Bilbao Crystallographic Server arrow COREPRESENTATIONS PG

Irreducible corepresentations of the Projective Magnetic Point Group 34π/3m1'


Table of characters of the unitary symmetry operations


1
3+
3-
m1-1
m12
m21
d1
d3+
d3-
dm1-1
dm12
dm21
1E'
1
e-2iπ/3
e2iπ/3
1
1
e-2iπ/3
e2iπ/3
1
1E''
1
e-2iπ/3
e2iπ/3
-1
1
e-2iπ/3
e2iπ/3
-1
2EA
2
eiπ/3
e-iπ/3
0
2
eiπ/3
e-iπ/3
0
2E12E2
2
2eiπ/3
2e-iπ/3
0
-2
2e-2iπ/3
2e2iπ/3
0
1EE
2
e-2iπ/3
e2iπ/3
0
-2
eiπ/3
e-iπ/3
0

Multiplication table of the symmetry operations


1
3+
3-
m1-1
m12
m21
d1
d3+
d3-
dm1-1
dm12
dm21
1'
3+'
3-'
m'1-1
m'12
m'21
d1'
d3+'
d3-'
dm'1-1
dm'12
dm'21
1
1
3+
3-
m1-1
m12
m21
d1
d3+
d3-
dm1-1
dm12
dm21
1'
3+'
3-'
m'1-1
m'12
m'21
d1'
d3+'
d3-'
dm'1-1
dm'12
dm'21
3+
3+
d3-
1
dm21
dm1-1
dm12
d3+
3-
d1
m21
m1-1
m12
3+'
d3-'
1'
dm'21
dm'1-1
dm'12
d3+'
3-'
d1'
m'21
m'1-1
m'12
3-
3-
1
d3+
dm12
dm21
dm1-1
d3-
d1
3+
m12
m21
m1-1
3-'
1'
d3+'
dm'12
dm'21
dm'1-1
d3-'
d1'
3+'
m'12
m'21
m'1-1
m1-1
m1-1
dm12
dm21
d1
3+
3-
dm1-1
m12
m21
1
d3+
d3-
m'1-1
dm'12
dm'21
d1'
3+'
3-'
dm'1-1
m'12
m'21
1'
d3+'
d3-'
m12
m12
dm21
dm1-1
3-
d1
3+
dm12
m21
m1-1
d3-
1
d3+
m'12
dm'21
dm'1-1
3-'
d1'
3+'
dm'12
m'21
m'1-1
d3-'
1'
d3+'
m21
m21
dm1-1
dm12
3+
3-
d1
dm21
m1-1
m12
d3+
d3-
1
m'21
dm'1-1
dm'12
3+'
3-'
d1'
dm'21
m'1-1
m'12
d3+'
d3-'
1'
d1
d1
d3+
d3-
dm1-1
dm12
dm21
1
3+
3-
m1-1
m12
m21
d1'
d3+'
d3-'
dm'1-1
dm'12
dm'21
1'
3+'
3-'
m'1-1
m'12
m'21
d3+
d3+
3-
d1
m21
m1-1
m12
3+
d3-
1
dm21
dm1-1
dm12
d3+'
3-'
d1'
m'21
m'1-1
m'12
3+'
d3-'
1'
dm'21
dm'1-1
dm'12
d3-
d3-
d1
3+
m12
m21
m1-1
3-
1
d3+
dm12
dm21
dm1-1
d3-'
d1'
3+'
m'12
m'21
m'1-1
3-'
1'
d3+'
dm'12
dm'21
dm'1-1
dm1-1
dm1-1
m12
m21
1
d3+
d3-
m1-1
dm12
