Bilbao Crystallographic Server arrow COREPRESENTATIONS PG

Irreducible corepresentations of the Magnetic Point Group 6/mmm (N. 27.1.100)


Table of characters of the unitary symmetry operations


(1)
(2)
(3)
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
C12
C13
C14
C15
C16
C17
C18
GM1+
A1g
GM1+
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
GM1-
A1u
GM1-
1
1
1
1
1
1
-1
-1
-1
-1
-1
-1
1
1
1
-1
-1
-1
GM2+
A2g
GM2+
1
1
1
1
-1
-1
1
1
1
1
-1
-1
1
1
1
1
1
1
GM2-
A2u
GM2-
1
1
1
1
-1
-1
-1
-1
-1
-1
1
1
1
1
1
-1
-1
-1
GM4+
B2g
GM3+
1
1
-1
-1
1
-1
1
1
-1
-1
1
-1
1
1
-1
1
1
-1
GM4-
B2u
GM3-
1
1
-1
-1
1
-1
-1
-1
1
1
-1
1
1
1
-1
-1
-1
1
GM3+
B1g
GM4+
1
1
-1
-1
-1
1
1
1
-1
-1
-1
1
1
1
-1
1
1
-1
GM3-
B1u
GM4-
1
1
-1
-1
-1
1
-1
-1
1
1
1
-1
1
1
-1
-1
-1
1
GM6+
E2g
GM5+
2
-1
2
-1
0
0
2
-1
2
-1
0
0
2
-1
-1
2
-1
-1
GM6-
E2u
GM5-
2
-1
2
-1
0
0
-2
1
-2
1
0
0
2
-1
-1
-2
1
1
GM5+
E1g
GM6+
2
-1
-2
1
0
0
2
-1
-2
1
0
0
2
-1
1
2
-1
1
GM5-
E1u
GM6-
2
-1
-2
1
0
0
-2
1
2
-1
0
0
2
-1
1
-2
1
-1
GM9+
E3g
GM7
2
-2
0
0
0
0
2
-2
0
0
0
0
-2
2
0
-2
2
0
GM8+
E2g
GM8
2
1
0
-√3
0
0
2
1
0
-√3
0
0
-2
-1
√3
-2
-1
√3
GM7+
E1g
GM9
2
1
0
√3
0
0
2
1
0
√3
0
0
-2
-1
-√3
-2
-1
-√3
GM9-
E3u
GM10
2
-2
0
0
0
0
-2
2
0
0
0
0
-2
2
0
2
-2
0
GM8-
E2u
GM11
2
1
0
-√3
0
0
-2
-1
0
√3
0
0
-2
-1
√3
2
1
-√3
GM7-
E1u
GM12
2
1
0
√3
0
0
-2
-1
0
-√3
0
0
-2
-1
-√3
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: 1
C8: 3+001, 3-001
C9: m001, dm001
C10: 6-001, 6+001
C11: m110, m100, m010, dm110, dm100, dm010
C12: m110, m120, m210, dm110, dm120, dm210
C13: d1
C14: d3+001, d3-001
C15: d6-001, d6+001
C16: d1
C17: d3+001, d3-001
C18: d6-001, d6+001

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbolGM1+GM1-GM2+GM2-GM3+GM3-GM4+GM4-GM5+GM5-GM6+GM6-GM7GM8GM9GM10GM11GM12
1
(
 1 0 0
 0 1 0
 0 0 1
)
(
 1 0
 0 1
)
1
1
1
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
)
(
 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
1
1
1
1
(
  ei2π/3  0
  0 e-i2π/3
)
(
  ei2π/3  0
  0 e-i2π/3
)
(
  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
)
(
 -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
1
1
1
1
(
 e-i2π/3  0
  0  ei2π/3
)
(
 e-i2π/3  0
  0  ei2π/3
)
(
 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
)
(
 -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
-1
-1
-1
(
 1 0
 0 1
)
(
 1 0
 0 1
)
(
 -1  0
  0 -1
)
(
 -1  0
  0 -1
)
(
 -i  0
  0  i
)
(
 -i  0
  0  i
)
(
 -i  0
  0  i
)
(
 -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
-1
-1
-1
-1
(
  ei2π/3  0
  0 e-i2π/3
)
(
  ei2π/3  0
  0 e-i2π/3
)
(
 e-iπ/3  0
  0  eiπ/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
)
(
  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
-1
-1
-1
-1
(
 e-i2π/3  0
  0  ei2π/3
)
(
 e-i2π/3  0
  0  ei2π/3
)
(
  eiπ/3  0
  0 e-iπ/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
