Bilbao Crystallographic Server COREPRESENTATIONS PG

Irreducible corepresentations of the Magnetic Point Group -42'm' (N. 14.5.52)

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`
2'010
 1
 1
 1
 1
 1
 1
 1
 1
10
 ` 1 0 0 0 -1 0 0 0 -1`
 ` 0 -i -i 0`
2'100
 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`
d2'010
 1
 1
 1
 1
 -1
 -1
 -1
 -1
14
 ` 1 0 0 0 -1 0 0 0 -1`
 ` 0 i i 0`
d2'100
 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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