dm21
d1
3+
3-
dm'1-1
m'12
m'21
1'
d3+'
d3-'
m'1-1
dm'12
dm'21
d1'
3+'
3-'
dm12
dm12
m21
m1-1
d3-
1
d3+
m12
dm21
dm1-1
3-
d1
3+
dm'12
m'21
m'1-1
d3-'
1'
d3+'
m'12
dm'21
dm'1-1
3-'
d1'
3+'
dm21
dm21
m1-1
m12
d3+
d3-
1
m21
dm1-1
dm12
3+
3-
d1
dm'21
m'1-1
m'12
d3+'
d3-'
1'
m'21
dm'1-1
dm'12
3+'
3-'
d1'
1'
1'
3+'
3-'
m'1-1
m'12
m'21
d1'
d3+'
d3-'
dm'1-1
dm'12
dm'21
d1
d3+
d3-
dm1-1
dm12
dm21
1
3+
3-
m1-1
m12
m21
3+'
3+'
d3-'
1'
dm'21
dm'1-1
dm'12
d3+'
3-'
d1'
m'21
m'1-1
m'12
d3+
3-
d1
m21
m1-1
m12
3+
d3-
1
dm21
dm1-1
dm12
3-'
3-'
1'
d3+'
dm'12
dm'21
dm'1-1
d3-'
d1'
3+'
m'12
m'21
m'1-1
d3-
d1
3+
m12
m21
m1-1
3-
1
d3+
dm12
dm21
dm1-1
m'1-1
m'1-1
dm'12
dm'21
d1'
3+'
3-'
dm'1-1
m'12
m'21
1'
d3+'
d3-'
dm1-1
m12
m21
1
d3+
d3-
m1-1
dm12
dm21
d1
3+
3-
m'12
m'12
dm'21
dm'1-1
3-'
d1'
3+'
dm'12
m'21
m'1-1
d3-'
1'
d3+'
dm12
m21
m1-1
d3-
1
d3+
m12
dm21
dm1-1
3-
d1
3+
m'21
m'21
dm'1-1
dm'12
3+'
3-'
d1'
dm'21
m'1-1
m'12
d3+'
d3-'
1'
dm21
m1-1
m12
d3+
d3-
1
m21
dm1-1
dm12
3+
3-
d1
d1'
d1'
d3+'
d3-'
dm'1-1
dm'12
dm'21
1'
3+'
3-'
m'1-1
m'12
m'21
1
3+
3-
m1-1
m12
m21
d1
d3+
d3-
dm1-1
dm12
dm21
d3+'
d3+'
3-'
d1'
m'21
m'1-1
m'12
3+'
d3-'
1'
dm'21
dm'1-1
dm'12
3+
d3-
1
dm21
dm1-1
dm12
d3+
3-
d1
m21
m1-1
m12
d3-'
d3-'
d1'
3+'
m'12
m'21
m'1-1
3-'
1'
d3+'
dm'12
dm'21
dm'1-1
3-
1
d3+
dm12
dm21
dm1-1
d3-
d1
3+
m12
m21
m1-1
dm'1-1
dm'1-1
m'12
m'21
1'
d3+'
d3-'
m'1-1
dm'12
dm'21
d1'
3+'
3-'
m1-1
dm12
dm21
d1
3+
3-
dm1-1
m12
m21
1
d3+
d3-
dm'12
dm'12
m'21
m'1-1
d3-'
1'
d3+'
m'12
dm'21
dm'1-1
3-'
d1'
3+'
m12
dm21
dm1-1
3-
d1
3+
dm12
m21
m1-1
d3-
1
d3+
dm'21
dm'21
m'1-1
m'12
d3+'
d3-'
1'
m'21
dm'1-1
dm'12
3+'
3-'
d1'
m21
dm1-1
dm12
3+
3-
d1
dm21
m1-1
m12
d3+
d3-
1