)
(
 -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
1
1
-1
-1
(
 0 1
 1 0
)
(
 0 1
 1 0
)
(
 0 1
 1 0
)
(
 0 1
 1 0
)
(
  0 -1
  1  0
)
(
  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
1
1
-1
-1
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0 e-i2π/3
  ei2π/3  0
)
(
  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
)
(
  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
1
1
-1
-1
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0  ei2π/3
 e-i2π/3  0
)
(
  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
)
(
  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
-1
-1
1
1
(
 0 1
 1 0
)
(
 0 1
 1 0
)
(
  0 -1
 -1  0
)
(
  0 -1
 -1  0
)
(
 0 i
 i 0
)
(
 0 i
 i 0
)
(
 0 i
 i 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
-1
-1
1
1
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0  eiπ/3
 e-iπ/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
)
(
 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
-1
-1
1
1
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0 e-iπ/3
  eiπ/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
)
(
 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
)
1
1
-1
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
)
(
 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
)
3+001
1
-1
1
-1
1
-1
1
-1
(
  ei2π/3  0
  0 e-i2π/3
)
(
 e-iπ/3  0
  0  eiπ/3
)
(
  ei2π/3  0
  0 e-i2π/3
)
(
 e-iπ/3  0
  0  eiπ/3
)
(
 -1  0
  0 -1
)
(
 e-iπ/3  0
  0  eiπ/3
)
(
  eiπ/3  0
  0 e-iπ/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
)
3-001
1
-1
1
-1
1
-1
1
-1
(
 e-i2π/3  0
  0  ei2π/3
)
(
  eiπ/3  0
  0 e-iπ/3
)
(
 e-i2π/3  0
  0  ei2π/3
)
(
  eiπ/3  0
  0 e-iπ/3
)
(
 -1  0
  0 -1
)
(
  eiπ/3  0
  0 e-iπ/3
)
(
 e-iπ/3  0
  0  eiπ/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
)
m001
1
-1
1
-1
-1
1
-1
1
(
 1 0
 0 1
)
(
 -1  0
  0 -1
)
(
 -1  0
  0 -1
)
(
 1 0
 0 1
)
(
 -i  0
  0  i
)
(
 -i  0
  0  i
)
(
 -i  0
  0  i
)
(
  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
)
6-001
1
-1
1
-1
-1
1
-1
1
(
  ei2π/3  0
  0 e-i2π/3
)
(
 e-iπ/3  0
  0  eiπ/3
)
(
 e-iπ/3  0
  0  eiπ/3
)
(
  ei2π/3  0
  0 e-i2π/3
)
(
  i  0
  0 -i
)
(
 e-i5π/6  0
  0  ei5π/6
)
(
 e-iπ/6  0
  0  eiπ/6
)
(
 -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
)
6+001
1
-1
1
-1
-1
1
-1
1
(
 e-i2π/3  0
  0  ei2π/3
)
(
  eiπ/3  0
  0 e-iπ/3
)
(
  eiπ/3  0
  0 e-iπ/3
)
(
 e-i2π/3  0
  0  ei2π/3
)
(
 -i  0
  0  i
)
(
  ei5π/6  0
  0 e-i5π/6
)
(
  eiπ/6  0
  0 e-iπ/6
)
(
  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
)
m110
1
-1
-1
1
1
-1
-1
1
(
 0 1
 1 0
)
(
  0 -1
 -1  0
)
(
 0 1
 1 0
)
(
  0 -1
 -1  0
)
(
  0 -1
  1  0
)
(
  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
)
m100
1
-1
-1
1
1
-1
-1
1
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0  eiπ/3
