Bilbao Crystallographic Server arrow COREPRESENTATIONS PG

Irreducible corepresentations of the Projective Magnetic Point Group 65π/3mm1'


Table of characters of the unitary symmetry operations


1
6+
3+
2
3-
6-
m11
m10
m01
m21
m12
dm1-1
m1-1
dm21
dm12
d1
d6+
d3+
d2
d3-
d6-
dm11
dm10
dm01
1E11E2
2
0
2e-2iπ/3
0
2e2iπ/3
0
0
0
0
2
0
2e-2iπ/3
0
2e2iπ/3
0
0
2E2A
2
3eiπ/6
eiπ/3
0
e-iπ/3
3e-iπ/6
0
0
0
2
3eiπ/6
eiπ/3
0
e-iπ/3
3e-iπ/6
0
2E1B
2
3e-5iπ/6
eiπ/3
0
e-iπ/3
3e5iπ/6
0
0
0
2
3e-5iπ/6
eiπ/3
0
e-iπ/3
3e5iπ/6
0
1E2'1E2''
2
2e-5iπ/6
2eiπ/3
2i
2e-iπ/3
2e5iπ/6
0
0
0
-2
2eiπ/6
2e-2iπ/3
-2i
2e2iπ/3
2e-iπ/6
0
2E3'2E3''
2
2eiπ/6
2eiπ/3
-2i
2e-iπ/3
2e-iπ/6
0
0
0
-2
2e-5iπ/6
2e-2iπ/3
2i
2e2iπ/3
2e5iπ/6
0
1E11E3
2
eiπ/6
e-2iπ/3
2i
e2iπ/3
e-iπ/6
0
0
0
-2
e-5iπ/6
eiπ/3
-2i
e-iπ/3
e5iπ/6
0
2E12E2
2
e-5iπ/6
e-2iπ/3
-2i
e2iπ/3
e5iπ/6
0
0
0
-2
eiπ/6
eiπ/3
2i
e-iπ/3
e-iπ/6
0

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'
6+'
3+'
2'
3-'
6-'
m'11
m'21
m'10
m'1-1
m'01
m'12
d1'
d6+'
d3+'
d2'
d3-'
d6-'
dm'11
dm'21
dm'10
dm'1-1
dm'01
dm'12
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
1'
6+'
3+'
2'
3-'
6-'
m'11
m'21
m'10
m'1-1
m'01
m'12
d1'
d6+'
d3+'
d2'
d3-'
d6-'
dm'11
dm'21
dm'10
dm'1-1
dm'01
dm'12
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
6+'
3+'
d2'
3-'
6-'
1'
m'12
dm'11
dm'21
m'10
m'1-1
dm'01
d6+'
d3+'
2'
d3-'
d6-'
d1'
dm'12
m'11
m'21
dm'10
dm'1-1
m'01
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
3+'
d2'
d3-'
6-'
1'
6+'
dm'01
dm'12
m'11
dm'21
m'10
dm'1-1
d3+'
2'
3-'
d6-'
d1'
d6+'
m'01
m'12
dm'11
m'21
dm'10
m'1-1
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
2'
3-'
6-'
d1'
d6+'
d3+'
m'1-1
dm'01
dm'12
dm'11
m'21
m'10
d2'
d3-'
d6-'
1'
6+'
3+'
dm'1-1
m'01
m'12
m'11
dm'21
dm'10
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
3-'
6-'
1'
d6+'
d3+'
2'
m'10
dm'1-1
m'01
dm'12
dm'11
dm'21
d3-'
d6-'
d1'
6+'
3+'
d2'
dm'10
m'1-1
dm'01
m'12
m'11
m'21
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
6-'
1'
6+'
d3+'
2'
3-'
dm'21
dm'10
m'1-1
m'01
dm'12
m'11
d6-'
d1'
d6+'
3+'
d2'
d3-'
m'21
m'10
dm'1-1
dm'01
m'12
dm'11
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-
m'11
dm'21
m'10
dm'1-1
dm'01
m'12
d1'
6+'
d3+'
2'
3-'
d6-'
dm'11
m'21
dm'10
m'1-1
m'01
dm'12
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-
m'21
dm'10
dm'1-1
m'01
dm'12
dm'11
6-'
d1'
6+'
3+'
d2'
3-'
dm'21
m'10
m'1-1
dm'01
m'12
m'11
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
m'10
m'1-1
m'01
m'12
m'11
dm'21
d3-'
6-'
d1'
d6+'
d3+'
d2'
dm'10
dm'1-1
dm'01
dm'12
dm'11
m'21
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+
m'1-1
m'01
dm'12
m'11
dm'21
m'10
d2'
3-'
d6-'
d1'
d6+'
3+'
dm'1-1
dm'01
m'12
dm'11
m'21
dm'10
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+
m'01
dm'12
dm'11
dm'21
m'10
m'1-1
3+'
2'
d3-'
d6-'
d1'
6+'
dm'01
