Bilbao Crystallographic Server arrow COREPRESENTATIONS PG

Irreducible corepresentations of the Projective Magnetic Point Group 62π/3mm


Table of characters of the unitary symmetry operations


1
6+
3+
2
d2
3-
6-
m11
m10
m01
dm11
dm10
dm01
m21
m1-1
m12
dm21
dm1-1
dm12
d1
d6+
d3+
d3-
d6-
1E1'
1
e2iπ/3
e-2iπ/3
1
e2iπ/3
e-2iπ/3
1
-1
1
e2iπ/3
e-2iπ/3
e2iπ/3
e-2iπ/3
1E1''
1
e2iπ/3
e-2iπ/3
1
e2iπ/3
e-2iπ/3
-1
1
1
e2iπ/3
e-2iπ/3
e2iπ/3
e-2iπ/3
1E2'
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
1
1
1
e-iπ/3
e-2iπ/3
e2iπ/3
eiπ/3
1E2''
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
-1
-1
1
e-iπ/3
e-2iπ/3
e2iπ/3
eiπ/3
2E1A
2
e-iπ/3
eiπ/3
2
e-iπ/3
eiπ/3
0
0
2
e-iπ/3
eiπ/3
e-iπ/3
eiπ/3
2E2B
2
e2iπ/3
eiπ/3
-2
e-iπ/3
e-2iπ/3
0
0
2
e2iπ/3
eiπ/3
e-iπ/3
e-2iπ/3
1E22E3
2
0
2eiπ/3
0
2e-iπ/3
0
0
0
-2
0
2e-2iπ/3
2e2iπ/3
0
1E12E2
2
3e2iπ/3
e-2iπ/3
0
e2iπ/3
3e-2iπ/3
0
0
-2
3e-iπ/3
eiπ/3
e-iπ/3
3eiπ/3
2E11E3
2
3e-iπ/3
e-2iπ/3
0
e2iπ/3
3eiπ/3
0
0
-2
3e2iπ/3
eiπ/3
e-iπ/3
3e-2iπ/3

Multiplication table of the symmetry operations


1
6+
3+
2
3-
6-
m11
m21
m10
m1-1
m01
m12
d1
d6+
d3+
d2
d3-
d6-
dm11
dm21
dm10
dm1-1
dm01
dm12
1
1
6+
3+
2
3-
6-
m11
m21
m10
m1-1
m01
m12
d1
d6+
d3+
d2
d3-
d6-
dm11
dm21
dm10
dm1-1
dm01
dm12
6+
6+
3+
d2
3-
6-
1
m12
dm11
dm21
m10
m1-1
dm01
d6+
d3+
2
d3-
d6-
d1
dm12
m11
m21
dm10
dm1-1
m01
3+
3+
d2
d3-
6-
1
6+
dm01
dm12
m11
dm21
m10
dm1-1
d3+
2
3-
d6-
d1
d6+
m01
m12
dm11
m21
dm10
m1-1
2
2
3-
6-
d1
d6+
d3+
m1-1
dm01
dm12
dm11
m21
m10
d2
d3-
d6-
1
6+
3+
dm1-1
m01
m12
m11
dm21
dm10
3-
3-
6-
1
d6+
d3+
2
m10
dm1-1
m01
dm12
dm11
dm21
d3-
d6-
d1
6+
3+
d2
dm10
m1-1
dm01
m12
m11
m21
6-
6-
1
6+
d3+
2
3-
dm21
dm10
m1-1
m01
dm12
m11
d6-
d1
d6+
3+
d2
d3-
m21
m10
dm1-1
dm01
m12
dm11
m11
m11
dm21
m10
dm1-1
dm01
m12
d1
6+
d3+
2
3-
d6-
dm11
m21
dm10
m1-1
m01
dm12
1
d6+
3+
d2
d3-
6-
m21
m21
dm10
dm1-1
m01
dm12
dm11
6-
d1
6+
3+
d2
3-
dm21
m10
m1-1
dm01
m12
m11
d6-
1
d6+
d3+
2
d3-
m10
m10
m1-1
m01
m12
m11
dm21
d3-
6-
d1
d6+
d3+
d2
dm10
dm1-1
dm01
dm12
dm11
m21
3-
d6-
1
6+
3+
2
m1-1
m1-1
m01
dm12
m11
dm21
m10
d2
3-
d6-
d1
d6+
3+
dm1-1
dm01
m12
dm11
m21
dm10
2
d3-
6-
1
6+
d3+
m01
m01
dm12
dm11
dm21
m10
m1-1
3+
2
d3-
d6-
d1
6+