 e-iπ/3  0
)
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0  eiπ/3
 e-iπ/3  0
)
(
  0  1
 -1  0
)
(
  0 e-i2π/3
  e-iπ/3  0
)
(
  0 ei2π/3
  eiπ/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
)
m010
1
-1
-1
1
1
-1
-1
1
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0 e-iπ/3
  eiπ/3  0
)
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0 e-iπ/3
  eiπ/3  0
)
(
  0 -1
  1  0
)
(
  0  e-iπ/3
 e-i2π/3  0
)
(
  0  eiπ/3
 ei2π/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
)
m1-10
1
-1
-1
1
-1
1
1
-1
(
 0 1
 1 0
)
(
  0 -1
 -1  0
)
(
  0 -1
 -1  0
)
(
 0 1
 1 0
)
(
 0 i
 i 0
)
(
 0 i
 i 0
)
(
 0 i
 i 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
)
m120
1
-1
-1
1
-1
1
1
-1
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0  eiπ/3
 e-iπ/3  0
)
(
  0  eiπ/3
 e-iπ/3  0
)
(
  0 e-i2π/3
  ei2π/3  0
)
(
 0 i
 i 0
)
(
  0  e-iπ/6
 e-i5π/6  0
)
(
  0 e-i5π/6
  e-iπ/6  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
)
m210
1
-1
-1
1
-1
1
1
-1
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0 e-iπ/3
  eiπ/3  0
)
(
  0 e-iπ/3
  eiπ/3  0
)
(
  0  ei2π/3
 e-i2π/3  0
)
(
 0 i
 i 0
)
(
  0 e-i5π/6
  e-iπ/6  0
)
(
  0  e-iπ/6
 e-i5π/6  0
)
(
  0 -i
 -i  0
)
(
  0  eiπ/6
 ei5π/6  0
)
(
  0 ei5π/6
  eiπ/6  0
)
25
(
 1 0 0
 0 1 0
 0 0 1
)
(
 -1  0
  0 -1
)
d1
1
1
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
)
(
 -1  0
  0 -1
)
(
 -1  0
  0 -1
)
(
 -1  0
  0 -1
)
(
 -1  0
  0 -1
)
(
 -1  0
  0 -1
)
26
(
  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
1
1
1
1
(
  ei2π/3  0
  0 e-i2π/3
)
(
  ei2π/3  0
  0 e-i2π/3
)
(
  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
)
(
 1 0
 0 1
)
(
  ei2π/3  0
  0 e-i2π/3
)
(
 e-i2π/3  0
  0  ei2π/3
)
27
(
 -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
1
1
1
1
(
 e-i2π/3  0
  0  ei2π/3
)
(
 e-i2π/3  0
  0  ei2π/3
)
(
 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
)
(
 1 0
 0 1
)
(
 e-i2π/3  0
  0  ei2π/3
)
(
  ei2π/3  0
  0 e-i2π/3
)
28
(
 -1  0  0
  0 -1  0
  0  0  1
)
(
  i  0
  0 -i
)
d2001
1
1
1
1
-1
-1
-1
-1
(
 1 0
 0 1
)
(
 1 0
 0 1
)
(
 -1  0
  0 -1
)
(
 -1  0
  0 -1
)
(
  i  0
  0 -i
)
(
  i  0
  0 -i
)
(
  i  0
  0 -i
)
(
  i  0
  0 -i
)
(
  i  0
  0 -i
)
(
  i  0
  0 -i
)
29
(
  0  1  0
 -1  1  0
  0  0  1
)
(
 -(√3-i)/2  0
  0 -(√3+i)/2
)
d6-001
1
1
1
1
-1
-1
-1
-1
(
  ei2π/3  0
  0 e-i2π/3
)
(
  ei2π/3  0
  0 e-i2π/3
)
(
 e-iπ/3  0
  0  eiπ/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
)
(
 -i  0
  0  i
)
(
  eiπ/6  0
  0 e-iπ/6
)
(
  ei5π/6  0
  0 e-i5π/6
)
30
(
  1 -1  0
  1  0  0
  0  0  1
)
(
 -(√3+i)/2  0
  0 -(√3-i)/2
)
d6+001
1
1
1
1
-1
-1
-1
-1
(
 e-i2π/3  0
  0  ei2π/3
)
(
 e-i2π/3  0
  0  ei2π/3
)
(
  eiπ/3  0
  0 e-iπ/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
)
(
  i  0
  0 -i
)
(