m'12
m'11
m'21
dm'10
dm'1-1
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
m'12
m'11
dm'21
dm'10
dm'1-1
dm'01
d6+'
3+'
2'
3-'
6-'
d1'
dm'12
dm'11
m'21
m'10
m'1-1
m'01
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
d1'
d6+'
d3+'
d2'
d3-'
d6-'
dm'11
dm'21
dm'10
dm'1-1
dm'01
dm'12
1'
6+'
3+'
2'
3-'
6-'
m'11
m'21
m'10
m'1-1
m'01
m'12
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
d6+'
d3+'
2'
d3-'
d6-'
d1'
dm'12
m'11
m'21
dm'10
dm'1-1
m'01
6+'
3+'
d2'
3-'
6-'
1'
m'12
dm'11
dm'21
m'10
m'1-1
dm'01
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
d3+'
2'
3-'
d6-'
d1'
d6+'
m'01
m'12
dm'11
m'21
dm'10
m'1-1
3+'
d2'
d3-'
6-'
1'
6+'
dm'01
dm'12
m'11
dm'21
m'10
dm'1-1
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
d2'
d3-'
d6-'
1'
6+'
3+'
dm'1-1
m'01
m'12
m'11
dm'21
dm'10
2'
3-'
6-'
d1'
d6+'
d3+'
m'1-1
dm'01
dm'12
dm'11
m'21
m'10
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
d3-'
d6-'
d1'
6+'
3+'
d2'
dm'10
m'1-1
dm'01
m'12
m'11
m'21
3-'
6-'
1'
d6+'
d3+'
2'
m'10
dm'1-1
m'01
dm'12
dm'11
dm'21
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
d6-'
d1'
d6+'
3+'
d2'
d3-'
m'21
m'10
dm'1-1
dm'01
m'12
dm'11
6-'
1'
6+'
d3+'
2'
3-'
dm'21
dm'10
m'1-1
m'01
dm'12
m'11
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-
dm'11
m'21
dm'10
m'1-1
m'01
dm'12
1'
d6+'
3+'
d2'
d3-'
6-'
m'11
dm'21
m'10
dm'1-1
dm'01
m'12
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-
dm'21
m'10
m'1-1
dm'01
m'12
m'11
d6-'
1'
d6+'
d3+'
2'
d3-'
m'21
dm'10
dm'1-1
m'01
dm'12
dm'11
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
dm'10
dm'1-1
dm'01
dm'12
dm'11
m'21
3-'
d6-'
1'
6+'
3+'
2'
m'10
m'1-1
m'01
m'12
m'11
dm'21
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+
dm'1-1
dm'01
m'12
dm'11
m'21
dm'10
2'
d3-'
6-'
1'
6+'
d3+'
m'1-1
m'01
dm'12
m'11
dm'21
m'10
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+
dm'01
m'12
m'11
m'21
dm'10
dm'1-1
d3+'
d2'
3-'
6-'
1'
d6+'
m'01
dm'12
dm'11
dm'21
m'10
m'1-1
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
dm'12
dm'11
m'21
m'10
m'1-1
m'01
6+'
d3+'
d2'
d3-'
d6-'
1'
m'12
m'11
dm'21
dm'10
dm'1-1
dm'01
d6+'
3+'
2'
3-'
6-'
d1'
1'
1'
6+'
3+'
2'
3-'
6-'
m'11
m'21
m'10
m'1-1
m'01
m'12
d1'
d6+'
d3+'
d2'
d3-'
d6-'
dm'11
dm'21
dm'10
dm'1-1
dm'01
dm'12
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
6+'
6+'
3+'
d2'
3-'
6-'
1'
m'12
dm'11
dm'21
m'10
m'1-1
dm'01
d6+'
d3+'
2'
d3-'
d6-'
d1'
dm'12
m'11
m'21
dm'10
dm'1-1
m'01
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
3+'
3+'
d2'
d3-'
6-'
1'
6+'
dm'01
dm'12
m'11
dm'21
m'10
dm'1-1
d3+'
2'
3-'
d6-'
d1'
d6+'
m'01
m'12
dm'11
m'21
dm'10
m'1-1
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
2'
2'
3-'
6-'
d1'
d6+'
d3+'
m'1-1
dm'01
dm'12
dm'11
m'21
m'10
d2'
d3-'
d6-'
1'
6+'
3+'
dm'1-1
m'01
m'12
m'11
dm'21
dm'10
