Bilbao Crystallographic Server arrow COREPRESENTATIONS PG

Irreducible corepresentations of the Magnetic Point Group 6/mm'm' (N. 27.6.105)


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+
2E1g
GM3+
1
-(1-i3)/2
-(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
GM5-
2E1u
GM3-
1
-(1-i3)/2
-(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
-1
(1-i3)/2
(1+i3)/2
-1
(1-i3)/2
(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
-1
(1-i3)/2
(1+i3)/2
-1
(1-i3)/2
(1+i3)/2
GM2+
2E2g
GM4+
1
-(1-i3)/2
-(1+i3)/2
-1
(1-i3)/2
(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
-1
(1-i3)/2
(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
-1
(1-i3)/2
(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
-1
(1-i3)/2
(1+i3)/2
GM2-
2E2u
GM4-
1
-(1-i3)/2
-(1+i3)/2
-1
(1-i3)/2
(1+i3)/2
-1
(1-i3)/2
(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
-1
(1-i3)/2
(1+i3)/2
-1
(1-i3)/2
(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
GM6+
1E1g
GM5+
1
-(1+i3)/2
-(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
GM6-
1E1u
GM5-
1
-(1+i3)/2
-(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
-1
(1+i3)/2
(1-i3)/2
-1
(1+i3)/2
(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
-1
(1+i3)/2
(1-i3)/2
-1
(1+i3)/2
(1-i3)/2
GM3+
1E2g
GM6+
1
-(1+i3)/2
-(1-i3)/2
-1
(1+i3)/2
(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
-1
(1+i3)/2
(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
-1
(1+i3)/2
(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
-1
(1+i3)/2
(1-i3)/2
GM3-
1E2u
GM6-
1
-(1+i3)/2
-(1-i3)/2
-1
(1+i3)/2
(1-i3)/2
-1
(1+i3)/2
(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
-1
(1+i3)/2
(1-i3)/2
-1
(1+i3)/2
(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
GM12+
2E1g
GM7
1
-1
-1
-i
i
-i
1
-1
-1
-i
i
-i
-1
1
1
i
-i
i
-1
1
1
i
-i
i
GM11+
1E1g
GM8
1
-1
-1
i
-i
i
1
-1
-1
i
-i
i
-1
1
1
-i
i
-i
-1
1
1
-i
i
-i
GM9+
2E2g
GM9
1
(1-i3)/2
(1+i3)/2
-i
-(3+i)/2
-(3-i)/2
1
(1-i3)/2
(1+i3)/2
-i
-(3+i)/2
-(3-i)/2
-1
-(1-i3)/2
-(1+i3)/2
i
(3+i)/2
(3-i)/2
-1
-(1-i3)/2
-(1+i3)/2
i
(3+i)/2
(3-i)/2
GM7+
1E3g
GM10
1
(1-i3)/2
(1+i3)/2
i
(3+i)/2
(3-i)/2
1
(1-i3)/2
(1+i3)/2
i
(3+i)/2
(3-i)/2
-1
-(1-i3)/2
-(1+i3)/2
-i
-(3+i)/2
-(3-i)/2
-1
-(1-i3)/2
-(1+i3)/2
-i
-(3+i)/2
-(3-i)/2
GM8+
2E3g
GM11
1
(1+i3)/2
(1-i3)/2
-i
(3-i)/2
(3+i)/2
1
(1+i3)/2
(1-i3)/2
-i
(3-i)/2
(3+i)/2
-1
-(1+i3)/2
-(1-i3)/2
i
-(3-i)/2
-(3+i)/2
-1
-(1+i3)/2
-(1-i3)/2
i