dm01
m12
m11
m21
dm10
dm1-1
d3+
d2
3-
6-
1
d6+
m12
m12
m11
dm21
dm10
dm1-1
dm01
d6+
3+
2
3-
6-
d1
dm12
dm11
m21
m10
m1-1
m01
6+
d3+
d2
d3-
d6-
1
d1
d1
d6+
d3+
d2
d3-
d6-
dm11
dm21
dm10
dm1-1
dm01
dm12
1
6+
3+
2
3-
6-
m11
m21
m10
m1-1
m01
m12
d6+
d6+
d3+
2
d3-
d6-
d1
dm12
m11
m21
dm10
dm1-1
m01
6+
3+
d2
3-
6-
1
m12
dm11
dm21
m10
m1-1
dm01
d3+
d3+
2
3-
d6-
d1
d6+
m01
m12
dm11
m21
dm10
m1-1
3+
d2
d3-
6-
1
6+
dm01
dm12
m11
dm21
m10
dm1-1
d2
d2
d3-
d6-
1
6+
3+
dm1-1
m01
m12
m11
dm21
dm10
2
3-
6-
d1
d6+
d3+
m1-1
dm01
dm12
dm11
m21
m10
d3-
d3-
d6-
d1
6+
3+
d2
dm10
m1-1
dm01
m12
m11
m21
3-
6-
1
d6+
d3+
2
m10
dm1-1
m01
dm12
dm11
dm21
d6-
d6-
d1
d6+
3+
d2
d3-
m21
m10
dm1-1
dm01
m12
dm11
6-
1
6+
d3+
2
3-
dm21
dm10
m1-1
m01
dm12
m11
dm11
dm11
m21
dm10
m1-1
m01
dm12
1
d6+
3+
d2
d3-
6-
m11
dm21
m10
dm1-1
dm01
m12
d1
6+
d3+
2
3-
d6-
dm21
dm21
m10
m1-1
dm01
m12
m11
d6-
1
d6+
d3+
2
d3-
m21
dm10
dm1-1
m01
dm12
dm11
6-
d1
6+
3+
d2
3-
dm10
dm10
dm1-1
dm01
dm12
dm11
m21
3-
d6-
1
6+
3+
2
m10
m1-1
m01
m12
m11
dm21
d3-
6-
d1
d6+
d3+
d2
dm1-1
dm1-1
dm01
m12
dm11
m21
dm10
2
d3-
6-
1
6+
d3+
m1-1
m01
dm12
m11
dm21
m10
d2
3-
d6-
d1
d6+
3+
dm01
dm01
m12
m11
m21
dm10
dm1-1
d3+
d2
3-
6-
1
d6+
m01
dm12
dm11
dm21
m10
m1-1
3+
2
d3-
d6-
d1
6+
dm12
dm12
dm11
m21
m10
m1-1
m01
6+
d3+
d2
d3-
d6-
1
m12
m11
dm21
dm10
dm1-1
dm01
d6+
3+
2
3-
6-
d1

Table of projective phases in group multiplication


1
6+
3+
2
3-
6-
m11
m21
m10
m1-1
m01
m12
d1
d6+
d3+
d2
d3-
d6-
dm11
dm21
dm10
dm1-1
dm01
dm12
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
6+
1
1
1
1
1
1
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
1
1
1
1
1
1
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
3+
1
1
1
1
1
1
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
1
1
1
1
1
1
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
2
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
1
1
1
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
1
1
1
1
1
1
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
6-
1
1
1
1
1
1
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
1
1
1
1
1
1
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
m11
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