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
3-'
3-'
6-'
1'
d6+'
d3+'
2'
m'10
dm'1-1
m'01
dm'12
dm'11
dm'21
d3-'
d6-'
d1'
6+'
3+'
d2'
dm'10
m'1-1
dm'01
m'12
m'11
m'21
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
6-'
6-'
1'
6+'
d3+'
2'
3-'
dm'21
dm'10
m'1-1
m'01
dm'12
m'11
d6-'
d1'
d6+'
3+'
d2'
d3-'
m'21
m'10
dm'1-1
dm'01
m'12
dm'11
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
m'11
m'11
dm'21
m'10
dm'1-1
dm'01
m'12
d1'
6+'
d3+'
2'
3-'
d6-'
dm'11
m'21
dm'10
m'1-1
m'01
dm'12
1'
d6+'
3+'
d2'
d3-'
6-'
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-
m'21
m'21
dm'10
dm'1-1
m'01
dm'12
dm'11
6-'
d1'
6+'
3+'
d2'
3-'
dm'21
m'10
m'1-1
dm'01
m'12
m'11
d6-'
1'
d6+'
d3+'
2'
d3-'
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-
m'10
m'10
m'1-1
m'01
m'12
m'11
dm'21
d3-'
6-'
d1'
d6+'
d3+'
d2'
dm'10
dm'1-1
dm'01
dm'12
dm'11
m'21
3-'
d6-'
1'
6+'
3+'
2'
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
m'1-1
m'1-1
m'01
dm'12
m'11
dm'21
m'10
d2'
3-'
d6-'
d1'
d6+'
3+'
dm'1-1
dm'01
m'12
dm'11
m'21
dm'10
2'
d3-'
6-'
1'
6+'
d3+'
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+
m'01
m'01
dm'12
dm'11
dm'21
m'10
m'1-1
3+'
2'
d3-'
d6-'
d1'
6+'
dm'01
m'12
m'11
m'21
dm'10
dm'1-1
d3+'
d2'
3-'
6-'
1'
d6+'
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+
m'12
m'12
m'11
dm'21
dm'10
dm'1-1
dm'01
d6+'
3+'
2'
3-'
6-'
d1'
dm'12
dm'11
m'21
m'10
m'1-1
m'01
6+'
d3+'
d2'
d3-'
d6-'
1'
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
d1'
d1'
d6+'
d3+'
d2'
d3-'
d6-'
dm'11
dm'21
dm'10
dm'1-1
dm'01
dm'12
1'
6+'
3+'
2'
3-'
6-'
m'11
m'21
m'10
m'1-1
m'01
m'12
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
d6+'
d6+'
d3+'
2'
d3-'
d6-'
d1'
dm'12
m'11
m'21
dm'10
dm'1-1
m'01
6+'
3+'
d2'
3-'
6-'
1'
m'12
dm'11
dm'21
m'10
m'1-1
dm'01
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
d3+'
d3+'
2'
3-'
d6-'
d1'
d6+'
m'01
m'12
dm'11
m'21
dm'10
m'1-1
3+'
d2'
d3-'
6-'
1'
6+'
dm'01
dm'12
m'11
dm'21
m'10
dm'1-1
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
d2'
d2'
d3-'
d6-'
1'
6+'
3+'
dm'1-1
m'01
m'12
m'11
dm'21
dm'10
2'
3-'
6-'
d1'
d6+'
d3+'
m'1-1
dm'01
dm'12
dm'11
m'21
m'10
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
d3-'
d3-'
d6-'
d1'
6+'
3+'
d2'
dm'10
m'1-1
dm'01
m'12
m'11
m'21
3-'
6-'
1'
d6+'
d3+'
2'
m'10
dm'1-1
m'01
dm'12
dm'11
dm'21
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
d6-'
d6-'
d1'
d6+'
3+'
d2'
d3-'
m'21
m'10
dm'1-1
dm'01
m'12
dm'11
6-'
1'
6+'
d3+'
2'
3-'
dm'21
dm'10
m'1-1
m'01
dm'12
m'11
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
dm'11
dm'11
m'21
dm'10
m'1-1
m'01
dm'12
1'
d6+'
3+'
d2'
d3-'
6-'
m'11
dm'21
m'10
dm'1-1
dm'01
m'12
d1'
6+'
d3+'
2'
3-'
d6-'
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-
dm'21
dm'21
m'10
m'1-1
dm'01
m'12
m'11
d6-'
1'
d6+'
d3+'
2'
d3-'
m'21
dm'10
dm'1-1
m'01
dm'12
