Bilbao Crystallographic Server arrow COREPRESENTATIONS PG

Irreducible corepresentations of the Projective Magnetic Point Group 4π'


Table of characters of the unitary symmetry operations


1
2
d1
d2
B
1
-1
1
-1
AA
2
2
2
2
1E2E
2
0
-2
0

Multiplication table of the symmetry operations


1
2
d1
d2
4+'
4-'
d4+'
d4-'
1
1
2
d1
d2
4+'
4-'
d4+'
d4-'
2
2
d1
d2
1
d4-'
4+'
4-'
d4+'
d1
d1
d2
1
2
d4+'
d4-'
4+'
4-'
d2
d2
1
2
d1
4-'
d4+'
d4-'
4+'
4+'
4+'
d4-'
d4+'
4-'
d2
d1
2
1
4-'
4-'
4+'
d4-'
d4+'
d1
2
1
d2
d4+'
d4+'
4-'
4+'
d4-'
2
1
d2
d1
d4-'
d4-'
d4+'
4-'
4+'
1
d2
d1
2

Table of projective phases in group multiplication


1
2
d1
d2
4+'
4-'
d4+'
d4-'
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
d1
1
1
1
1
1
1
1
1
d2
1
1
1
1
1
1
1
1
4+'
1
1
1
1
-1
-1
-1
-1
4-'
1
1
1
1
-1
-1
-1
-1
d4+'
1
1
1
1
-1
-1
-1
-1
d4-'
1
1
1
1
-1
-1
-1
-1

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbolBAA1E2E
1
(
 1 0
 0 1
)
(
 1 0
 0 1
)
1
1
(
 1 0
 0 1
)
(
 1 0
 0 1
)
2
(
 -1  0
  0 -1
)
(
 -i  0
  0  i
)
2
-1
(
 1 0
 0 1
)
(
 -i  0
  0  i
)
3
(
 1 0
 0 1
)
(
 -1  0
  0 -1
)
d1
1
(
 1 0
 0 1
)
(
 -1  0
  0 -1
)
4
(
 -1  0
  0 -1
)
(
  i  0
  0 -i
)
d2
-1
(
 1 0
 0 1
)
(
  i  0
  0 -i
)
5
(
  0 -1
  1  0
)
(
 e-iπ/4  0
  0  eiπ/4
)
4+'
-1
(
  0  1
 -1  0
)
(
  0 -i
  1  0
)
6
(
  0  1
 -1  0
)
(
  eiπ/4  0
  0 e-iπ/4
)
4-'
1
(
  0  1
 -1  0
)
(
  0  1
 -i  0
)
7
(
  0 -1
  1  0
)
(
  e3iπ/4  0
  0 e-3iπ/4
)
d4+'
-1
(
  0  1
 -1  0
)
(
  0  i
 -1  0
)
8
(
  0  1
 -1  0
)
(
 e-3iπ/4  0
  0  e3iπ/4
)
d4-'
1
(
  0  1
 -1  0
)
(
  0 -1
  i  0
)
k-Subgroupsmag
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