Bilbao Crystallographic Server arrow COREPRESENTATIONS PG

Irreducible corepresentations of the Magnetic Point Group mmm1' (N. 8.2.25)


Table of characters of the unitary symmetry operations


(1)
(2)
(3)
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
GM1+
Ag
GM1+
1
1
1
1
1
1
1
1
1
1
GM1-
Au
GM1-
1
1
1
1
-1
-1
-1
-1
1
-1
GM3+
B1g
GM2+
1
1
-1
-1
1
1
-1
-1
1
1
GM3-
B1u
GM2-
1
1
-1
-1
-1
-1
1
1
1
-1
GM4+
B3g
GM3+
1
-1
-1
1
1
-1
-1
1
1
1
GM4-
B3u
GM3-
1
-1
-1
1
-1
1
1
-1
1
-1
GM2+
B2g
GM4+
1
-1
1
-1
1
-1
1
-1
1
1
GM2-
B2u
GM4-
1
-1
1
-1
-1
1
-1
1
1
-1
GM5+
Eg
GM5
2
0
0
0
2
0
0
0
-2
-2
GM5-
Eu
GM6
2
0
0
0
-2
0
0
0
-2
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: 2001d2001
C3: 2010d2010
C4: 2100d2100
C51
C6: m001dm001
C7: m010dm010
C8: m100dm100
C9d1
C10d1