dm'11
6-'
d1'
6+'
3+'
d2'
3-'
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-
dm'10
dm'10
dm'1-1
dm'01
dm'12
dm'11
m'21
3-'
d6-'
1'
6+'
3+'
2'
m'10
m'1-1
m'01
m'12
m'11
dm'21
d3-'
6-'
d1'
d6+'
d3+'
d2'
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
dm'1-1
dm'1-1
dm'01
m'12
dm'11
m'21
dm'10
2'
d3-'
6-'
1'
6+'
d3+'
m'1-1
m'01
dm'12
m'11
dm'21
m'10
d2'
3-'
d6-'
d1'
d6+'
3+'
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+
dm'01
dm'01
m'12
m'11
m'21
dm'10
dm'1-1
d3+'
d2'
3-'
6-'
1'
d6+'
m'01
dm'12
dm'11
dm'21
m'10
m'1-1
3+'
2'
d3-'
d6-'
d1'
6+'
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+
dm'12
dm'12
dm'11
m'21
m'10
m'1-1
m'01
6+'
d3+'
d2'
d3-'
d6-'
1'
m'12
m'11
dm'21
dm'10
dm'1-1
dm'01
d6+'
3+'
2'
3-'
6-'
d1'
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

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'
6+'
3+'
2'
3-'
6-'
m'11
m'21
m'10
m'1-1
m'01
m'12
d1'
d6+'
d3+'
d2'
d3-'
d6-'
dm'11
dm'21
dm'10
dm'1-1
dm'01
dm'12
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
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
eiπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
1
1
1
1
1
1
eiπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
3+
1
1
1
1
1
1
e-2iπ/3
e-2iπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
1
1
1
1
1
1
e-2iπ/3
e-2iπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
2
1
1
1
1
1
1
i
i
i
-i
-i
-i
1
1
1
1
1
1
i
i
i
-i
-i
-i
-1
-1
-1
-1
-1
-1
i
i
i
-i
-i
-i
-1
-1
-1
-1
-1
-1
i
i
i
-i
-i
-i
3-
1
1
1
1
1
1
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e2iπ/3
e2iπ/3
1
1
1
1
1
1
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e2iπ/3
e2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-2iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e2iπ/3
e2iπ/3
6-
1
1
1
1
1
1
e5iπ/6
e5iπ/6
e5iπ/6
e5iπ/6
e5iπ/6
e-iπ/6
1
1
1
1
1
1
e5iπ/6
e5iπ/6
e5iπ/6
e5iπ/6
e5iπ/6
e-iπ/6
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e5iπ/6
e5iπ/6
e5iπ/6
e5iπ/6
e5iπ/6
e-iπ/6
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e-iπ/3
e5iπ/6
e5iπ/6
e5iπ/6
e5iπ/6
e5iπ/6
e-iπ/6
m11
1
e-5iπ/6
eiπ/3
-i
e2iπ/3
e-iπ/6
1
e5iπ/6
e-iπ/3
i
e-2iπ/3
eiπ/6
1
e-5iπ/6
eiπ/3
-i
e2iπ/3
e-iπ/6
1
e5iπ/6
e-iπ/3
i
e-2iπ/3
eiπ/6
1
e5iπ/6
e-iπ/3
i
e-2iπ/3
eiπ/6
1
e-5iπ/6
eiπ/3
-i
e2iπ/3
e-iπ/6
1
e5iπ/6
e-iπ/3
i
e-2iπ/3
eiπ/6
1
e-5iπ/6
eiπ/3
-i
e2iπ/3
e-iπ/6
m21
1
e-5iπ/6
eiπ/3
-i
e2iπ/3
e5iπ/6
e-5iπ/6
1
e5iπ/6
e-iπ/3
i
e-2iπ/3
1
e-5iπ/6
eiπ/3
-i
e2iπ/3
e5iπ/6
e-5iπ/6
1
e5iπ/6
e-iπ/3
i
e-2iπ/3
1
e5iπ/6
e-iπ/3
i
e-2iπ/3
e-5iπ/6
e5iπ/6
1
e-5iπ/6
eiπ/3
-i
e2iπ/3
1
e5iπ/6
e-iπ/3
i
e-2iπ/3
e-5iπ/6
e5iπ/6
1
e-5iπ/6
eiπ/3
-i
e2iπ/3
m10
1
e-5iπ/6
eiπ/3
-i
e-iπ/3
e5iπ/6
eiπ/3
e-5iπ/6
1
e5iπ/6
e-iπ/3
i
1
e-5iπ/6
eiπ/3
-i
e-iπ/3
e5iπ/6
eiπ/3
e-5iπ/6
1
e5iπ/6
e-iπ/3
i
1
e5iπ/6
e-iπ/3
i
eiπ/3
e-5iπ/6
e-iπ/3
