Bilbao Crystallographic Server arrow COREPRESENTATIONS PG

Irreducible corepresentations of the Magnetic Point Group -4'2m' (N. 14.4.51)


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
GM4GM2
B3B2
GM3GM4
2
-2
0
0
2
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 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 0
0 -1
)
(
0 -1
1 0
)
3
(
-1 0 0
0 1 0
0 0 -1
)
(
0 -1
1 0
)
2010
1
-1
(
-1 0
0 1
)
(
0 -i
-i 0
)
4
(
1 0 0
0 -1 0
0 0 -1
)
(
0 -i
-i 0
)
2100
1
-1
(
1 0
0 -1
)
(
-i 0
0 i
)
5
(
1 0 0
0 1 0
0 0 1
)
(
-1 0
0 -1
)
d1
1
1
(
1 0
0 1
)
(
-1 0
0 -1
)
6
(
-1 0 0
0 -1 0
0 0 1
)
(
i 0
0 -i
)
d2001
1
1
(
-1 0
0 -1
)
(
0 1
-1 0
)
7
(
-1 0 0
0 1 0
0 0 -1
)
(
0 1
-1 0
)
d2010
1
-1
(
-1 0
0 1
)
(
0 i
i 0
)
8
(
1 0 0
0 -1 0
0 0 -1
)
(
0 i
i 0
)
d2100
1
-1
(
1 0
0 -1
)
(
i 0
0 -i
)
9
(
0 1 0
-1 0 0
0 0 -1
)
(
(1-i)2/2 0
0 (1+i)2/2
)
4'+001
1
-1
(
0 -1
1 0
)
(
-1/2 -1/2
1/2 -1/2
)
10
(
0 -1 0
1 0 0
0 0 -1
)
(
(1+i)2/2 0
0 (1-i)2/2
)
4'-001
1
-1
(
0 1
-1 0
)
(
1/2 -1/2
1/2 1/2
)
11
(
0 -1 0
-1 0 0
0 0 1
)
(
0 -(1+i)2/2
(1-i)2/2 0
)
m'110
1
1
(
0 1
1 0
)
(
-i/2 i/2
i/2 i/2
)
12
(
0 1 0
1 0 0
0 0 1
)
(
0 -(1-i)2/2
(1+i)2/2 0
)
m'1-10
1
1
(
0 -1
-1 0
)
(
-i/2 -i/2
-i/2 i/2
)
13
(
0 1 0
-1 0 0
0 0 -1
)
(
-(1-i)2/2 0
0 -(1+i)2/2
)
d4'+001
1
-1
(
0 -1
1 0
)
(
1/2 1/2
-1/2 1/2
)
14
(
0 -1 0
1 0 0
0 0 -1
)
(
-(1+i)2/2 0
0 -(1-i)2/2
)
d4'-001
1
-1
(
0 1
-1 0
)
(
-1/2 1/2
-1/2 -1/2
)
15
(
0 -1 0
-1 0 0
0 0 1
)
(
0 (1+i)2/2
-(1-i)2/2 0
)
dm'110
1
1
(
0 1
1 0
)
(
i/2 -i/2
-i/2 -i/2
)
16
(
0 1 0
1 0 0
0 0 1
)
(
0 (1-i)2/2
-(1+i)2/2 0
)
dm'1-10
1
1
(
0 -1
-1 0
)
(
i/2 i/2
i/2 -i/2
)
k-Subgroupsmag
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