-(3-i)/2
-(3+i)/2
GM10+
1E2g
GM12
1
(1+i3)/2
(1-i3)/2
i
-(3-i)/2
-(3+i)/2
1
(1+i3)/2
(1-i3)/2
i
-(3-i)/2
-(3+i)/2
-1
-(1+i3)/2
-(1-i3)/2
-i
(3-i)/2
(3+i)/2
-1
-(1+i3)/2
-(1-i3)/2
-i
(3-i)/2
(3+i)/2
GM12-
2E1u
GM13
1
-1
-1
-i
i
-i
-1
1
1
i
-i
i
-1
1
1
i
-i
i
1
-1
-1
-i
i
-i
GM11-
1E1u
GM14
1
-1
-1
i
-i
i
-1
1
1
-i
i
-i
-1
1
1
-i
i
-i
1
-1
-1
i
-i
i
GM9-
2E2u
GM15
1
(1-i3)/2
(1+i3)/2
-i
-(3+i)/2
-(3-i)/2
-1
-(1-i3)/2
-(1+i3)/2
i
(3+i)/2
(3-i)/2
-1
-(1-i3)/2
-(1+i3)/2
i
(3+i)/2
(3-i)/2
1
(1-i3)/2
(1+i3)/2
-i
-(3+i)/2
-(3-i)/2
GM7-
1E3u
GM16
1
(1-i3)/2
(1+i3)/2
i
(3+i)/2
(3-i)/2
-1
-(1-i3)/2
-(1+i3)/2
-i
-(3+i)/2
-(3-i)/2
-1
-(1-i3)/2
-(1+i3)/2
-i
-(3+i)/2
-(3-i)/2
1
(1-i3)/2
(1+i3)/2
i
(3+i)/2
(3-i)/2
GM8-
2E3u
GM17
1
(1+i3)/2
(1-i3)/2
-i
(3-i)/2
(3+i)/2
-1
-(1+i3)/2
-(1-i3)/2
i
-(3-i)/2
-(3+i)/2
-1
-(1+i3)/2
-(1-i3)/2
i
-(3-i)/2
-(3+i)/2
1
(1+i3)/2
(1-i3)/2
-i
(3-i)/2
(3+i)/2
GM10-
1E2u
GM18
1
(1+i3)/2
(1-i3)/2
i
-(3-i)/2
-(3+i)/2
-1
-(1+i3)/2
-(1-i3)/2
-i
(3-i)/2
(3+i)/2
-1
-(1+i3)/2
-(1-i3)/2
-i
(3-i)/2
(3+i)/2
1
(1+i3)/2
(1-i3)/2
i
-(3-i)/2
-(3+i)/2
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
C71
C83+001
C93-001
C10: m001
C116-001
C126+001
C13d1
C14d3+001
C15d3-001
C16d2001
C17d6-001
C18d6+001
C19d1
C20d3+001
C21d3-001
C22dm001
C23d6-001
C24d6+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-GM7GM8GM9GM10GM11GM12GM13GM14GM15GM16GM17GM18
1
(
1 0 0
0 1 0
0 0 1
)
(
1 0
0 1
)
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
(
0 -1 0
1 -1 0
0 0 1
)
(
(1+i3)/2 0
0 (1-i3)/2
)
3+001
1
1
1
1
ei2π/3
ei2π/3
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
e-i2π/3
e-i2π/3
-1
-1
e-iπ/3
e-iπ/3
eiπ/3
eiπ/3
-1
-1
e-iπ/3
e-iπ/3
eiπ/3
eiπ/3
3
(
-1 1 0
-1 0 0
0 0 1
)
(
(1-i3)/2 0
0 (1+i3)/2
)
3-001
1
1
1
1
e-i2π/3
e-i2π/3
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
ei2π/3
ei2π/3
-1
-1
eiπ/3
eiπ/3
e-iπ/3
e-iπ/3
-1
-1
eiπ/3
eiπ/3
e-iπ/3
e-iπ/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
1
-1
-1
-i
i
-i
i
-i
i
-i
i
-i
i
-i
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
ei2π/3
e-iπ/3
e-iπ/3
e-i2π/3
e-i2π/3
eiπ/3
eiπ/3
i
-i
e-i5π/6
eiπ/6
e-iπ/6
ei5π/6
i
-i
e-i5π/6
eiπ/6
e-iπ/6
ei5π/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
e-i2π/3
eiπ/3
eiπ/3
ei2π/3
ei2π/3
e-iπ/3
e-iπ/3
-i
i
ei5π/6
e-iπ/6
eiπ/6
e-i5π/6
-i
i
ei5π/6
e-iπ/6
eiπ/6
e-i5π/6
7
(
-1 0 0
0 -1 0
0 0 -1
)
(
1 0
0 1
)
1
1
-1
1
-1
1
-1
1
-1
1
-1
1
-1
1
1
1
1
