Bilbao Crystallographic Server COREPRESENTATIONS PG

## Irreducible corepresentations of the Magnetic Point Group m'mm (N. 8.3.26)

### 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 A2 GM2 1 1 -1 -1 1 GM4 B2 GM3 1 -1 1 -1 1 GM2 B1 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: 2100, d2100 C3: m001, dm001 C4: m010, dm010 C5: d1

### 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`
 ` 0 -i -i 0`
2100
 1
 1
 -1
 -1
 ` 0 -1 1 0`
3
 ` 1 0 0 0 1 0 0 0 -1`
 ` -i 0 0 i`
m001
 1
 -1
 1
 -1
 ` i 0 0 -i`
4
 ` 1 0 0 0 -1 0 0 0 1`
 ` 0 -1 1 0`
m010
 1
 -1
 -1
 1
 ` 0 -i -i 0`
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`
 ` 0 i i 0`
d2100
 1
 1
 -1
 -1
 ` 0 1 -1 0`
7
 ` 1 0 0 0 1 0 0 0 -1`
 ` i 0 0 -i`
dm001
 1
 -1
 1
 -1
 ` -i 0 0 i`
8
 ` 1 0 0 0 -1 0 0 0 1`
 ` 0 1 -1 0`
dm010
 1
 -1
 -1
 1
 ` 0 i i 0`
9
 ` -1 0 0 0 -1 0 0 0 1`
 ` -i 0 0 i`
2'001
 1
 -1
 1
 -1
 ` 0 i i 0`
10
 ` -1 0 0 0 1 0 0 0 -1`
 ` 0 -1 1 0`
2'010
 1
 -1
 -1
 1
 ` i 0 0 -i`
11
 ` -1 0 0 0 -1 0 0 0 -1`
 ` 1 0 0 1`
1'
 1
 1
 1
 1
 ` 0 1 -1 0`
12
 ` -1 0 0 0 1 0 0 0 1`
 ` 0 -i -i 0`
m'100
 1
 1
 -1
 -1
 ` 1 0 0 1`
13
 ` -1 0 0 0 -1 0 0 0 1`
 ` i 0 0 -i`
d2'001
 1
 -1
 1
 -1
 ` 0 -i -i 0`
14
 ` -1 0 0 0 1 0 0 0 -1`
 ` 0 1 -1 0`
d2'010
 1
 -1
 -1
 1
 ` -i 0 0 i`
15
 ` -1 0 0 0 -1 0 0 0 -1`
 ` -1 0 0 -1`
d1'
 1
 1
 1
 1
 ` 0 -1 1 0`
16
 ` -1 0 0 0 1 0 0 0 1`
 ` 0 i i 0`
dm'100
 1
 1
 -1
 -1
 ` -1 0 0 -1`
k-Subgroupsmag
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