e5iπ/6
1
e-5iπ/6
eiπ/3
-i
1
e5iπ/6
e-iπ/3
i
eiπ/3
e-5iπ/6
e-iπ/3
e5iπ/6
1
e-5iπ/6
eiπ/3
-i
m1-1
1
e-5iπ/6
eiπ/3
i
e-iπ/3
e5iπ/6
-i
eiπ/3
e-5iπ/6
1
e5iπ/6
e-iπ/3
1
e-5iπ/6
eiπ/3
i
e-iπ/3
e5iπ/6
-i
eiπ/3
e-5iπ/6
1
e5iπ/6
e-iπ/3
1
e5iπ/6
e-iπ/3
-i
eiπ/3
e-5iπ/6
i
e-iπ/3
e5iπ/6
1
e-5iπ/6
eiπ/3
1
e5iπ/6
e-iπ/3
-i
eiπ/3
e-5iπ/6
i
e-iπ/3
e5iπ/6
1
e-5iπ/6
eiπ/3
m01
1
e-5iπ/6
e-2iπ/3
i
e-iπ/3
e5iπ/6
e2iπ/3
-i
eiπ/3
e-5iπ/6
1
e5iπ/6
1
e-5iπ/6
e-2iπ/3
i
e-iπ/3
e5iπ/6
e2iπ/3
-i
eiπ/3
e-5iπ/6
1
e5iπ/6
1
e5iπ/6
e2iπ/3
-i
eiπ/3
e-5iπ/6
e-2iπ/3
i
e-iπ/3
e5iπ/6
1
e-5iπ/6
1
e5iπ/6
e2iπ/3
-i
eiπ/3
e-5iπ/6
e-2iπ/3
i
e-iπ/3
e5iπ/6
1
e-5iπ/6
m12
1
eiπ/6
e-2iπ/3
i
e-iπ/3
e5iπ/6
e-iπ/6
e2iπ/3
-i
eiπ/3
e-5iπ/6
1
1
eiπ/6
e-2iπ/3
i
e-iπ/3
e5iπ/6
e-iπ/6
e2iπ/3
-i
eiπ/3
e-5iπ/6
1
1
e-iπ/6
e2iπ/3
-i
eiπ/3
e-5iπ/6
eiπ/6
e-2iπ/3
i
e-iπ/3
e5iπ/6
1
1
e-iπ/6
e2iπ/3
-i
eiπ/3
e-5iπ/6
eiπ/6
e-2iπ/3
i
e-iπ/3
e5iπ/6
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
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
eiπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
1
1
1
1
1
1
eiπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
e-5iπ/6
d3+
1
1
1
1
1
1
e-2iπ/3
e-2iπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
1
1
1
1
1
1
e-2iπ/3
e-2iπ/3
eiπ/3
eiπ/3
eiπ/3
eiπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
e2iπ/3
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eiπ/3
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e-2iπ/3
e-2iπ/3
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d2
1
1
1
1
1
1
i
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1
1
1
1
1
1
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1
1
1
1
1
1
e-iπ/3
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1
1
1
1
1
1
e-iπ/3
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e-2iπ/3
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e-2iπ/3
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e-2iπ/3
e-2iπ/3
e-2iπ/3
e-iπ/3
e-iπ/3
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d6-
1
1
1
1
1
1
e5iπ/6
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1
1
1
1
1
1
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1
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1
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1
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e2iπ/3
e-iπ/6
1
e5iπ/6
e-iπ/3
i
e-2iπ/3
eiπ/6
dm'21
1
e5iπ/6
e-iπ/3
i
e-2iπ/3
e-5iπ/6
e5iπ/6
1
e-5iπ/6
eiπ/3
-i
e2iπ/3
1
e5iπ/6
e-iπ/3
i
e-2iπ/3
e-5iπ/6
e5iπ/6
1
e-5iπ/6
eiπ/3
-i
e2iπ/3
1
e-5iπ/6
eiπ/3
-i
e2iπ/3
e5iπ/6
e-5iπ/6
1
e5iπ/6
e-iπ/3
i
e-2iπ/3
1
e-5iπ/6
eiπ/3
-i
e2iπ/3
e5iπ/6
e-5iπ/6
1
e5iπ/6
e-iπ/3
i
e-2iπ/3
dm'10
1
e5iπ/6
e-iπ/3
i
eiπ/3
e-5iπ/6
e-iπ/3
e5iπ/6
1
e-5iπ/6
eiπ/3
-i
1
e5iπ/6
e-iπ/3
i
eiπ/3
e-5iπ/6
e-iπ/3
e5iπ/6
1
e-5iπ/6
eiπ/3
-i
1
e-5iπ/6
eiπ/3
-i
