Bilbao Crystallographic Server arrow COREPRESENTATIONS PG

Irreducible corepresentations of the Magnetic Point Group 6/m1' (N. 23.2.83)


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
C19
C20
C21
C22
C23
C24
GM1+
Ag
GM1+
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
GM1-
Au
GM1-
1
1
1
1
1
1
-1
-1
-1
-1
-1
-1
1
1
1
1
1
1
-1
-1
-1
-1
-1
-1
GM4+
Bg
GM2+
1
1
1
-1
-1
-1
1
1
1
-1
-1
-1
1
1
1
-1
-1
-1
1
1
1
-1
-1
-1
GM4-
Bu
GM2-
1
1
1
-1
-1
-1
-1
-1
-1
1
1
1
1
1
1
-1
-1
-1
-1
-1
-1
1
1
1
GM5+GM6+
1E1g2E1g
GM3+GM5+
2
-1
-1
2
-1
-1
2
-1
-1
2
-1
-1
2
-1
-1
2
-1
-1
2
-1
-1
2
-1
-1
GM5-GM6-
1E1u2E1u
GM3-GM5-
2
-1
-1
2
-1
-1
-2
1
1
-2
1
1
2
-1
-1
2
-1
-1
-2
1
1
-2
1
1
GM2+GM3+
1E2g2E2g
GM4+GM6+
2
-1
-1
-2
1
1
2
-1
-1
-2
1
1
2
-1
-1
-2
1
1
2
-1
-1
-2
1
1
GM2-GM3-
1E2u2E2u
GM4-GM6-
2
-1
-1
-2
1
1
-2
1
1
2
-1
-1
2
-1
-1
-2
1
1
-2
1
1
2
-1
-1
GM12+GM11+
1E1g2E1g
GM7GM8
2
-2
-2
0
0
0
2
-2
-2
0
0
0
-2
2
2
0
0
0
-2
2
2
0
0
0
GM7+GM8+
1E3g2E3g
GM10GM11
2
1
1
0
√3
√3
2
1
1
0
√3
√3
-2
-1
-1
0
-√3
-√3
-2
-1
-1
0
-√3
-√3
GM10+GM9+
1E2g2E2g
GM12GM9
2
1
1
0
-√3
-√3
2
1
1
0
-√3
-√3
-2
-1
-1
0
√3
√3
-2
-1
-1
0
√3
√3
GM12-GM11-
1E1u2E1u
GM13GM14
2
-2
-2
0
0
0
-2
2
2
0
0
0
-2
2
2
0
0
0
2
-2
-2
0
0
0
GM9-GM10-
1E2u2E2u
GM15GM18
2
1
1
0
-√3
-√3
-2
-1
-1
0
√3
√3
-2
-1
-1
0
√3
√3
2
1
1
0
-√3
-√3
GM7-GM8-
1E3u2E3u
GM16GM17
2
1
1
0
√3
√3
-2
-1
-1
0
-√3
-√3
-2
-1
-1
0
-√3
-√3
2
1
1
0
√3
√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
C3: 3-001
C4: 2001
C5: 6-001
C6: 6+001
C7: 1
C8: 3+001
C9: 3-001
C10: m001
C11: 6-001
C12: 6+001
C13: d1
C14: d3+001
C15: d3-001
C16: d2001
C17: d6-001
C18: d6+001
C19: d1
C20: d3+001
C21: d3-001
C22: dm001
C23: d6-001
C24: d6+001

