Bilbao Crystallographic Server arrow Representations


Irreducible representations of the Double Point Group m3 (No. 29)

Table of characters

(1)
(2)
(3)
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
C12
C13
C14
GM1+
Ag
GM1+
1
1
1
1
1
1
1
1
1
1
1
1
1
1
GM1-
1Au
GM1-
1
1
1
1
1
1
1
-1
-1
-1
-1
-1
-1
-1
GM2+
1Eg
GM2+
1
1
-(1-i3)/2
-(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
1
1
-(1-i3)/2
-(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
GM2-
1Eu
GM2-
1
1
-(1-i3)/2
-(1+i3)/2
1
-(1-i3)/2
-(1+i3)/2
-1
-1
(1-i3)/2
(1+i3)/2
-1
(1-i3)/2
(1+i3)/2
GM3+
2Eg
GM3+
1
1
-(1+i3)/2
-(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
1
1
-(1+i3)/2
-(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
GM3-
2Eu
GM3-
1
1
-(1+i3)/2
-(1-i3)/2
1
-(1+i3)/2
-(1-i3)/2
-1
-1
(1+i3)/2
(1-i3)/2
-1
(1+i3)/2
(1-i3)/2
GM4+
Tg
GM4+
3
-1
0
0
3
0
0
3
-1
0
0
3
0
0
GM4-
Tu
GM4-
3
-1
0
0
3
0
0
-3
1
0
0
-3
0
0
GM5+
Eg
GM5
2
0
1
1
-2
-1
-1
2
0
1
1
-2
-1
-1
GM7+
2Fg
GM6
2
0
-(1-i3)/2
-(1+i3)/2
-2
(1-i3)/2
(1+i3)/2
2
0
-(1-i3)/2
-(1+i3)/2
-2
(1-i3)/2
(1+i3)/2
GM6+
1Fg
GM7
2
0
-(1+i3)/2
-(1-i3)/2
-2
(1+i3)/2
(1-i3)/2
2
0
-(1+i3)/2
-(1-i3)/2
-2
(1+i3)/2
(1-i3)/2
GM5-
Eu
GM8
2
0
1
1
-2
-1
-1
-2
0
-1
-1
2
1
1
GM7-
2Fu
GM9
2
0
-(1-i3)/2
-(1+i3)/2
-2
(1-i3)/2
(1+i3)/2
-2
0
(1-i3)/2
(1+i3)/2
2
-(1-i3)/2
-(1+i3)/2
GM6-
1Fu
GM10
2
0
-(1+i3)/2
-(1-i3)/2
-2
(1+i3)/2
(1-i3)/2
-2
0
(1+i3)/2
(1-i3)/2
2
-(1+i3)/2
-(1-i3)/2
(1): Notation of the irreps according to Koster GF, Dimmok JO, Wheeler RG and Statz H, (1963) Properties of the thirty-two point groups, M.I.T. Press, Cambridge, Mass.
(2): Notation of the irreps according to Mulliken RS (1933) Phys. Rev. 43, 279-302.
(3): Notation of the irreps according to C. J. Bradley, A. P. Cracknell, The Mathematical Theory of Symmetry in Solids (Clarendon Press, Oxford, 1972) for the GM point.

Lists of symmetry operations in the conjugacy classes

C1: 1
C2: 2001, 2010, 2100d2001d2010d2100
C3: 3+111, 3+-11-1, 3+1-1-1, 3+-1-11
C4: 3-111, 3-1-1-1, 3--1-11, 3--11-1
C5d1
C6d3+111d3+-11-1d3+1-1-1d3+-1-11
C7d3-111d3-1-1-1d3--1-11d3--11-1
C8: -1
C9: m001, m010, m100dm001dm010dm100
C10: -3+111, -3+-11-1, -3+1-1-1, -3+-1-11
C11: -3-111, -3-1-1-1, -3--1-11, -3--11-1
C12d-1
C13d-3+111d-3+-11-1d-3+1-1-1d-3+-1-11
C14d-3-111d-3-1-1-1d-3--1-11d-3--11-1

List of pairs of conjugated irreducible representations

(*GM2+,*GM3+)
(*GM2-,*GM3-)
(*GM6,*GM7)
(*GM9,*GM10)
Matrices of the representations of the group

The number in parenthesis after the label of the irrep indicates the "reality" of the irrep: (1) for real, (-1) for pseudoreal and (0) for complex representations.