1
1
-1
-1
-1
-1
-1
-1
8
(
0 1 0
-1 1 0
0 0 -1
)
(
(1+i3)/2 0
0 (1-i3)/2
)
3+001
1
-1
1
-1
ei2π/3
e-iπ/3
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
e-i2π/3
eiπ/3
-1
-1
e-iπ/3
e-iπ/3
eiπ/3
eiπ/3
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
9
(
1 -1 0
1 0 0
0 0 -1
)
(
(1-i3)/2 0
0 (1+i3)/2
)
3-001
1
-1
1
-1
e-i2π/3
eiπ/3
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
ei2π/3
e-iπ/3
-1
-1
eiπ/3
eiπ/3
e-iπ/3
e-iπ/3
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
10
(
1 0 0
0 1 0
0 0 -1
)
(
-i 0
0 i
)
m001
1
-1
-1
1
1
-1
-1
1
1
-1
-1
1
-i
i
-i
i
-i
i
i
-i
i
-i
i
-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
e-iπ/3
e-iπ/3
ei2π/3
e-i2π/3
eiπ/3
eiπ/3
e-i2π/3
i
-i
e-i5π/6
eiπ/6
e-iπ/6
ei5π/6
-i
i
eiπ/6
e-i5π/6
ei5π/6
e-iπ/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
eiπ/3
eiπ/3
e-i2π/3
ei2π/3
e-iπ/3
e-iπ/3
ei2π/3
-i
i
ei5π/6
e-iπ/6
eiπ/6
e-i5π/6
i
-i
e-iπ/6
ei5π/6
e-i5π/6
eiπ/6
13
(
1 0 0
0 1 0
0 0 1
)
(
-1 0
0 -1
)
d1
1
1
1
1
1
1
1
1
1
1
1
1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
14
(
0 -1 0
1 -1 0
0 0 1
)
(
-(1+i3)/2 0
0 -(1-i3)/2
)
d3+001
1
1
1
1
ei2π/3
ei2π/3
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
e-i2π/3
e-i2π/3
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
15
(
-1 1 0
-1 0 0
0 0 1
)
(
-(1-i3)/2 0
0 -(1+i3)/2
)
d3-001
1
1
1
1
e-i2π/3
e-i2π/3
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
ei2π/3
ei2π/3
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
16
(
-1 0 0
0 -1 0
0 0 1
)
(
i 0
0 -i
)
d2001
1
1
-1
-1
1
1
-1
-1
1
1
-1
-1
i
-i
i
-i
i
-i
i
-i
i
-i
i
-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
ei2π/3
e-iπ/3
e-iπ/3
e-i2π/3
e-i2π/3
eiπ/3
eiπ/3
-i
i
eiπ/6
e-i5π/6
ei5π/6
e-iπ/6
-i
i
eiπ/6
e-i5π/6
ei5π/6
e-iπ/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
e-i2π/3
eiπ/3
eiπ/3
ei2π/3
ei2π/3
e-iπ/3
e-iπ/3
i
-i
e-iπ/6
ei5π/6
e-i5π/6
eiπ/6
i
-i
e-iπ/6
ei5π/6
e-i5π/6
eiπ/6
19
(
-1 0 0
0 -1 0
0 0 -1
)
(
-1 0
0 -1
)
d1
1
-1
1
-1
1
-1
1
-1
1
-1
1
-1
-1
-1
-1
-1
-1
-1
1
1
1
1
1
1
20
(
0 1 0
-1 1 0
0 0 -1
)
(
-(1+i3)/2 0
0 -(1-i3)/2
)
d3+001
1
-1
1
-1
ei2π/3
e-iπ/3
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
e-i2π/3
eiπ/3
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
-1
-1
e-iπ/3
e-iπ/3
eiπ/3
eiπ/3
21
(
1 -1 0
1 0 0
0 0 -1
)
(
-(1-i3)/2 0
0 -(1+i3)/2
)
d3-001
1
-1
1
-1
e-i2π/3
eiπ/3
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
ei2π/3