e-iπ/3
e5iπ/6
eiπ/3
e-5iπ/6
1
e5iπ/6
e-iπ/3
i
1
e-5iπ/6
eiπ/3
-i
e-iπ/3
e5iπ/6
eiπ/3
e-5iπ/6
1
e5iπ/6
e-iπ/3
i
dm'1-1
1
e5iπ/6
e-iπ/3
-i
eiπ/3
e-5iπ/6
i
e-iπ/3
e5iπ/6
1
e-5iπ/6
eiπ/3
1
e5iπ/6
e-iπ/3
-i
eiπ/3
e-5iπ/6
i
e-iπ/3
e5iπ/6
1
e-5iπ/6
eiπ/3
1
e-5iπ/6
eiπ/3
i
e-iπ/3
e5iπ/6
-i
eiπ/3
e-5iπ/6
1
e5iπ/6
e-iπ/3
1
e-5iπ/6
eiπ/3
i
e-iπ/3
e5iπ/6
-i
eiπ/3
e-5iπ/6
1
e5iπ/6
e-iπ/3
dm'01
1
e5iπ/6
e2iπ/3
-i
eiπ/3
e-5iπ/6
e-2iπ/3
i
e-iπ/3
e5iπ/6
1
e-5iπ/6
1
e5iπ/6
e2iπ/3
-i
eiπ/3
e-5iπ/6
e-2iπ/3
i
e-iπ/3
e5iπ/6
1
e-5iπ/6
1
e-5iπ/6
e-2iπ/3
i
e-iπ/3
e5iπ/6
e2iπ/3
-i
eiπ/3
e-5iπ/6
1
e5iπ/6
1
e-5iπ/6
e-2iπ/3
i
e-iπ/3
e5iπ/6
e2iπ/3
-i
eiπ/3
e-5iπ/6
1
e5iπ/6
dm'12
1
e-iπ/6
e2iπ/3
-i
eiπ/3
e-5iπ/6
eiπ/6
e-2iπ/3
i
e-iπ/3
e5iπ/6
1
1
e-iπ/6
e2iπ/3
-i
eiπ/3
e-5iπ/6
eiπ/6
e-2iπ/3
i
e-iπ/3
e5iπ/6
1
1
eiπ/6
e-2iπ/3
i
e-iπ/3
e5iπ/6
e-iπ/6
e2iπ/3
-i
eiπ/3
e-5iπ/6
1
1
eiπ/6
e-2iπ/3
i
e-iπ/3
e5iπ/6
e-iπ/6
e2iπ/3
-i
eiπ/3
e-5iπ/6
1

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbol1E11E22E2A2E1B1E2'1E2''2E3'2E3''1E11E32E12E2
1
(
1 0
0 1
)
(
1 0
0 1
)
1
(
1 0
0 1
)
(
1 0
0 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+
(
e-iπ/3 0
0 e2iπ/3
)
(
1 0
0 eiπ/3
)
(
-1 0
0 e-2iπ/3
)
(
e-5iπ/6 0
0 e-5iπ/6
)
(
eiπ/6 0
0 eiπ/6
)
(
i 0
0 e-iπ/6
)
(
-i 0
0 e5iπ/6
)
3
(
0 -1
1 -1
)
(
eiπ/3 0
0 e-iπ/3
)
3+
(
e-2iπ/3 0
0 e-2iπ/3
)
(
1 0
0 e2iπ/3
)
(
1 0
0 e2iπ/3
)
(
eiπ/3 0
0 eiπ/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 0
0 1
)
(
1 0
0 -1
)
(
-1 0
0 1
)
(
i 0
0 i
)
(
-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 0
0 e2iπ/3
)
(
1 0
0 e-2iπ/3
)
(
1 0
0 e-2iπ/3
)
(
e-iπ/3 0
0 e-iπ/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-
(
eiπ/3 0
0 e-2iπ/3
)
(
1 0
0 e-iπ/3
)
(
-1 0
0 e2iπ/3
)
(
e5iπ/6 0
0 e5iπ/6
)
(
e-iπ/6 0
0 e-iπ/6
)
(
-i 0
0 eiπ/6
)
(
i 0
0 e-5iπ/6
)
7
(
0 -1
-1 0
)
(
0 e-2iπ/3
e-iπ/3 0
)
m11
(
0 1
1 0
)
(
0 1
1 0
)
(
0 1
1 0
)
(
-i 0
0 i
)
(
-i 0
0 i
)
(
0 -1
1 0
)
(
0 -1
1 0
)
8
(
-1 0
-1 1
)
(
0 eiπ/6
e5iπ/6 0
)
m21
(
0 -i
i 0
)
(
0 e-5iπ/6
e5iπ/6 0
)
(
0 eiπ/6
e-iπ/6 0
)
(
i 0
0 -i
)
(
-i 0
0 i
)
(
0 e2iπ/3
eiπ/3 0
)
(
0 e-iπ/3
e-2iπ/3 0
)
9
(
-1 1
0 1
)
(
0 -1
1 0
)
m10
(
0 -1
-1 0
)
(
0 eiπ/3
e-iπ/3 0
)
(
0 eiπ/3
e-iπ/3 0
)
(
-i 0
0 i
)
(
-i 0
0 i
)
(
0 eiπ/3
e2iπ/3 0
)
(
0 eiπ/3
e2iπ/3 0
)
10
(
0 1
1 0
)
(
0 e5iπ/6
eiπ/6 0
)
m1-1
(
0 i
-i 0
)
(
0 -i
i 0
)
(
0 i
-i 0
)
(
-i 0
0 i
)
(
i 0
0 -i
)
(
0 -1
1 0
)
(
0 1
-1 0
)
11
(
1 0
1 -1
)
(
0 e2iπ/3
eiπ/3 0
)
m01
(
0 1
1 0
)
(
0 e2iπ/3
e-2iπ/3 0
)
(
0 e2iπ/3
e-2iπ/3 0
)
(
-i 0
0 i
)
(
-i 0
0 i
)
(
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
(
0 -i
i 0
)
(
0 e-iπ/6
eiπ/6 0
)
(
0 e5iπ/6
e-5iπ/6 0
)
(
i 0
0 -i
)
(
-i 0
0 i
)
(
0 e-2iπ/3
e-iπ/3 0
)
(
0 eiπ/3
e2iπ/3 0
)
13
(
1 0
0 1
)
(
-1 0
0 -1
)
d1
(
1 0
0 1
)
(
1 0
0 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+