N
Matrix presentation
Seitz Symbol
GM1+(1)
GM1-(1)
GM2+(0)
GM2-(0)
GM3+(0)
GM3-(0)
GM4+(1)
GM4-(1)
GM5(-1)
GM6(0)
GM7(0)
GM8(-1)
GM9(0)
GM10(0)
1
(
1 0 0
0 1 0
0 0 1
)
(
1 0
0 1
)
1
1
1
1
1
1
1
(
1 0 0
0 1 0
0 0 1
)
(
1 0 0
0 1 0
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 0 0
0 -1 0
0 0 1
)
(
-i 0
0 i
)
2001
1
1
1
1
1
1
(
1 0 0
0 -1 0
0 0 -1
)
(
1 0 0
0 -1 0
0 0 -1
)
(
-i 0
0 i
)
(
-i 0
0 i
)
(
-i 0
0 i
)
(
-i 0
0 i
)
(
-i 0
0 i
)
(
-i 0
0 i
)
3
(
-1 0 0
0 1 0
0 0 -1
)
(
0 -1
1 0
)
2010
1
1
1
1
1
1
(
-1 0 0
0 -1 0
0 0 1
)
(
-1 0 0
0 -1 0
0 0 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
)
4
(
1 0 0
0 -1 0
0 0 -1
)
(
0 -i
-i 0
)
2100
1
1
1
1
1
1
(
-1 0 0
0 1 0
0 0 -1
)
(
-1 0 0
0 1 0
0 0 -1
)
(
0 -i
-i 0
)
(
0 -i
-i 0
)
(
0 -i
-i 0
)
(
0 -i
-i 0
)
(
0 -i
-i 0
)
(
0 -i
-i 0
)
5
(
0 0 1
1 0 0
0 1 0
)
(
(1-i)/2 -(1+i)/2
(1-i)/2 (1+i)/2
)
3+111
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
(
0 0 1
1 0 0
0 1 0
)
(
0 0 1
1 0 0
0 1 0
)
(
e-iπ/42/2 e-i3π/42/2
e-iπ/42/2 eiπ/42/2
)
(
ei5π/122/2 e-iπ/122/2
ei5π/122/2 ei11π/122/2
)
(
e-i11π/122/2 ei7π/122/2
e-i11π/122/2 e-i5π/122/2
)
(
e-iπ/42/2 e-i3π/42/2
e-iπ/42/2 eiπ/42/2
)
(
ei5π/122/2 e-iπ/122/2
ei5π/122/2 ei11π/122/2
)
(
e-i11π/122/2 ei7π/122/2
e-i11π/122/2 e-i5π/122/2
)
6
(
0 0 1
-1 0 0
0 -1 0
)
(
(1+i)/2 -(1-i)/2
(1+i)/2 (1-i)/2
)
3+111
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
(
0 0 -1
1 0 0
0 -1 0
)
(
0 0 -1
1 0 0
0 -1 0
)
(
eiπ/42/2 ei3π/42/2
eiπ/42/2 e-iπ/42/2
)
(
ei11π/122/2 e-i7π/122/2
ei11π/122/2 ei5π/122/2
)
(
e-i5π/122/2 eiπ/122/2
e-i5π/122/2 e-i11π/122/2
)
(
eiπ/42/2 ei3π/42/2
eiπ/42/2 e-iπ/42/2
)
(
ei11π/122/2 e-i7π/122/2
ei11π/122/2 ei5π/122/2
)
(
e-i5π/122/2 eiπ/122/2
e-i5π/122/2 e-i11π/122/2
)
7
(
0 0 -1
-1 0 0
0 1 0
)
(
(1+i)/2 (1-i)/2
-(1+i)/2 (1-i)/2
)
3+111
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
(
0 0 1
-1 0 0
0 -1 0
)
(
0 0 1
-1 0 0
0 -1 0
)
(
eiπ/42/2 e-iπ/42/2
