Bilbao Crystallographic Server arrow COREPRESENTATIONS PG

Irreducible corepresentations of the Magnetic Point Group 21' (N. 3.2.7)


Table of characters of the unitary symmetry operations


(1)
(2)
(3)
C1
C2
C3
C4
GM1
A
GM1
1
1
1
1
GM2
B
GM2
1
-1
1
-1
GM4GM3
2E1E
GM3GM4
2
0
-2
0
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: 2010
C3d1
C4d2010

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbolGM1GM2GM3GM4
1
(
1 0 0
0 1 0
0 0 1
)
(
1 0
0 1
)
1
1
1
(
1 0
0 1
)
2
(
-1 0 0
0 1 0
0 0 -1
)
(
0 -1
1 0
)
2010
1
-1
(
-i 0
0 i
)
3
(
1 0 0
0 1 0
0 0 1
)
(
-1 0
0 -1
)
d1
1
1
(
-1 0
0 -1
)
4
(
-1 0 0
0 1 0
0 0 -1
)
(
0 1
-1 0
)
d2010
1
-1
(
i 0
0 -i
)
5
(
1 0 0
0 1 0
0 0 1
)
(
1 0
0 1
)
1'
1
1
(
0 -1
1 0
)
6
(
-1 0 0
0 1 0
0 0 -1
)
(
0 -1
1 0
)
2'010
1
-1
(
0 i
i 0
)
7
(
1 0 0
0 1 0
0 0 1
)
(
-1 0
0 -1
)
d1'
1
1
(
0 1
-1 0
)
8
(
-1 0 0
0 1 0
0 0 -1
)
(
0 1
-1 0
)
d2'010
1
-1
(
0 -i
-i 0
)
k-Subgroupsmag
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