Table of projective phases in group multiplication


1
3+
3-
m1-1
m12
m21
d1
d3+
d3-
dm1-1
dm12
dm21
1'
3+'
3-'
m'1-1
m'12
m'21
d1'
d3+'
d3-'
dm'1-1
dm'12
dm'21
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3+
1
1
1
e-2iπ/3
e-2iπ/3
e-2iπ/3
1
1
1
e-2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
3-
1
1
1
e2iπ/3
e2iπ/3
e2iπ/3
1
1
1
e2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
m1-1
1
e-2iπ/3
e2iπ/3
1
e2iπ/3
e-2iπ/3
1
e-2iπ/3
e2iπ/3
1
e2iπ/3
e-2iπ/3
1
e2iπ/3
e-2iπ/3
1
e-2iπ/3
e2iπ/3
1
e2iπ/3
e-2iπ/3
1
e-2iπ/3
e2iπ/3
m12
1
e-2iπ/3
e2iπ/3
e-2iπ/3
1
e2iπ/3
1
e-2iπ/3
e2iπ/3
e-2iπ/3
1
e2iπ/3
1
e2iπ/3
e-2iπ/3
e2iπ/3
1
e-2iπ/3
1
e2iπ/3
e-2iπ/3
e2iπ/3
1
e-2iπ/3
m21
1
e-2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
1
1
e-2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
1
1
e2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
1
1
e2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
1
d1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
d3+
1
1
1
e-2iπ/3
e-2iπ/3
e-2iπ/3
1
1
1
e-2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
d3-
1
1
1
e2iπ/3
e2iπ/3
e2iπ/3
1
1
1
e2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
dm1-1
1
e-2iπ/3
e2iπ/3
1
e2iπ/3
e-2iπ/3
1
e-2iπ/3
e2iπ/3
1
e2iπ/3
e-2iπ/3
1
e2iπ/3
e-2iπ/3
1
e-2iπ/3
e2iπ/3
1
e2iπ/3
e-2iπ/3
1
e-2iπ/3
e2iπ/3
dm12
1
e-2iπ/3
e2iπ/3
e-2iπ/3
1
e2iπ/3
1
e-2iπ/3
e2iπ/3
e-2iπ/3
1
e2iπ/3
1
e2iπ/3
e-2iπ/3
e2iπ/3
1
e-2iπ/3
1
e2iπ/3
e-2iπ/3
e2iπ/3
1
e-2iπ/3
dm21
1
e-2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
1
1
e-2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
1
1
e2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
1
1
e2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
1
1'
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3+'
1
1
1
e2iπ/3
e2iπ/3
e2iπ/3
1
1
1
e2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
3-'
1
1
1
e-2iπ/3
e-2iπ/3
e-2iπ/3
1
1
1
e-2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
m'1-1
1
e2iπ/3
e-2iπ/3
1
e-2iπ/3
e2iπ/3
1
e2iπ/3
e-2iπ/3
1
e-2iπ/3
e2iπ/3
1
e-2iπ/3
e2iπ/3
1
e2iπ/3
e-2iπ/3
1
e-2iπ/3
e2iπ/3
1
e2iπ/3
e-2iπ/3
m'12
1
e2iπ/3
e-2iπ/3
e2iπ/3
1
e-2iπ/3
1
e2iπ/3
e-2iπ/3
e2iπ/3
1
e-2iπ/3
1
e-2iπ/3
e2iπ/3
e-2iπ/3
1
e2iπ/3
1
e-2iπ/3
e2iπ/3
e-2iπ/3
1
e2iπ/3
m'21
1
e2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
1
1
e2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
1
1
e-2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
1
1
e-2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
1
d1'
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
d3+'
1
1
1
e2iπ/3
e2iπ/3
e2iπ/3
1
1
1
e2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
d3-'
1
1
1
e-2iπ/3
e-2iπ/3
e-2iπ/3
1
1
1
e-2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
dm'1-1
1
e2iπ/3
e-2iπ/3
1
e-2iπ/3
e2iπ/3
1
e2iπ/3
e-2iπ/3
1
e-2iπ/3
e2iπ/3
1
e-2iπ/3
e2iπ/3
1
e2iπ/3
e-2iπ/3
1
e-2iπ/3
e2iπ/3
1
e2iπ/3
e-2iπ/3
dm'12
1
e2iπ/3
e-2iπ/3
e2iπ/3
1
e-2iπ/3
1
e2iπ/3
e-2iπ/3
e2iπ/3
1
e-2iπ/3
1
e-2iπ/3
e2iπ/3
e-2iπ/3
1
e2iπ/3
1
e-2iπ/3
e2iπ/3
e-2iπ/3
1
e2iπ/3
dm'21
1
e2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
1
1
e2iπ/3
e-2iπ/3
e-2iπ/3
e2iπ/3
1
1
e-2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
1
1
e-2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
1