1
eiπ/3
e2iπ/3
-1
e-2iπ/3
e-iπ/3
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
1
eiπ/3
e2iπ/3
-1
e-2iπ/3
e-iπ/3
m21
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
e-iπ/3
1
eiπ/3
e2iπ/3
-1
e-2iπ/3
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
e-iπ/3
1
eiπ/3
e2iπ/3
-1
e-2iπ/3
m10
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
e-2iπ/3
e-iπ/3
1
eiπ/3
e2iπ/3
-1
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
e-2iπ/3
e-iπ/3
1
eiπ/3
e2iπ/3
-1
m1-1
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
-1
e-2iπ/3
e-iπ/3
1
eiπ/3
e2iπ/3
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
-1
e-2iπ/3
e-iπ/3
1
eiπ/3
e2iπ/3
m01
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
e2iπ/3
-1
e-2iπ/3
e-iπ/3
1
eiπ/3
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
e2iπ/3
-1
e-2iπ/3
e-iπ/3
1
eiπ/3
m12
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
eiπ/3
e2iπ/3
-1
e-2iπ/3
e-iπ/3
1
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
eiπ/3
e2iπ/3
-1
e-2iπ/3
e-iπ/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
d6+
1
1
1
1
1
1
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
1
1
1
1
1
1
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
d3+
1
1
1
1
1
1
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
1
1
1
1
1
1
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
d2
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
1
1
1
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
1
1
1
1
1
1
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
d6-
1
1
1
1
1
1
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
1
1
1
1
1
1
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
dm11
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
1
eiπ/3
e2iπ/3
-1
e-2iπ/3
e-iπ/3
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
1
eiπ/3
e2iπ/3
-1
e-2iπ/3
e-iπ/3
dm21
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
e-iπ/3
1
eiπ/3
e2iπ/3
-1
e-2iπ/3
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
e-iπ/3
1
eiπ/3
e2iπ/3
-1
e-2iπ/3
dm10
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
e-2iπ/3
e-iπ/3
1
eiπ/3
e2iπ/3
-1
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