e-i3π/42/2 e-iπ/42/2
)
(
ei11π/122/2 ei5π/122/2
e-iπ/122/2 ei5π/122/2
)
(
e-i5π/122/2 e-i11π/122/2
ei7π/122/2 e-i11π/122/2
)
(
eiπ/42/2 e-iπ/42/2
e-i3π/42/2 e-iπ/42/2
)
(
ei11π/122/2 ei5π/122/2
e-iπ/122/2 ei5π/122/2
)
(
e-i5π/122/2 e-i11π/122/2
ei7π/122/2 e-i11π/122/2
)
8
(
0 0 -1
1 0 0
0 -1 0
)
(
(1-i)/2 (1+i)/2
-(1-i)/2 (1+i)/2
)
3+111
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
(
0 0 -1
-1 0 0
0 1 0
)
(
0 0 -1
-1 0 0
0 1 0
)
(
e-iπ/42/2 eiπ/42/2
ei3π/42/2 eiπ/42/2
)
(
ei5π/122/2 ei11π/122/2
e-i7π/122/2 ei11π/122/2
)
(
e-i11π/122/2 e-i5π/122/2
eiπ/122/2 e-i5π/122/2
)
(
e-iπ/42/2 eiπ/42/2
ei3π/42/2 eiπ/42/2
)
(
ei5π/122/2 ei11π/122/2
e-i7π/122/2 ei11π/122/2
)
(
e-i11π/122/2 e-i5π/122/2
eiπ/122/2 e-i5π/122/2
)
9
(
0 1 0
0 0 1
1 0 0
)
(
(1+i)/2 (1+i)/2
-(1-i)/2 (1-i)/2
)
3-111
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
(
0 1 0
0 0 1
1 0 0
)
(
0 1 0
0 0 1
1 0 0
)
(
eiπ/42/2 eiπ/42/2
ei3π/42/2 e-iπ/42/2
)
(
e-i5π/122/2 e-i5π/122/2
eiπ/122/2 e-i11π/122/2
)
(
ei11π/122/2 ei11π/122/2
e-i7π/122/2 ei5π/122/2
)
(
eiπ/42/2 eiπ/42/2
ei3π/42/2 e-iπ/42/2
)
(
e-i5π/122/2 e-i5π/122/2
eiπ/122/2 e-i11π/122/2
)
(
ei11π/122/2 ei11π/122/2
e-i7π/122/2 ei5π/122/2
)
10
(
0 -1 0
0 0 1
-1 0 0
)
(
(1-i)/2 -(1-i)/2
(1+i)/2 (1+i)/2
)
3-111
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
(
0 -1 0
0 0 -1
1 0 0
)
(
0 -1 0
0 0 -1
1 0 0
)
(
e-iπ/42/2 ei3π/42/2
eiπ/42/2 eiπ/42/2
)
(
e-i11π/122/2 eiπ/122/2
e-i5π/122/2 e-i5π/122/2
)
(
ei5π/122/2 e-i7π/122/2
ei11π/122/2 ei11π/122/2
)
(
e-iπ/42/2 ei3π/42/2
eiπ/42/2 eiπ/42/2
)
(
e-i11π/122/2 eiπ/122/2
e-i5π/122/2 e-i5π/122/2
)
(
ei5π/122/2 e-i7π/122/2
ei11π/122/2 ei11π/122/2
)
11
(
0 1 0
0 0 -1
-1 0 0
)
(
(1+i)/2 -(1+i)/2
(1-i)/2 (1-i)/2
)
3-111
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
(
0 -1 0
0 0 1
-1 0 0
)
(
0 -1 0
0 0 1
-1 0 0
)
(
eiπ/42/2 e-i3π/42/2
e-iπ/42/2 e-iπ/42/2
)
(
e-i5π/122/2 ei7π/122/2
