Bilbao Crystallographic Server COREPRESENTATIONS PG

Irreducible corepresentations of the Magnetic Point Group 4m'm' (N. 13.4.47)

Table of characters of the unitary symmetry operations

 (1) (2) (3) C1 C2 C3 C4 C5 C6 C7 C8 GM1 A GM1 1 1 1 1 1 1 1 1 GM2 B GM2 1 1 -1 -1 1 1 -1 -1 GM3 2E GM3 1 -1 i -i 1 -1 i -i GM4 1E GM4 1 -1 -i i 1 -1 -i i GM7 2E2 GM5 1 -i -(1-i)√2/2 -(1+i)√2/2 -1 i (1-i)√2/2 (1+i)√2/2 GM5 2E1 GM6 1 -i (1-i)√2/2 (1+i)√2/2 -1 i -(1-i)√2/2 -(1+i)√2/2 GM8 1E2 GM7 1 i -(1+i)√2/2 -(1-i)√2/2 -1 -i (1+i)√2/2 (1-i)√2/2 GM6 1E1 GM8 1 i (1+i)√2/2 (1-i)√2/2 -1 -i -(1+i)√2/2 -(1-i)√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: 2001 C3: 4+001 C4: 4-001 C5: d1 C6: d2001 C7: d4+001 C8: d4-001

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbolGM1GM2GM3GM4GM5GM6GM7GM8
1
 1 0 0 0 1 0 0 0 1
 1 0 0 1
1
 1
 1
 1
 1
 1
 1
 1
 1
2
 -1 0 0 0 -1 0 0 0 1
 -i 0 0 i
2001
 1
 1
 -1
 -1
 -i
 -i
 i
 i
3
 0 -1 0 1 0 0 0 0 1
 (1-i)√2/2 0 0 (1+i)√2/2
4+001
 1
 -1
 i
 -i
 ei3π/4
 e-iπ/4
 e-i3π/4
 eiπ/4
4
 0 1 0 -1 0 0 0 0 1
 (1+i)√2/2 0 0 (1-i)√2/2
4-001
 1
 -1
 -i
 i
 e-i3π/4
 eiπ/4
 ei3π/4
 e-iπ/4
5
 1 0 0 0 1 0 0 0 1
 -1 0 0 -1
d1
 1
 1
 1
 1
 -1
 -1
 -1
 -1
6
 -1 0 0 0 -1 0 0 0 1
 i 0 0 -i
d2001
 1
 1
 -1
 -1
 i
 i
 -i
 -i
7
 0 -1 0 1 0 0 0 0 1
 -(1-i)√2/2 0 0 -(1+i)√2/2
d4+001
 1
 -1
 i
 -i
 e-iπ/4
 ei3π/4
 eiπ/4
 e-i3π/4
8
 0 1 0 -1 0 0 0 0 1
 -(1+i)√2/2 0 0 -(1-i)√2/2
d4-001
 1
 -1
 -i
 i
 eiπ/4
 e-i3π/4
 e-iπ/4
 ei3π/4
9
 1 0 0 0 -1 0 0 0 1
 0 -1 1 0
m'010
 1
 1
 1
 1
 1
 1
 1
 1
10
 -1 0 0 0 1 0 0 0 1
 0 -i -i 0
m'100
 1
 1
 -1
 -1
 i
 i
 -i
 -i
11
 0 -1 0 -1 0 0 0 0 1
 0 -(1+i)√2/2 (1-i)√2/2 0
m'110
 1
 -1
 -i
 i
 e-i3π/4
 eiπ/4
 ei3π/4
 e-iπ/4
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
 i
 -i
 ei3π/4
 e-iπ/4
 e-i3π/4
 eiπ/4
13
 1 0 0 0 -1 0 0 0 1
 0 1 -1 0
dm'010
 1
 1
 1
 1
 -1
 -1
 -1
 -1
14
 -1 0 0 0 1 0 0 0 1
 0 i i 0
dm'100
 1
 1
 -1
 -1
 -i
 -i
 i
 i
15
 0 -1 0 -1 0 0 0 0 1
 0 (1+i)√2/2 -(1-i)√2/2 0
dm'110
 1
 -1
 -i
 i
 eiπ/4
 e-i3π/4
 e-iπ/4
 ei3π/4
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
 i
 -i
 e-iπ/4
 ei3π/4
 eiπ/4
 e-i3π/4
k-Subgroupsmag
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