e-2iπ/3
e-iπ/3
1
eiπ/3
e2iπ/3
-1
dm1-1
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
-1
e-2iπ/3
e-iπ/3
1
eiπ/3
e2iπ/3
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
-1
e-2iπ/3
e-iπ/3
1
eiπ/3
e2iπ/3
dm01
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
e2iπ/3
-1
e-2iπ/3
e-iπ/3
1
eiπ/3
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
e2iπ/3
-1
e-2iπ/3
e-iπ/3
1
eiπ/3
dm12
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
eiπ/3
e2iπ/3
-1
e-2iπ/3
e-iπ/3
1
1
e-iπ/3
e-2iπ/3
-1
e2iπ/3
eiπ/3
eiπ/3
e2iπ/3
-1
e-2iπ/3
e-iπ/3
1

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbol1E1'1E1''1E2'1E2''2E1A2E2B1E22E31E12E22E11E3
1
(
1 0
0 1
)
(
1 0
0 1
)
1
1
1
1
1
(
1 0
0 1
)
(
1 0
0 1
)
(
1 0
0 1
)
(
1 0
0 1
)
(
1 0
0 1
)
2
(
1 -1
1 0
)
(
eiπ/6 0
0 e-iπ/6
)
6+
e2iπ/3
e2iπ/3
e-iπ/3
e-iπ/3
(
1 0
0 e-2iπ/3
)
(
-1 0
0 eiπ/3
)
(
eiπ/6 0
0 e-5iπ/6
)
(
i 0
0 e5iπ/6
)
(
-i 0
0 e-iπ/6
)
3
(
0 -1
1 -1
)
(
eiπ/3 0
0 e-iπ/3
)
3+
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
(
1 0
0 e2iπ/3
)
(
1 0
0 e2iπ/3
)
(
eiπ/3 0
0 eiπ/3
)
(
-1 0
0 e-iπ/3
)
(
-1 0
0 e-iπ/3
)
4
(
-1 0
0 -1
)
(
-i 0
0 i
)
2
1
1
-1
-1
(
1 0
0 1
)
(
-1 0
0 -1
)
(
-i 0
0 i
)
(
i 0
0 -i
)
(
-i 0
0 i
)
5
(
-1 1
-1 0
)
(
e-iπ/3 0
0 eiπ/3
)
3-
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
(
1 0
0 e-2iπ/3
)
(
1 0
0 e-2iπ/3
)
(
e-iπ/3 0
0 e-iπ/3
)
(
-1 0
0 eiπ/3
)
(
-1 0
0 eiπ/3
)
6
(
0 1
-1 1
)
(
e-iπ/6 0
0 eiπ/6
)
6-
e-2iπ/3
e-2iπ/3
eiπ/3
eiπ/3
(
1 0
0 e2iπ/3
)
(
-1 0
0 e-iπ/3
)
(
e-iπ/6 0
0 e5iπ/6
)
(
-i 0
0 e-5iπ/6
)
(
i 0
0 eiπ/6
)
7
(
0 -1
-1 0
)
(
0 e-2iπ/3
e-iπ/3 0
)
m11
1
-1
1
-1
(
0 1
1 0
)
(
0 1
1 0
)
(
0 -1
1 0
)
(
0 -1
1 0
)
(
0 -1
1 0
)
8
(
-1 0
-1 1
)
(
0 eiπ/6
e5iπ/6 0
)
m21
-1
1
1
-1
(
0 e-iπ/3
eiπ/3 0
)
(
0 e2iπ/3
e-2iπ/3 0
)
(
0 -i
-i 0
)
(
0 e-5iπ/6
e-iπ/6 0
)
(
0 eiπ/6
e5iπ/6 0
)
9
(
-1 1
0 1
)
(
0 -1
1 0
)
m10
1
-1
1
-1
(
0 e-2iπ/3
e2iπ/3 0
)
(
0 e-2iπ/3
e2iπ/3 0
)
(
0 1
-1 0
)
(
0 e-2iπ/3
e-iπ/3 0
)
(
0 e-2iπ/3
e-iπ/3 0
)
10
(
0 1
1 0
)
(
0 e5iπ/6
eiπ/6 0
)
m1-1
-1
1
1
-1
(
0 -1
-1 0
)
(
0 1
1 0
)
(
0 -i
-i 0
)
(
0 i
i 0
)
(
0 -i
-i 0
)
11
(
1 0
1 -1
)
(
0 e2iπ/3
eiπ/3 0
)
m01
1
-1
1
-1