e-i11π/122/2 e-i11π/122/2
)
(
ei11π/122/2 e-iπ/122/2
ei5π/122/2 ei5π/122/2
)
(
eiπ/42/2 e-i3π/42/2
e-iπ/42/2 e-iπ/42/2
)
(
e-i5π/122/2 ei7π/122/2
e-i11π/122/2 e-i11π/122/2
)
(
ei11π/122/2 e-iπ/122/2
ei5π/122/2 ei5π/122/2
)
12
(
0 -1 0
0 0 -1
1 0 0
)
(
(1-i)/2 (1-i)/2
-(1+i)/2 (1+i)/2
)
3-111
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
(
0 1 0
0 0 -1
-1 0 0
)
(
0 1 0
0 0 -1
-1 0 0
)
(
e-iπ/42/2 e-iπ/42/2
e-i3π/42/2 eiπ/42/2
)
(
e-i11π/122/2 e-i11π/122/2
ei7π/122/2 e-i5π/122/2
)
(
ei5π/122/2 ei5π/122/2
e-iπ/122/2 ei11π/122/2
)
(
e-iπ/42/2 e-iπ/42/2
e-i3π/42/2 eiπ/42/2
)
(
e-i11π/122/2 e-i11π/122/2
ei7π/122/2 e-i5π/122/2
)
(
ei5π/122/2 ei5π/122/2
e-iπ/122/2 ei11π/122/2
)
13
(
-1 0 0
0 -1 0
0 0 -1
)
(
1 0
0 1
)
1
1
-1
1
-1
1
-1
(
1 0 0
0 1 0
0 0 1
)
(
-1 0 0
0 -1 0
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 0 0
0 1 0
0 0 -1
)
(
-i 0
0 i
)
m001
1
-1
1
-1
1
-1
(
1 0 0
0 -1 0
0 0 -1
)
(
-1 0 0
0 1 0
0 0 1
)
(
-i 0
0 i
)
(
-i 0
0 i
)
(
-i 0
0 i
)
(
i 0
0 -i
)
(
i 0
0 -i
)
(
i 0
0 -i
)
15
(
1 0 0
0 -1 0
0 0 1
)
(
0 -1
1 0
)
m010
1
-1
1
-1
1
-1
(
-1 0 0
0 -1 0
0 0 1
)
(
1 0 0
0 1 0
0 0 -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
)
16
(
-1 0 0
0 1 0
0 0 1
)
(
0 -i
-i 0
)
m100
1
-1
1
-1
1
-1
(
-1 0 0
0 1 0
0 0 -1
)
(
1 0 0
0 -1 0
0 0 1
)
(
0 -i
-i 0
)
(
0 -i
-i 0
)
(
0 -i
-i 0
)
(
0 i
i 0
)
(
0 i
i 0
)
(
0 i
i 0
)
17
(
0 0 -1
-1 0 0
0 -1 0
)
(
(1-i)/2 -(1+i)/2
(1-i)/2 (1+i)/2
)
3+111
1
-1
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
(
0 0 1
1 0 0
0 1 0
)
(
0 0 -1
-1 0 0
0 -1 0
)
(
e-iπ/42/2 e-i3π/42/2
e-iπ/42/2 eiπ/42/2
)
(
ei5π/122/2 e-iπ/122/2
ei5π/122/2 ei11π/122/2
)
(
e-i11π/122/2 ei7π/122/2
e-i11π/122/2 e-i5π/122/2
)
(
ei3π/42/2 eiπ/42/2
ei3π/42/2 e-i3π/42/2
)
(
e-i7π/122/2 ei11π/122/2
e-i7π/122/2 e-iπ/122/2
)
(
eiπ/122/2 e-i5π/122/2
eiπ/122/2 ei7π/122/2
)
18
(
0 0 -1
1 0 0
0 1 0
)
(
(1+i)/2 -(1-i)/2
(1+i)/2 (1-i)/2
)
3+111
1
-1
