Bilbao Crystallographic Server arrow COREPRESENTATIONS PG

Irreducible corepresentations of the Magnetic Point Group 2221' (N. 6.2.18)


Table of characters of the unitary symmetry operations


(1)
(2)
(3)
C1
C2
C3
C4
C5
GM1
A1
GM1
1
1
1
1
1
GM3
B1
GM2
1
1
-1
-1
1
GM4
B3
GM3
1
-1
-1
1
1
GM2
B2
GM4
1
-1
1
-1
1
GM5
E
GM5
2
0
0
0
-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
C5d1

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbolGM1GM2GM3GM4GM5
1
(
1 0 0
0 1 0
0 0 1
)
(
1 0
0 1
)
1
1
1
1
1
(
1 0
0 1
)
2
(
-1 0 0
0 -1 0
0 0 1
)
(
-i 0
0 i
)
2001
1
1
-1
-1
(
0 -1
1 0
)
3
(
-1 0 0
0 1 0
0 0 -1
)
(
0 -1
1 0
)
2010
1
-1
-1
1
(
0 -i
-i 0
)
4
(
1 0 0
0 -1 0
0 0 -1
)
(
0 -i
-i 0
)
2100
1
-1
1
-1
(
-i 0
0 i
)
5
(
1 0 0
0 1 0
0 0 1
)
(
-1 0
0 -1
)
d1
1
1
1
1
(
-1 0
0 -1
)
6
(
-1 0 0
0 -1 0
0 0 1
)
(
i 0
0 -i
)
d2001
1
1
-1
-1
(
0 1
-1 0
)
7
(
-1 0 0
0 1 0
0 0 -1
)
(
0 1
-1 0
)
d2010
1
-1
-1
1
(
0 i
i 0
)
8
(
1 0 0
0 -1 0
0 0 -1
)
(
0 i
i 0
)
d2100
1
-1
1
-1
(
i 0
0 -i
)
9
(
1 0 0
0 1 0
0 0 1
)
(
1 0
0 1
)
1'
1
1
1
1
(
0 1
-1 0
)
10
(
-1 0 0
0 -1 0
0 0 1
)
(
-i 0
0 i
)
2'001
1
1
-1
-1
(
1 0
0 1
)
11
(
-1 0 0
0 1 0
0 0 -1
)
(
0 -1
1 0
)
2'010
1
-1
-1
1
(
i 0
0 -i
)
12
(
1 0 0
0 -1 0
0 0 -1
)
(
0 -i
-i 0
)
2'100
1
-1
1
-1
(
0 -i
-i 0
)
13
(
1 0 0
0 1 0
0 0 1
)
(
-1 0
0 -1
)
d1'
1
1
1
1
(
0 -1
1 0
)
14
(
-1 0 0
0 -1 0
0 0 1
)
(
i 0
0 -i
)
d2'001
1
1
-1
-1
(
-1 0
0 -1
)
15
(
-1 0 0
0 1 0
0 0 -1
)
(
0 1
-1 0
)
d2'010
1
-1
-1
1
(
-i 0
0 i
)
16
(
1 0 0
0 -1 0
0 0 -1
)
(
0 i
i 0
)
d2'100
1
-1
1
-1
(
0 i
i 0
)
k-Subgroupsmag
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