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+
2E1g1E1g
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-
2E1u1E1u
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+
2E2g1E2g
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-
2E2u1E2u
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+
2E1g1E1g
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-
2E1u1E1u
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-
2E2u1E2u
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
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+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+i3)/2 0
0 (1-i3)/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-i3)/2 0
0 (1+i3)/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+i3)/2 0
0 (1-i3)/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-i3)/2 0
0 (1+i3)/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+i3)/2 0
0 -(1-i3)/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-i3)/2 0
0 -(1+i3)/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+i3)/2 0
0 -(1-i3)/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-i3)/2 0
0 -(1+i3)/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+i3)/2 0
0 (1-i3)/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-i3)/2 0
0 (1+i3)/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+i3)/2 0
0 (1-i3)/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-i3)/2 0
0 (1+i3)/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+i3)/2 0
0 -(1-i3)/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-i3)/2 0
0 -(1+i3)/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+i3)/2 0
0 -(1-i3)/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-i3)/2 0
0 -(1+i3)/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
Bilbao Crystallographic Server
http://www.cryst.ehu.es
Licencia de Creative Commons
For comments, please mail to
administrador.bcs@ehu.eus