Bilbao Crystallographic Server COREPRESENTATIONS PG

Irreducible corepresentations of the Magnetic Point Group -4' (N. 10.3.34)

Table of characters of the unitary symmetry operations

 (1) (2) (3) C1 C2 C3 C4 GM1 A GM1 1 1 1 1 GM2GM2 BB GM2GM2 2 -2 2 -2 GM4GM3 1E2E 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: 2001 C3: d1 C4: d2001

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbolGM1GM2GM2GM3GM4
1
 ` 1 0 0 0 1 0 0 0 1`
 ` 1 0 0 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 0 0 -1`
 ` -i 0 0 i`
3
 ` 1 0 0 0 1 0 0 0 1`
 ` -1 0 0 -1`
d1
 1
 ` 1 0 0 1`
 ` -1 0 0 -1`
4
 ` -1 0 0 0 -1 0 0 0 1`
 ` i 0 0 -i`
d2001
 1
 ` -1 0 0 -1`
 ` i 0 0 -i`
5
 ` 0 1 0 -1 0 0 0 0 -1`
 ` (1-i)√2/2 0 0 (1+i)√2/2`
4'+001
 1
 ` 0 -1 1 0`
 ` 0 i 1 0`
6
 ` 0 -1 0 1 0 0 0 0 -1`
 ` (1+i)√2/2 0 0 (1-i)√2/2`
4'-001
 1
 ` 0 1 -1 0`
 ` 0 -1 -i 0`
7
 ` 0 1 0 -1 0 0 0 0 -1`
 ` -(1-i)√2/2 0 0 -(1+i)√2/2`
d4'+001
 1
 ` 0 -1 1 0`
 ` 0 -i -1 0`
8
 ` 0 -1 0 1 0 0 0 0 -1`
 ` -(1+i)√2/2 0 0 -(1-i)√2/2`
d4'-001
 1
 ` 0 1 -1 0`
 ` 0 1 i 0`
k-Subgroupsmag
 Bilbao Crystallographic Serverhttp://www.cryst.ehu.es