e-iπ/3
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
-1
-1
eiπ/3
eiπ/3
e-iπ/3
e-iπ/3
22
(
1 0 0
0 1 0
0 0 -1
)
(
i 0
0 -i
)
dm001
1
-1
-1
1
1
-1
-1
1
1
-1
-1
1
i
-i
i
-i
i
-i
-i
i
-i
i
-i
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
e-iπ/3
e-iπ/3
ei2π/3
e-i2π/3
eiπ/3
eiπ/3
e-i2π/3
-i
i
eiπ/6
e-i5π/6
ei5π/6
e-iπ/6
i
-i
e-i5π/6
eiπ/6
e-iπ/6
ei5π/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
eiπ/3
eiπ/3
e-i2π/3
ei2π/3
e-iπ/3
e-iπ/3
ei2π/3
i
-i
e-iπ/6
ei5π/6
e-i5π/6
eiπ/6
-i
i
ei5π/6
e-iπ/6
eiπ/6
e-i5π/6
25
(
0 1 0
1 0 0
0 0 -1
)
(
0 -(1+i3)/2
(1-i3)/2 0
)
2'110
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
26
(
1 -1 0
0 -1 0
0 0 -1
)
(
0 -1
1 0
)
2'100
1
1
1
1
e-i2π/3
e-i2π/3
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
ei2π/3
ei2π/3
-1
-1
eiπ/3
eiπ/3
e-iπ/3
e-iπ/3
-1
-1
eiπ/3
eiπ/3
e-iπ/3
e-iπ/3
27
(
-1 0 0
-1 1 0
0 0 -1
)
(
0 -(1-i3)/2
(1+i3)/2 0
)
2'010
1
1
1
1
ei2π/3
ei2π/3
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
e-i2π/3
e-i2π/3
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
28
(
0 -1 0
-1 0 0
0 0 -1
)
(
0 -(3-i)/2
(3+i)/2 0
)
2'1-10
1
1
-1
-1
1
1
-1
-1
1
1
-1
-1
-i
i
-i
i
-i
i
-i
i
-i
i
-i
i
29
(
-1 1 0
0 1 0
0 0 -1
)
(
0 -i
-i 0
)
2'120
1
1
-1
-1
e-i2π/3
e-i2π/3
eiπ/3
eiπ/3
ei2π/3
ei2π/3
e-iπ/3
e-iπ/3
-i
i
ei5π/6
e-iπ/6
eiπ/6
e-i5π/6
-i
i
ei5π/6
e-iπ/6
eiπ/6
e-i5π/6
30
(
1 0 0
1 -1 0
0 0 -1
)
(
0 (3+i)/2
-(3-i)/2 0
)
2'210
1
1
-1
-1
ei2π/3
ei2π/3
e-iπ/3
e-iπ/3
e-i2π/3
e-i2π/3
eiπ/3
eiπ/3
-i
i
eiπ/6
e-i5π/6
ei5π/6
e-iπ/6
-i
i
eiπ/6
e-i5π/6
ei5π/6
e-iπ/6
31
(
0 -1 0
-1 0 0
0 0 1
)
(
0 -(1+i3)/2
(1-i3)/2 0
)
m'110
1
-1
1
-1
1
-1
1
-1
1
-1
1
-1
1
1
1
1
1
1
-1
-1
-1
-1
-1
-1
32
(
-1 1 0
0 1 0
0 0 1
)
(
0 -1
1 0
)
m'100
1
-1
1
-1
e-i2π/3
eiπ/3
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
ei2π/3
e-iπ/3
-1
-1
eiπ/3
eiπ/3
e-iπ/3
e-iπ/3
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
33
(
1 0 0
1 -1 0
0 0 1
)
(
0 -(1-i3)/2
(1+i3)/2 0
)
m'010
1
-1
1
-1
ei2π/3
e-iπ/3
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
e-i2π/3
eiπ/3
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
-1
-1
e-iπ/3
e-iπ/3
eiπ/3
eiπ/3
34
(
0 1 0
1 0 0
0 0 1
)
(
0 -(3-i)/2
(3+i)/2 0
)
m'1-10
1
-1
-1
1
1
-1
-1
1
1
-1
-1
1
-i
i
-i
i
-i
i
i
-i
i
-i
i
-i
35
(
1 -1 0
0 -1 0
0 0 1
)
(
0 -i
-i 0
)
m'120
1
-1
-1
1
e-i2π/3
eiπ/3
eiπ/3
e-i2π/3
ei2π/3
e-iπ/3
e-iπ/3
ei2π/3
-i
i
ei5π/6
e-iπ/6
eiπ/6
e-i5π/6
i
-i