 e-iπ/6  0
  0  eiπ/6
)
(
 e-i5π/6  0
  0  ei5π/6
)
31
(
  0  1  0
  1  0  0
  0  0 -1
)
(
  0  (1+i√3)/2
 -(1-i√3)/2  0
)
d2110
1
1
-1
-1
1
1
-1
-1
(
 0 1
 1 0
)
(
 0 1
 1 0
)
(
 0 1
 1 0
)
(
 0 1
 1 0
)
(
  0  1
 -1  0
)
(
  0  1
 -1  0
)
(
  0  1
 -1  0
)
(
  0  1
 -1  0
)
(
  0  1
 -1  0
)
(
  0  1
 -1  0
)
32
(
  1 -1  0
  0 -1  0
  0  0 -1
)
(
  0  1
 -1  0
)
d2100
1
1
-1
-1
1
1
-1
-1
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0 e-i2π/3
  ei2π/3  0
)
(
  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
)
(
  0 -1
  1  0
)
(
  0  eiπ/3
 ei2π/3  0
)
(
  0  e-iπ/3
 e-i2π/3  0
)
33
(
 -1  0  0
 -1  1  0
  0  0 -1
)
(
  0  (1-i√3)/2
 -(1+i√3)/2  0
)
d2010
1
1
-1
-1
1
1
-1
-1
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0  ei2π/3
 e-i2π/3  0
)
(
  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
)
(
  0  1
 -1  0
)
(
  0 ei2π/3
  eiπ/3  0
)
(
  0 e-i2π/3
  e-iπ/3  0
)
34
(
  0 -1  0
 -1  0  0
  0  0 -1
)
(
  0  (√3-i)/2
 -(√3+i)/2  0
)
d21-10
1
1
-1
-1
-1
-1
1
1
(
 0 1
 1 0
)
(
 0 1
 1 0
)
(
  0 -1
 -1  0
)
(
  0 -1
 -1  0
)
(
  0 -i
 -i  0
)
(
  0 -i
 -i  0
)
(
  0 -i
 -i  0
)
(
  0 -i
 -i  0
)
(
  0 -i
 -i  0
)
(
  0 -i
 -i  0
)
35
(
 -1  1  0
  0  1  0
  0  0 -1
)
(
 0 i
 i 0
)
d2120
1
1
-1
-1
-1
-1
1
1
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0  eiπ/3
 e-iπ/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
)
(
  0 -i
 -i  0
)
(
  0 ei5π/6
  eiπ/6  0
)
(
  0  eiπ/6
 ei5π/6  0
)
36
(
  1  0  0
  1 -1  0
  0  0 -1
)
(
  0 -(√3+i)/2
  (√3-i)/2  0
)
d2210
1
1
-1
-1
-1
-1
1
1
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0 e-iπ/3
  eiπ/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
)
(
  0 -i
 -i  0
)
(
  0  eiπ/6
 ei5π/6  0
)
(
  0 ei5π/6
  eiπ/6  0
)
37
(
 -1  0  0
  0 -1  0
  0  0 -1
)
(
 -1  0
  0 -1
)
d1
1
-1
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
)
(
 -1  0
  0 -1
)
(
 -1  0
  0 -1
)
(
 1 0
 0 1
)
(
 1 0
 0 1
)
(
 1 0
 0 1
)
38
(
  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
1
-1
1
-1
(
  ei2π/3  0
  0 e-i2π/3
)
(
 e-iπ/3  0
  0  eiπ/3
)
(
  ei2π/3  0
  0 e-i2π/3
)
(
 e-iπ/3  0
  0  eiπ/3
)
(
 1 0
 0 1
)
(
  ei2π/3  0
  0 e-i2π/3
)
(
 e-i2π/3  0
  0  ei2π/3
)
(
 -1  0
  0 -1
)
(
 e-iπ/3  0
  0  eiπ/3
)
(
  eiπ/3  0
  0 e-iπ/3
)
39
(
  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
1
-1
1
-1
(
 e-i2π/3  0
  0  ei2π/3
)
(
  eiπ/3  0
  0 e-iπ/3
)
(
 e-i2π/3  0
  0  ei2π/3
)
(
  eiπ/3  0
  0 e-iπ/3
)
(
 1 0
 0 1
)
(
 e-i2π/3  0
  0  ei2π/3
)
(
  ei2π/3  0
  0 e-i2π/3
)
(
 -1  0
  0 -1
)
(
  eiπ/3  0
  0 e-iπ/3
)
(
 e-iπ/3  0
  0  eiπ/3
)
40
(
  1  0  0
  0  1  0
  0  0 -1
)
(
  i  0
  0 -i
)
dm001
1
-1
1
-1
-1
1
-1
1
(
 1 0
 0 1
)
(
 -1  0
  0 -1
)
(
 -1  0
  0 -1
)
(
 1 0
 0 1
)
(
  i  0
  0 -i
)
(
  i  0
  0 -i
)
(
  i  0
  0 -i
)
(
 -i  0
  0  i
)
(