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-GM5GM6
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
)
2
(
-1 0 0
0 -1 0
0 0 1
)
(
-i 0
0 i
)
2001
1
1
1
1
-1
-1
-1
-1
(
0 -1
1 0
)
(
0 -1
1 0
)
3
(
-1 0 0
0 1 0
0 0 -1
)
(
0 -1
1 0
)
2010
1
1
-1
-1
-1
-1
1
1
(
0 -i
-i 0
)
(
0 -i
-i 0
)
4
(
1 0 0
0 -1 0
0 0 -1
)
(
0 -i
-i 0
)
2100
1
1
-1
-1
1
1
-1
-1
(
-i 0
0 i
)
(
-i 0
0 i
)
5
(
-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
)
6
(
1 0 0
0 1 0
0 0 -1
)
(
-i 0
0 i
)
m001
1
-1
1
-1
-1
1
-1
1
(
0 -1
1 0
)
(
0 1
-1 0
)
7
(
1 0 0
0 -1 0
0 0 1
)
(
0 -1
1 0
)
m010
1
-1
-1
1
-1
1
1
-1
(
0 -i
-i 0
)
(
0 i
i 0
)
8
(
-1 0 0
0 1 0
0 0 1
)
(
0 -i
-i 0
)
m100
1
-1
-1
1
1
-1
-1
1
(
-i 0
0 i
)
(
i 0
0 -i
)
9
(
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
)
10
(
-1 0 0
0 -1 0
0 0 1
)
(
i 0
0 -i
)
d2001
1
1
1
1
-1
-1
-1
-1
(
0 1
-1 0
)
(
0 1
-1 0
)
11
(
-1 0 0
0 1 0
0 0 -1
)
(
0 1
-1 0
)
d2010
1
1
-1
-1
-1
-1
1
1
(
0 i
i 0
)
(
0 i
i 0
)
12
(
1 0 0
0 -1 0
0 0 -1
)
(
0 i
i 0
)
d2100
1
1
-1
-1
1
1
-1
-1
(
i 0
0 -i
)
(
i 0
0 -i
)
13
(
-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
)
14
(
1 0 0
0 1 0
0 0 -1
)
(
i 0
0 -i
)
dm001
1
-1
1
-1
-1
1
-1
1
(
0 1
-1 0
)
(
0 -1
1 0
)
15
(
1 0 0
0 -1 0
0 0 1
)
(
0 1
-1 0
)
dm010
1
-1
-1
1
-1
1
1
-1
(
0 i
i 0
)
(
0 -i
-i 0
)
16
(
-1 0 0
0 1 0
0 0 1
)
(
0 i
i 0
)
dm100
1
-1
-1
1
1
-1
-1
1
(
i 0
0 -i
)
(
-i 0
0 i
)
17
(
1 0 0
0 1 0
0 0 1
)
(
1 0
0 1
)
1'
1
-1
1
-1
1
-1
1
-1
(
0 1
-1 0
)
(
0 -1
1 0
)
18
(
-1 0 0
0 -1 0
0 0 1
)
(
-i 0
0 i
)
2'001
1
-1
1
-1
-1
1
-1
1
(
1 0
0 1
)
(
-1 0
0 -1
)
19
(
-1 0 0
0 1 0
0 0 -1
)
(
0 -1
1 0
)
2'010
1
-1
-1
1
-1
1
1
-1
(
i 0
0 -i
)
(
-i 0
0 i
)
20
(
1 0 0
0 -1 0
0 0 -1
)
(
0 -i
-i 0
)
2'100
1
-1
-1
1
1
-1
-1
1
(
0 -i
-i 0
)
(
0 i
i 0
)
21
(
-1 0 0
0 -1 0
0 0 -1
)
(
1 0
0 1
)
1'
1
1
1
1
1
1
1
1
(
0 1
-1 0
)
(
0 1
-1 0
)
22
(
1 0 0
0 1 0
0 0 -1
)
(
-i 0
0 i
)
m'001
1
1
1
1
-1
-1
-1
-1
(
1 0
0 1
)
(
1 0
0 1
)
23
(
1 0 0
0 -1 0
0 0 1
)
(
0 -1
1 0
)
m'010
1
1
-1
-1
-1
-1
1
1
(
i 0
0 -i
)
(
i 0
0 -i
)
24
(
-1 0 0
0 1 0
0 0 1
)
(
0 -i
-i 0
)
m'100
1
1
-1
-1
1
1
-1
-1
(
0 -i
-i 0
)
(
0 -i
-i 0
)
25
(
1 0 0
0 1 0
0 0 1
)
(
-1 0
0 -1
)
d1'
1
-1
1
-1
1
-1
1
-1
(
0 -1
1 0
)
(
0 1
-1 0
)
26
(
-1 0 0
0 -1 0
0 0 1
)
(
i 0
0 -i
)
d2'001
1
-1
1
-1
-1
1
-1
1
(
-1 0
0 -1
)
(
1 0
0 1
)
27
(
-1 0 0
0 1 0
0 0 -1
)
(
0 1
-1 0
)
d2'010
1
-1
-1
1
-1
1
1
-1
(
-i 0
0 i
)
(
i 0
0 -i
)
28
(
1 0 0
0 -1 0
0 0 -1
)
(
0 i
i 0
)
d2'100
1
-1
-1
1
1
-1
-1
1
(
0 i
i 0
)
(
0 -i
-i 0
)
29
(
-1 0 0
0 -1 0
0 0 -1
)
(
-1 0
0 -1
)
d1'
1
1
1
1
1
1
1
1
(
0 -1
1 0
)
(
0 -1
1 0
)
30
(
1 0 0
0 1 0
0 0 -1
)
(
i 0
0 -i
)
dm'001
1
1
1
1
-1
-1
-1
-1
(
-1 0
0 -1
)
(
-1 0
0 -1
)
31
(
1 0 0
0 -1 0
0 0 1
)
(
0 1
-1 0
)
dm'010
1
1
-1
-1
-1
-1
1
1
(
-i 0
0 i
)
(
-i 0
0 i
)
32
(
-1 0 0
0 1 0
0 0 1
)
(
0 i
i 0
)
dm'100
1
1
-1
-1
1
1
-1
-1
(
0 i
i 0
)
(
0 i
i 0
)
k-Subgroupsmag
Bilbao Crystallographic Server
http://www.cryst.ehu.es
Licencia de Creative Commons
For comments, please mail to
administrador.bcs@ehu.eus