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbolGM1+GM1-GM2+GM2-GM3+GM5+GM3-GM5-GM4+GM6+GM4-GM6-GM7GM8GM10GM11GM12GM9GM13GM14GM15GM18GM16GM17
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
)
(
 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
)
(
  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
)
(
 e-iπ/3  0
  0  eiπ/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
)
(
 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
)
(
  eiπ/3  0
  0 e-iπ/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
)
(
 -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
(
  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
)
(
 e-i5π/6  0
  0  ei5π/6
)
(
  eiπ/6  0
  0 e-iπ/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
)
(
 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
)
(
  ei5π/6  0
  0 e-i5π/6
)
(
 e-iπ/6  0
  0  eiπ/6
)
7
(
 -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
)
(
 1 0
 0 1
)
(
 1 0
 0 1
)
(
 -1  0
  0 -1
)
(
 -1  0
  0 -1
)
(
 -1  0
  0 -1
)
8
(
  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
)
(
 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
)
(
  ei2π/3  0
  0 e-i2π/3
)
9
(
  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
)
(
  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
)
(
 e-i2π/3  0
  0  ei2π/3
)
10
(
  1  0  0
  0  1  0
  0  0 -1
)
(
 -i  0
  0  i
)
m001
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
)
11
(
  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
)
(
 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
)
(
  eiπ/6  0
  0 e-iπ/6
)
(
 e-i5π/6  0
  0  ei5π/6
)
12
(
 -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
)
(
  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
)
(
 e-iπ/6  0
  0  eiπ/6
)
(
  ei5π/6  0
  0 e-i5π/6
)
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
)
(
 -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
)
(
  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
)
(
  ei2π/3  0
  0 e-i2π/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
)
(
 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
)
(
 e-i2π/3  0
  0  ei2π/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
)
(
 -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
)
d6-001
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
)
(
  eiπ/6  0
  0 e-iπ/6
)
(
 e-i5π/6  0
  0  ei5π/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
)
(
 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
)
(
 e-iπ/6  0
  0  eiπ/6
)
(
  ei5π/6  0
  0 e-i5π/6
)
19
(
 -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
)
(
 -1  0
  0 -1
)
(
 -1  0
  0 -1
)
(
 1 0
 0 1
)
(
 1 0
 0 1
)
(
 1 0
 0 1
)
20
(
  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
)
(
 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
)
(
 e-iπ/3  0
  0  eiπ/3
)
21
(
  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
)
(
  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
)
(
  eiπ/3  0
  0 e-iπ/3
)
22
(
  1  0  0
  0  1  0
  0  0 -1
)
(
  i  0
  0 -i
)
dm001
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
)
23
(
  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
)
(
 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
)
(
 e-i5π/6  0
  0  ei5π/6
)
(
  eiπ/6  0
  0 e-iπ/6
)
24
(
 -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
)
(
  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
)
(
  ei5π/6  0
  0 e-i5π/6
)
(
 e-iπ/6  0
  0  eiπ/6
)
25
(
 1 0 0
 0 1 0
 0 0 1
)
(
 1 0
 0 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
)
26
(
  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
(
  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  e-iπ/3
 e-i2π/3  0
)
27
(
 -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
(
  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  eiπ/3
 ei2π/3  0
)
28
(
 -1  0  0
  0 -1  0
  0  0  1
)
(
 -i  0
  0  i
)
2'001
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
)
29
(
  0  1  0
 -1  1  0
  0  0  1
)
(
 (√3-i)/2  0
  0 (√3+i)/2
)
6'-001
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 e-i5π/6
  e-iπ/6  0
)
(
  0  eiπ/6
 ei5π/6  0
)
30
(
  1 -1  0
  1  0  0
  0  0  1
)
(
 (√3+i)/2  0
  0 (√3-i)/2
)
6'+001
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 ei5π/6
  eiπ/6  0
)
(
  0  e-iπ/6
 e-i5π/6  0
)
31
(
 -1  0  0
  0 -1  0
  0  0 -1
)
(
 1 0
 0 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
(
  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
(
  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 ei2π/3
  eiπ/3  0
)
33
(
  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
(
  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 e-i2π/3
  e-iπ/3  0
)
34
(
  1  0  0
  0  1  0
  0  0 -1
)
(
 -i  0
  0  i
)
m'001
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
(
  0 -1  0
  1 -1  0
  0  0 -1
)
(
 (√3-i)/2  0
  0 (√3+i)/2
)
6'-001
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  eiπ/6
 ei5π/6  0
)
(
  0 e-i5π/6
  e-iπ/6  0
)
36
(
 -1  1  0
 -1  0  0
  0  0 -1
)
(
 (√3+i)/2  0
  0 (√3-i)/2
)
6'+001
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  e-iπ/6
 e-i5π/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
(
 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
)
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
(
  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 ei2π/3
  eiπ/3  0
)
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
(
  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 e-i2π/3
  e-iπ/3  0
)
40
(
 -1  0  0
  0 -1  0
  0  0  1
)
(
  i  0
  0 -i
)
d2'001
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
)
41
(
  0  1  0
 -1  1  0
  0  0  1
)
(
 -(√3-i)/2  0
  0 -(√3+i)/2
)
d6'-001
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  eiπ/6
 ei5π/6  0
)
(
  0 e-i5π/6
  e-iπ/6  0
)
42
(
  1 -1  0
  1  0  0
  0  0  1
)
(
 -(√3+i)/2  0
  0 -(√3-i)/2
)
d6'+001
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  e-iπ/6
 e-i5π/6  0
)
(
  0 ei5π/6
  eiπ/6  0
)
43
(
 -1  0  0
  0 -1  0
  0  0 -1
)
(
 -1  0
  0 -1
)
d1'
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
(
  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
(
  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  e-iπ/3
 e-i2π/3  0
)
45
(
  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
(
  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  eiπ/3
 ei2π/3  0
)
46
(
  1  0  0
  0  1  0
  0  0 -1
)
(
  i  0
  0 -i
)
dm'001
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
(
  0 -1  0
  1 -1  0
  0  0 -1
)
(
 -(√3-i)/2  0
  0 -(√3+i)/2
)
d6'-001
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 e-i5π/6
  e-iπ/6  0
)
(
  0  eiπ/6
 ei5π/6  0
)
48
(
 -1  1  0
 -1  0  0
  0  0 -1
)
(
 -(√3+i)/2  0
  0 -(√3-i)/2
)
d6'+001
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 ei5π/6
  eiπ/6  0
)
(
  0  e-iπ/6
 e-i5π/6  0
)
k-Subgroupsmag
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