 -i  0
  0  i
)
(
 -i  0
  0  i
)
41
(
  0 -1  0
  1 -1  0
  0  0 -1
)
(
 -(√3-i)/2  0
  0 -(√3+i)/2
)
d6-001
1
-1
1
-1
-1
1
-1
1
(
  ei2π/3  0
  0 e-i2π/3
)
(
 e-iπ/3  0
  0  eiπ/3
)
(
 e-iπ/3  0
  0  eiπ/3
)
(
  ei2π/3  0
  0 e-i2π/3
)
(
 -i  0
  0  i
)
(
  eiπ/6  0
  0 e-iπ/6
)
(
  ei5π/6  0
  0 e-i5π/6
)
(
  i  0
  0 -i
)
(
 e-i5π/6  0
  0  ei5π/6
)
(
 e-iπ/6  0
  0  eiπ/6
)
42
(
 -1  1  0
 -1  0  0
  0  0 -1
)
(
 -(√3+i)/2  0
  0 -(√3-i)/2
)
d6+001
1
-1
1
-1
-1
1
-1
1
(
 e-i2π/3  0
  0  ei2π/3
)
(
  eiπ/3  0
  0 e-iπ/3
)
(
  eiπ/3  0
  0 e-iπ/3
)
(
 e-i2π/3  0
  0  ei2π/3
)
(
  i  0
  0 -i
)
(
 e-iπ/6  0
  0  eiπ/6
)
(
 e-i5π/6  0
  0  ei5π/6
)
(
 -i  0
  0  i
)
(
  ei5π/6  0
  0 e-i5π/6
)
(
  eiπ/6  0
  0 e-iπ/6
)
43
(
  0 -1  0
 -1  0  0
  0  0  1
)
(
  0  (1+i√3)/2
 -(1-i√3)/2  0
)
dm110
1
-1
-1
1
1
-1
-1
1
(
 0 1
 1 0
)
(
  0 -1
 -1  0
)
(
 0 1
 1 0
)
(
  0 -1
 -1  0
)
(
  0  1
 -1  0
)
(
  0  1
 -1  0
)
(
  0  1
 -1  0
)
(
  0 -1
  1  0
)
(
  0 -1
  1  0
)
(
  0 -1
  1  0
)
44
(
 -1  1  0
  0  1  0
  0  0  1
)
(
  0  1
 -1  0
)
dm100
1
-1
-1
1
1
-1
-1
1
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0  eiπ/3
 e-iπ/3  0
)
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0  eiπ/3
 e-iπ/3  0
)
(
  0 -1
  1  0
)
(
  0  eiπ/3
 ei2π/3  0
)
(
  0  e-iπ/3
 e-i2π/3  0
)
(
  0  1
 -1  0
)
(
  0 e-i2π/3
  e-iπ/3  0
)
(
  0 ei2π/3
  eiπ/3  0
)
45
(
  1  0  0
  1 -1  0
  0  0  1
)
(
  0  (1-i√3)/2
 -(1+i√3)/2  0
)
dm010
1
-1
-1
1
1
-1
-1
1
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0 e-iπ/3
  eiπ/3  0
)
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0 e-iπ/3
  eiπ/3  0
)
(
  0  1
 -1  0
)
(
  0 ei2π/3
  eiπ/3  0
)
(
  0 e-i2π/3
  e-iπ/3  0
)
(
  0 -1
  1  0
)
(
  0  e-iπ/3
 e-i2π/3  0
)
(
  0  eiπ/3
 ei2π/3  0
)
46
(
 0 1 0
 1 0 0
 0 0 1
)
(
  0  (√3-i)/2
 -(√3+i)/2  0
)
dm1-10
1
-1
-1
1
-1
1
1
-1
(
 0 1
 1 0
)
(
  0 -1
 -1  0
)
(
  0 -1
 -1  0
)
(
 0 1
 1 0
)
(
  0 -i
 -i  0
)
(
  0 -i
 -i  0
)
(
  0 -i
 -i  0
)
(
 0 i
 i 0
)
(
 0 i
 i 0
)
(
 0 i
 i 0
)
47
(
  1 -1  0
  0 -1  0
  0  0  1
)
(
 0 i
 i 0
)
dm120
1
-1
-1
1
-1
1
1
-1
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0  eiπ/3
 e-iπ/3  0
)
(
  0  eiπ/3
 e-iπ/3  0
)
(
  0 e-i2π/3
  ei2π/3  0
)
(
  0 -i
 -i  0
)
(
  0 ei5π/6
  eiπ/6  0
)
(
  0  eiπ/6
 ei5π/6  0
)
(
 0 i
 i 0
)
(
  0  e-iπ/6
 e-i5π/6  0
)
(
  0 e-i5π/6
  e-iπ/6  0
)
48
(
 -1  0  0
 -1  1  0
  0  0  1
)
(
  0 -(√3+i)/2
  (√3-i)/2  0
)
dm210
1
-1
-1
1
-1
1
1
-1
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0 e-iπ/3
  eiπ/3  0
)
(
  0 e-iπ/3
  eiπ/3  0
)
(
  0  ei2π/3
 e-i2π/3  0
)
(
  0 -i
 -i  0
)
(
  0  eiπ/6
 ei5π/6  0
)
(
  0 ei5π/6
  eiπ/6  0
)
(
 0 i
 i 0
)
(
  0 e-i5π/6
  e-iπ/6  0
)
(
  0  e-iπ/6
 e-i5π/6  0
)
k-Subgroupsmag
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