(
e-iπ/3 0
0 e2iπ/3
)
(
1 0
0 eiπ/3
)
(
-1 0
0 e-2iπ/3
)
(
eiπ/6 0
0 eiπ/6
)
(
e-5iπ/6 0
0 e-5iπ/6
)
(
-i 0
0 e5iπ/6
)
(
i 0
0 e-iπ/6
)
15
(
0 -1
1 -1
)
(
e-2iπ/3 0
0 e2iπ/3
)
d3+
(
e-2iπ/3 0
0 e-2iπ/3
)
(
1 0
0 e2iπ/3
)
(
1 0
0 e2iπ/3
)
(
e-2iπ/3 0
0 e-2iπ/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 0
0 1
)
(
1 0
0 -1
)
(
-1 0
0 1
)
(
-i 0
0 -i
)
(
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 0
0 e2iπ/3
)
(
1 0
0 e-2iπ/3
)
(
1 0
0 e-2iπ/3
)
(
e2iπ/3 0
0 e2iπ/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-
(
eiπ/3 0
0 e-2iπ/3
)
(
1 0
0 e-iπ/3
)
(
-1 0
0 e2iπ/3
)
(
e-iπ/6 0
0 e-iπ/6
)
(
e5iπ/6 0
0 e5iπ/6
)
(
i 0
0 e-5iπ/6
)
(
-i 0
0 eiπ/6
)
19
(
0 -1
-1 0
)
(
0 eiπ/3
e2iπ/3 0
)
dm11
(
0 1
1 0
)
(
0 1
1 0
)
(
0 1
1 0
)
(
i 0
0 -i
)
(
i 0
0 -i
)
(
0 1
-1 0
)
(
0 1
-1 0
)
20
(
-1 0
-1 1
)
(
0 e-5iπ/6
e-iπ/6 0
)
dm21
(
0 -i
i 0
)
(
0 e-5iπ/6
e5iπ/6 0
)
(
0 eiπ/6
e-iπ/6 0
)
(
-i 0
0 i
)
(
i 0
0 -i
)
(
0 e-iπ/3
e-2iπ/3 0
)
(
0 e2iπ/3
eiπ/3 0
)
21
(
-1 1
0 1
)
(
0 1
-1 0
)
dm10
(
0 -1
-1 0
)
(
0 eiπ/3
e-iπ/3 0
)
(
0 eiπ/3
e-iπ/3 0
)
(
i 0
0 -i
)
(
i 0
0 -i
)
(
0 e-2iπ/3
e-iπ/3 0
)
(
0 e-2iπ/3
e-iπ/3 0
)
22
(
0 1
1 0
)
(
0 e-iπ/6
e-5iπ/6 0
)
dm1-1
(
0 i
-i 0
)
(
0 -i
i 0
)
(
0 i
-i 0
)
(
i 0
0 -i
)
(
-i 0
0 i
)
(
0 1
-1 0
)
(
0 -1
1 0
)
23
(
1 0
1 -1
)
(
0 e-iπ/3
e-2iπ/3 0
)
dm01
(
0 1
1 0
)
(
0 e2iπ/3
e-2iπ/3 0
)
(
0 e2iπ/3
e-2iπ/3 0
)
(
i 0
0 -i
)
(
i 0
0 -i
)
(
0 e2iπ/3
eiπ/3 0
)
(
0 e2iπ/3
eiπ/3 0
)
24
(
1 -1
0 -1
)
(
0 i
i 0
)
dm12
(
0 -i
i 0
)
(
0 e-iπ/6
eiπ/6 0
)
(
0 e5iπ/6
e-5iπ/6 0
)
(
-i 0
0 i
)
(
i 0
0 -i
)
(
0 eiπ/3
e2iπ/3 0
)
(
0 e-2iπ/3
e-iπ/3 0
)
25
(
1 0
0 1
)
(
1 0
0 1
)
1'
(
0 -1
-1 0
)
(
0 -1
-1 0
)
(
0 -1
-1 0
)
(
0 -1
1 0
)
(
0 -1
1 0
)
(
0 1
-1 0
)
(
0 1
-1 0
)
26
(
1 -1
1 0
)
(
eiπ/6 0
0 e-iπ/6
)
6+'
(
0 e2iπ/3
e-iπ/3 0
)
(
0 -1
e-2iπ/3 0
)
(
0 1
eiπ/3 0
)
(
0 e-iπ/6
e5iπ/6 0
)
(
0 e5iπ/6
e-iπ/6 0
)
(
0 i
e5iπ/6 0
)
(
0 -i
e-iπ/6 0
)
27
(
0 -1
1 -1
)
(
eiπ/3 0
0 e-iπ/3
)
3+'
(
0 eiπ/3
eiπ/3 0
)
(
0 -1
e-iπ/3 0
)
(
0 -1
e-iπ/3 0
)
(
0 e2iπ/3
e-iπ/3 0
)
(
0 e2iπ/3
e-iπ/3 0
)
(
0 -1
e2iπ/3 0
)
(
0 -1
e2iπ/3 0
)
28
(
-1 0
0 -1
)
(
-i 0
0 i
)
2'
(
0 1
-1 0
)
(
0 -1
1 0
)
(
0 1
-1 0
)
(
0 i
-i 0
)
(
0 -i
i 0
)
(
0 i
-i 0
)
(
0 -i
i 0
)
29
(
-1 1
-1 0
)
(
e-iπ/3 0
0 eiπ/3
)
3-'
(
0 e-iπ/3
e-iπ/3 0
)
(
0 -1
eiπ/3 0
)
(
0 -1
eiπ/3 0
)
(
0 e-2iπ/3
eiπ/3 0
)
(
0 e-2iπ/3
eiπ/3 0
)
(
0 -1
e-2iπ/3 0
)
(
0 -1
e-2iπ/3 0
)
30
(
0 1
-1 1
)
(
e-iπ/6 0
0 eiπ/6
)
6-'
(
0 e-2iπ/3
eiπ/3 0
)
(
0 -1
e2iπ/3 0
)
(
0 1
e-iπ/3 0
)
(
0 eiπ/6
e-5iπ/6 0
)
(
0 e-5iπ/6
eiπ/6 0
)
(
0 -i
e-5iπ/6 0
)
(
0 i
eiπ/6 0
)
31
(
0 -1
-1 0
)
(
0 e-2iπ/3
e-iπ/3 0
)
m'11
(
-1 0
0 -1
)
(
-1 0
0 -1
)
(
-1 0
0 -1
)
(
0 i
i 0
)
(
0 i
i 0
)
(
1 0
0 1
)
(
1 0
0 1
)
32
(
-1 0
-1 1
)
(
0 eiπ/6
e5iπ/6 0
)
m'21
(
i 0
0 -i
)
(
eiπ/6 0
0 e-iπ/6
)
(