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbol1E'1E''2EA2E12E21EE
1
(
1 0
0 1
)
(
1 0
0 1
)
1
1
1
(
1 0
0 1
)
(
1 0
0 1
)
(
1 0
0 1
)
2
(
0 -1
1 -1
)
(
eiπ/3 0
0 e-iπ/3
)
3+
e-2iπ/3
e-2iπ/3
(
1 0
0 e2iπ/3
)
(
eiπ/3 0
0 eiπ/3
)
(
-1 0
0 e-iπ/3
)
3
(
-1 1
-1 0
)
(
e-iπ/3 0
0 eiπ/3
)
3-
e2iπ/3
e2iπ/3
(
1 0
0 e-2iπ/3
)
(
e-iπ/3 0
0 e-iπ/3
)
(
-1 0
0 eiπ/3
)
4
(
0 1
1 0
)
(
0 e5iπ/6
eiπ/6 0
)
m1-1
1
-1
(
0 1
1 0
)
(
-i 0
0 i
)
(
0 -1
1 0
)
5
(
1 -1
0 -1
)
(
0 -i
-i 0
)
m12
1
-1
(
0 e-2iπ/3
e2iπ/3 0
)
(
-i 0
0 i
)
(
0 eiπ/3
e2iπ/3 0
)
6
(
-1 0
-1 1
)
(
0 eiπ/6
e5iπ/6 0
)
m21
1
-1
(
0 e2iπ/3
e-2iπ/3 0
)
(
-i 0
0 i
)
(
0 e-iπ/3
e-2iπ/3 0
)
7
(
1 0
0 1
)
(
-1 0
0 -1
)
d1
1
1
(
1 0
0 1
)
(
-1 0
0 -1
)
(
-1 0
0 -1
)
8
(
0 -1
1 -1
)
(
e-2iπ/3 0
0 e2iπ/3
)
d3+
e-2iπ/3
e-2iπ/3
(
1 0
0 e2iπ/3
)
(
e-2iπ/3 0
0 e-2iπ/3
)
(
1 0
0 e2iπ/3
)
9
(
-1 1
-1 0
)
(
e2iπ/3 0
0 e-2iπ/3
)
d3-
e2iπ/3
e2iπ/3
(
1 0
0 e-2iπ/3
)
(
e2iπ/3 0
0 e2iπ/3
)
(
1 0
0 e-2iπ/3
)
10
(
0 1
1 0
)
(
0 e-iπ/6
e-5iπ/6 0
)
dm1-1
1
-1
(
0 1
1 0
)
(
i 0
0 -i
)
(
0 1
-1 0
)
11
(
1 -1
0 -1
)
(
0 i
i 0
)
dm12
1
-1
(
0 e-2iπ/3
e2iπ/3 0
)
(
i 0
0 -i
)
(
0 e-2iπ/3
e-iπ/3 0
)
12
(
-1 0
-1 1
)
(
0 e-5iπ/6
e-iπ/6 0
)
dm21
1
-1
(
0 e2iπ/3
e-2iπ/3 0
)
(
i 0
0 -i
)
(
0 e2iπ/3
eiπ/3 0
)
13
(
1 0
0 1
)
(
1 0
0 1
)
1'
-1
-1
(
0 -1
-1 0
)
(
0 -1
1 0
)
(
0 1
-1 0
)
14
(
0 -1
1 -1
)
(
eiπ/3 0
0 e-iπ/3
)
3+'
eiπ/3
eiπ/3
(
0 -1
e-iπ/3 0
)
(
0 e2iπ/3
e-iπ/3 0
)
(
0 -1
e2iπ/3 0
)
15
(
-1 1
-1 0
)
(
e-iπ/3 0
0 eiπ/3
)
3-'
e-iπ/3
e-iπ/3
(
0 -1
eiπ/3 0
)
(
0 e-2iπ/3
eiπ/3 0
)
(
0 -1
e-2iπ/3 0
)
16
(
0 1
1 0
)
(
0 e5iπ/6
eiπ/6 0
)
m'1-1
-1
1
(
-1 0
0 -1
)
(
0 i
i 0
)
(
1 0
0 1
)
17
(
1 -1
0 -1
)
(
0 -i
-i 0
)
m'12
-1
1
(
eiπ/3 0
0 e-iπ/3
)
(
0 i
i 0
)
(
e-2iπ/3 0
0 e2iπ/3
)
18
(
-1 0
-1 1
)
(
0 eiπ/6
e5iπ/6 0
)
m'21
-1
1
(
e-iπ/3 0
0 eiπ/3
)
(
0 i
i 0
)
(
e2iπ/3 0
0 e-2iπ/3
)
19
(
1 0
0 1
)
(
-1 0
0 -1
)
d1'
-1
-1
(
0 -1
-1 0
)
(
0 1
-1 0
)
(
0 -1
1 0
)
20
(
0 -1
1 -1
)
(
e-2iπ/3 0
0 e2iπ/3
)
d3+'
eiπ/3
eiπ/3
(
0 -1
e-iπ/3 0
)
(
0 e-iπ/3
e2iπ/3 0
)
(
0 1
e-iπ/3 0
)
21
(
-1 1
-1 0
)
(
e2iπ/3 0
0 e-2iπ/3
)
d3-'
e-iπ/3
e-iπ/3
(
0 -1
eiπ/3 0
)
(
0 eiπ/3
e-2iπ/3 0
)
(
0 1
eiπ/3 0
)
22
(
0 1
1 0
)
(
0 e-iπ/6
e-5iπ/6 0
)
dm'1-1
-1
1
(
-1 0
0 -1
)
(
0 -i
-i 0
)
(
-1 0
0 -1
)
23
(
1 -1
0 -1
)
(
0 i
i 0
)
dm'12
-1
1
(
eiπ/3 0
0 e-iπ/3
)
(
0 -i
-i 0
)
(
eiπ/3 0
0 e-iπ/3
)
24
(
-1 0
-1 1
)
(
0 e-5iπ/6
e-iπ/6 0
)
dm'21
-1
1
(
e-iπ/3 0
0 eiπ/3
)
(
0 -i
-i 0
)
(
e-iπ/3 0
0 eiπ/3
)
k-Subgroupsmag
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