(
0 e2iπ/3
e-2iπ/3 0
)
(
0 e2iπ/3
e-2iπ/3 0
)
(
0 -1
1 0
)
(
0 e-iπ/3
e-2iπ/3 0
)
(
0 e-iπ/3
e-2iπ/3 0
)
12
(
1 -1
0 -1
)
(
0 -i
-i 0
)
m12
-1
1
1
-1
(
0 eiπ/3
e-iπ/3 0
)
(
0 e-2iπ/3
e2iπ/3 0
)
(
0 -i
-i 0
)
(
0 e-iπ/6
e-5iπ/6 0
)
(
0 e5iπ/6
eiπ/6 0
)
13
(
1 0
0 1
)
(
-1 0
0 -1
)
d1
1
1
1
1
(
1 0
0 1
)
(
1 0
0 1
)
(
-1 0
0 -1
)
(
-1 0
0 -1
)
(
-1 0
0 -1
)
14
(
1 -1
1 0
)
(
e-5iπ/6 0
0 e5iπ/6
)
d6+
e2iπ/3
e2iπ/3
e-iπ/3
e-iπ/3
(
1 0
0 e-2iπ/3
)
(
-1 0
0 eiπ/3
)
(
e-5iπ/6 0
0 eiπ/6
)
(
-i 0
0 e-iπ/6
)
(
i 0
0 e5iπ/6
)
15
(
0 -1
1 -1
)
(
e-2iπ/3 0
0 e2iπ/3
)
d3+
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
(
1 0
0 e2iπ/3
)
(
1 0
0 e2iπ/3
)
(
e-2iπ/3 0
0 e-2iπ/3
)
(
1 0
0 e2iπ/3
)
(
1 0
0 e2iπ/3
)
16
(
-1 0
0 -1
)
(
i 0
0 -i
)
d2
1
1
-1
-1
(
1 0
0 1
)
(
-1 0
0 -1
)
(
i 0
0 -i
)
(
-i 0
0 i
)
(
i 0
0 -i
)
17
(
-1 1
-1 0
)
(
e2iπ/3 0
0 e-2iπ/3
)
d3-
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
(
1 0
0 e-2iπ/3
)
(
1 0
0 e-2iπ/3
)
(
e2iπ/3 0
0 e2iπ/3
)
(
1 0
0 e-2iπ/3
)
(
1 0
0 e-2iπ/3
)
18
(
0 1
-1 1
)
(
e5iπ/6 0
0 e-5iπ/6
)
d6-
e-2iπ/3
e-2iπ/3
eiπ/3
eiπ/3
(
1 0
0 e2iπ/3
)
(
-1 0
0 e-iπ/3
)
(
e5iπ/6 0
0 e-iπ/6
)
(
i 0
0 eiπ/6
)
(
-i 0
0 e-5iπ/6
)
19
(
0 -1
-1 0
)
(
0 eiπ/3
e2iπ/3 0
)
dm11
1
-1
1
-1
(
0 1
1 0
)
(
0 1
1 0
)
(
0 1
-1 0
)
(
0 1
-1 0
)
(
0 1
-1 0
)
20
(
-1 0
-1 1
)
(
0 e-5iπ/6
e-iπ/6 0
)
dm21
-1
1
1
-1
(
0 e-iπ/3
eiπ/3 0
)
(
0 e2iπ/3
e-2iπ/3 0
)
(
0 i
i 0
)
(
0 eiπ/6
e5iπ/6 0
)
(
0 e-5iπ/6
e-iπ/6 0
)
21
(
-1 1
0 1
)
(
0 1
-1 0
)
dm10
1
-1
1
-1
(
0 e-2iπ/3
e2iπ/3 0
)
(
0 e-2iπ/3
e2iπ/3 0
)
(
0 -1
1 0
)
(
0 eiπ/3
e2iπ/3 0
)
(
0 eiπ/3
e2iπ/3 0
)
22
(
0 1
1 0
)
(
0 e-iπ/6
e-5iπ/6 0
)
dm1-1
-1
1
1
-1
(
0 -1
-1 0
)
(
0 1
1 0
)
(
0 i
i 0
)
(
0 -i
-i 0
)
(
0 i
i 0
)
23
(
1 0
1 -1
)
(
0 e-iπ/3
e-2iπ/3 0
)
dm01
1
-1
1
-1
(
0 e2iπ/3
e-2iπ/3 0
)
(
0 e2iπ/3
e-2iπ/3 0
)
(
0 1
-1 0
)
(
0 e2iπ/3
eiπ/3 0
)
(
0 e2iπ/3
eiπ/3 0
)
24
(
1 -1
0 -1
)
(
0 i
i 0
)
dm12
-1
1
1
-1
(
0 eiπ/3
e-iπ/3 0
)
(
0 e-2iπ/3
e2iπ/3 0
)
(
0 i
i 0
)
(
0 e5iπ/6
eiπ/6 0
)
(
0 e-iπ/6
e-5iπ/6 0
)
k-Subgroupsmag
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http://www.cryst.ehu.es
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