e-5iπ/6 0
0 e5iπ/6
)
(
0 -i
-i 0
)
(
0 i
i 0
)
(
e-iπ/3 0
0 eiπ/3
)
(
e2iπ/3 0
0 e-2iπ/3
)
33
(
-1 1
0 1
)
(
0 -1
1 0
)
m'10
(
1 0
0 1
)
(
e-2iπ/3 0
0 e2iπ/3
)
(
e-2iπ/3 0
0 e2iπ/3
)
(
0 i
i 0
)
(
0 i
i 0
)
(
e-2iπ/3 0
0 e2iπ/3
)
(
e-2iπ/3 0
0 e2iπ/3
)
34
(
0 1
1 0
)
(
0 e5iπ/6
eiπ/6 0
)
m'1-1
(
-i 0
0 i
)
(
i 0
0 -i
)
(
-i 0
0 i
)
(
0 i
i 0
)
(
0 -i
-i 0
)
(
1 0
0 1
)
(
-1 0
0 -1
)
35
(
1 0
1 -1
)
(
0 e2iπ/3
eiπ/3 0
)
m'01
(
-1 0
0 -1
)
(
e-iπ/3 0
0 eiπ/3
)
(
e-iπ/3 0
0 eiπ/3
)
(
0 i
i 0
)
(
0 i
i 0
)
(
e2iπ/3 0
0 e-2iπ/3
)
(
e2iπ/3 0
0 e-2iπ/3
)
36
(
1 -1
0 -1
)
(
0 -i
-i 0
)
m'12
(
i 0
0 -i
)
(
e5iπ/6 0
0 e-5iπ/6
)
(
e-iπ/6 0
0 eiπ/6
)
(
0 -i
-i 0
)
(
0 i
i 0
)
(
eiπ/3 0
0 e-iπ/3
)
(
e-2iπ/3 0
0 e2iπ/3
)
37
(
1 0
0 1
)
(
-1 0
0 -1
)
d1'
(
0 -1
-1 0
)
(
0 -1
-1 0
)
(
0 -1
-1 0
)
(
0 1
-1 0
)
(
0 1
-1 0
)
(
0 -1
1 0
)
(
0 -1
1 0
)
38
(
1 -1
1 0
)
(
e-5iπ/6 0
0 e5iπ/6
)
d6+'
(
0 e2iπ/3
e-iπ/3 0
)
(
0 -1
e-2iπ/3 0
)
(
0 1
eiπ/3 0
)
(
0 e5iπ/6
e-iπ/6 0
)
(
0 e-iπ/6
e5iπ/6 0
)
(
0 -i
e-iπ/6 0
)
(
0 i
e5iπ/6 0
)
39
(
0 -1
1 -1
)
(
e-2iπ/3 0
0 e2iπ/3
)
d3+'
(
0 eiπ/3
eiπ/3 0
)
(
0 -1
e-iπ/3 0
)
(
0 -1
e-iπ/3 0
)
(
0 e-iπ/3
e2iπ/3 0
)
(
0 e-iπ/3
e2iπ/3 0
)
(
0 1
e-iπ/3 0
)
(
0 1
e-iπ/3 0
)
40
(
-1 0
0 -1
)
(
i 0
0 -i
)
d2'
(
0 1
-1 0
)
(
0 -1
1 0
)
(
0 1
-1 0
)
(
0 -i
i 0
)
(
0 i
-i 0
)
(
0 -i
i 0
)
(
0 i
-i 0
)
41
(
-1 1
-1 0
)
(
e2iπ/3 0
0 e-2iπ/3
)
d3-'
(
0 e-iπ/3
e-iπ/3 0
)
(
0 -1
eiπ/3 0
)
(
0 -1
eiπ/3 0
)
(
0 eiπ/3
e-2iπ/3 0
)
(
0 eiπ/3
e-2iπ/3 0
)
(
0 1
eiπ/3 0
)
(
0 1
eiπ/3 0
)
42
(
0 1
-1 1
)
(
e5iπ/6 0
0 e-5iπ/6
)
d6-'
(
0 e-2iπ/3
eiπ/3 0
)
(
0 -1
e2iπ/3 0
)
(
0 1
e-iπ/3 0
)
(
0 e-5iπ/6
eiπ/6 0
)
(
0 eiπ/6
e-5iπ/6 0
)
(
0 i
eiπ/6 0
)
(
0 -i
e-5iπ/6 0
)
43
(
0 -1
-1 0
)
(
0 eiπ/3
e2iπ/3 0
)
dm'11
(
-1 0
0 -1
)
(
-1 0
0 -1
)
(
-1 0
0 -1
)
(
0 -i
-i 0
)
(
0 -i
-i 0
)
(
-1 0
0 -1
)
(
-1 0
0 -1
)
44
(
-1 0
-1 1
)
(
0 e-5iπ/6
e-iπ/6 0
)
dm'21
(
i 0
0 -i
)
(
eiπ/6 0
0 e-iπ/6
)
(
e-5iπ/6 0
0 e5iπ/6
)
(
0 i
i 0
)
(
0 -i
-i 0
)
(
e2iπ/3 0
0 e-2iπ/3
)
(
e-iπ/3 0
0 eiπ/3
)
45
(
-1 1
0 1
)
(
0 1
-1 0
)
dm'10
(
1 0
0 1
)
(
e-2iπ/3 0
0 e2iπ/3
)
(
e-2iπ/3 0
0 e2iπ/3
)
(
0 -i
-i 0
)
(
0 -i
-i 0
)
(
eiπ/3 0
0 e-iπ/3
)
(
eiπ/3 0
0 e-iπ/3
)
46
(
0 1
1 0
)
(
0 e-iπ/6
e-5iπ/6 0
)
dm'1-1
(
-i 0
0 i
)
(
i 0
0 -i
)
(
-i 0
0 i
)
(
0 -i
-i 0
)
(
0 i
i 0
)
(
-1 0
0 -1
)
(
1 0
0 1
)
47
(
1 0
1 -1
)
(
0 e-iπ/3
e-2iπ/3 0
)
dm'01
(
-1 0
0 -1
)
(
e-iπ/3 0
0 eiπ/3
)
(
e-iπ/3 0
0 eiπ/3
)
(
0 -i
-i 0
)
(
0 -i
-i 0
)
(
e-iπ/3 0
0 eiπ/3
)
(
e-iπ/3 0
0 eiπ/3
)
48
(
1 -1
0 -1
)
(
0 i
i 0
)
dm'12
(
i 0
0 -i
)
(
e5iπ/6 0
0 e-5iπ/6
)
(
e-iπ/6 0
0 eiπ/6
)
(
0 i
i 0
)
(
0 -i
-i 0
)
(
e-2iπ/3 0
0 e2iπ/3
)
(
eiπ/3 0
0 e-iπ/3
)
k-Subgroupsmag
Bilbao Crystallographic Server
http://www.cryst.ehu.es
For comments, please mail to
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