1
-1
1
(
 0 1
 1 0
)
(
  0 -1
 -1  0
)
(
  0 -i
 -i  0
)
(
  0 -i
 -i  0
)
(
  0 -i
 -i  0
)
23
(
 -1  1  0
  0  1  0
  0  0 -1
)
(
 0 i
 i 0
)
d2120
1
-1
-1
1
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0  eiπ/3
 e-iπ/3  0
)
(
  0 -i
 -i  0
)
(
  0 ei5π/6
  eiπ/6  0
)
(
  0  eiπ/6
 ei5π/6  0
)
24
(
  1  0  0
  1 -1  0
  0  0 -1
)
(
  0 -(√3+i)/2
  (√3-i)/2  0
)
d2210
1
-1
-1
1
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0 e-iπ/3
  eiπ/3  0
)
(
  0 -i
 -i  0
)
(
  0  eiπ/6
 ei5π/6  0
)
(
  0 ei5π/6
  eiπ/6  0
)
k-Subgroupsmag
Bilbao Crystallographic Server
http://www.cryst.ehu.es		 Licencia de Creative Commons
For comments, please mail to
administrador.bcs@ehu.eus