e-iπ/6
ei5π/6
e-i5π/6
eiπ/6
36
(
-1 0 0
-1 1 0
0 0 1
)
(
0 (3+i)/2
-(3-i)/2 0
)
m'210
1
-1
-1
1
ei2π/3
e-iπ/3
e-iπ/3
ei2π/3
e-i2π/3
eiπ/3
eiπ/3
e-i2π/3
-i
i
eiπ/6
e-i5π/6
ei5π/6
e-iπ/6
i
-i
e-i5π/6
eiπ/6
e-iπ/6
ei5π/6
37
(
0 1 0
1 0 0
0 0 -1
)
(
0 (1+i3)/2
-(1-i3)/2 0
)
d2'110
1
1
1
1
1
1
1
1
1
1
1
1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
38
(
1 -1 0
0 -1 0
0 0 -1
)
(
0 1
-1 0
)
d2'100
1
1
1
1
e-i2π/3
e-i2π/3
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
ei2π/3
ei2π/3
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
39
(
-1 0 0
-1 1 0
0 0 -1
)
(
0 (1-i3)/2
-(1+i3)/2 0
)
d2'010
1
1
1
1
ei2π/3
ei2π/3
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
e-i2π/3
e-i2π/3
-1
-1
e-iπ/3
e-iπ/3
eiπ/3
eiπ/3
-1
-1
e-iπ/3
e-iπ/3
eiπ/3
eiπ/3
40
(
0 -1 0
-1 0 0
0 0 -1
)
(
0 (3-i)/2
-(3+i)/2 0
)
d2'1-10
1
1
-1
-1
1
1
-1
-1
1
1
-1
-1
i
-i
i
-i
i
-i
i
-i
i
-i
i
-i
41
(
-1 1 0
0 1 0
0 0 -1
)
(
0 i
i 0
)
d2'120
1
1
-1
-1
e-i2π/3
e-i2π/3
eiπ/3
eiπ/3
ei2π/3
ei2π/3
e-iπ/3
e-iπ/3
i
-i
e-iπ/6
ei5π/6
e-i5π/6
eiπ/6
i
-i
e-iπ/6
ei5π/6
e-i5π/6
eiπ/6
42
(
1 0 0
1 -1 0
0 0 -1
)
(
0 -(3+i)/2
(3-i)/2 0
)
d2'210
1
1
-1
-1
ei2π/3
ei2π/3
e-iπ/3
e-iπ/3
e-i2π/3
e-i2π/3
eiπ/3
eiπ/3
i
-i
e-i5π/6
eiπ/6
e-iπ/6
ei5π/6
i
-i
e-i5π/6
eiπ/6
e-iπ/6
ei5π/6
43
(
0 -1 0
-1 0 0
0 0 1
)
(
0 (1+i3)/2
-(1-i3)/2 0
)
dm'110
1
-1
1
-1
1
-1
1
-1
1
-1
1
-1
-1
-1
-1
-1
-1
-1
1
1
1
1
1
1
44
(
-1 1 0
0 1 0
0 0 1
)
(
0 1
-1 0
)
dm'100
1
-1
1
-1
e-i2π/3
eiπ/3
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
ei2π/3
e-iπ/3
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
-1
-1
eiπ/3
eiπ/3
e-iπ/3
e-iπ/3
45
(
1 0 0
1 -1 0
0 0 1
)
(
0 (1-i3)/2
-(1+i3)/2 0
)
dm'010
1
-1
1
-1
ei2π/3
e-iπ/3
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
e-i2π/3
eiπ/3
-1
-1
e-iπ/3
e-iπ/3
eiπ/3
eiπ/3
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
46
(
0 1 0
1 0 0
0 0 1
)
(
0 (3-i)/2
-(3+i)/2 0
)
dm'1-10
1
-1
-1
1
1
-1
-1
1
1
-1
-1
1
i
-i
i
-i
i
-i
-i
i
-i
i
-i
i
47
(
1 -1 0
0 -1 0
0 0 1
)
(
0 i
i 0
)
dm'120
1
-1
-1
1
e-i2π/3
eiπ/3
eiπ/3
e-i2π/3
ei2π/3
e-iπ/3
e-iπ/3
ei2π/3
i
-i
e-iπ/6
ei5π/6
e-i5π/6
eiπ/6
-i
i
ei5π/6
e-iπ/6
eiπ/6
e-i5π/6
48
(
-1 0 0
-1 1 0
0 0 1
)
(
0 -(3+i)/2
(3-i)/2 0
)
dm'210
1
-1
-1
1
ei2π/3
e-iπ/3
e-iπ/3
ei2π/3
e-i2π/3
eiπ/3
eiπ/3
e-i2π/3
i
-i
e-i5π/6
eiπ/6
e-iπ/6
ei5π/6
-i
i
eiπ/6
e-i5π/6
ei5π/6
e-iπ/6
k-Subgroupsmag
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