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
(
0 0 -1
1 0 0
0 -1 0
)
(
0 0 1
-1 0 0
0 1 0
)
(
eiπ/42/2 ei3π/42/2
eiπ/42/2 e-iπ/42/2
)
(
ei11π/122/2 e-i7π/122/2
ei11π/122/2 ei5π/122/2
)
(
e-i5π/122/2 eiπ/122/2
e-i5π/122/2 e-i11π/122/2
)
(
e-i3π/42/2 e-iπ/42/2
e-i3π/42/2 ei3π/42/2
)
(
e-iπ/122/2 ei5π/122/2
e-iπ/122/2 e-i7π/122/2
)
(
ei7π/122/2 e-i11π/122/2
ei7π/122/2 eiπ/122/2
)
19
(
0 0 1
1 0 0
0 -1 0
)
(
(1+i)/2 (1-i)/2
-(1+i)/2 (1-i)/2
)
3+111
1
-1
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
(
0 0 1
-1 0 0
0 -1 0
)
(
0 0 -1
1 0 0
0 1 0
)
(
eiπ/42/2 e-iπ/42/2
e-i3π/42/2 e-iπ/42/2
)
(
ei11π/122/2 ei5π/122/2
e-iπ/122/2 ei5π/122/2
)
(
e-i5π/122/2 e-i11π/122/2
ei7π/122/2 e-i11π/122/2
)
(
e-i3π/42/2 ei3π/42/2
eiπ/42/2 ei3π/42/2
)
(
e-iπ/122/2 e-i7π/122/2
ei11π/122/2 e-i7π/122/2
)
(
ei7π/122/2 eiπ/122/2
e-i5π/122/2 eiπ/122/2
)
20
(
0 0 1
-1 0 0
0 1 0
)
(
(1-i)/2 (1+i)/2
-(1-i)/2 (1+i)/2
)
3+111
1
-1
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
(
0 0 -1
-1 0 0
0 1 0
)
(
0 0 1
1 0 0
0 -1 0
)
(
e-iπ/42/2 eiπ/42/2
ei3π/42/2 eiπ/42/2
)
(
ei5π/122/2 ei11π/122/2
e-i7π/122/2 ei11π/122/2
)
(
e-i11π/122/2 e-i5π/122/2
eiπ/122/2 e-i5π/122/2
)
(
ei3π/42/2 e-i3π/42/2
e-iπ/42/2 e-i3π/42/2
)
(
e-i7π/122/2 e-iπ/122/2
ei5π/122/2 e-iπ/122/2
)
(
eiπ/122/2 ei7π/122/2
e-i11π/122/2 ei7π/122/2
)
21
(
0 -1 0
0 0 -1
-1 0 0
)
(
(1+i)/2 (1+i)/2
-(1-i)/2 (1-i)/2
)
3-111
1
-1
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
(
0 1 0
0 0 1
1 0 0
)
(
0 -1 0
0 0 -1
-1 0 0
)
(
eiπ/42/2 eiπ/42/2
ei3π/42/2 e-iπ/42/2
)
(
e-i5π/122/2 e-i5π/122/2
eiπ/122/2 e-i11π/122/2
)
(
ei11π/122/2 ei11π/122/2
e-i7π/122/2 ei5π/122/2
)
(
e-i3π/42/2 e-i3π/42/2
e-iπ/42/2 ei3π/42/2
)
(
ei7π/122/2 ei7π/122/2
e-i11π/122/2 eiπ/122/2
)
(
e-iπ/122/2 e-iπ/122/2
ei5π/122/2 e-i7π/122/2
)
22
(
0 1 0
0 0 -1
1 0 0
)
(
(1-i)/2 -(1-i)/2
(1+i)/2 (1+i)/2
)
3-111
1
-1
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
(
0 -1 0
0 0 -1
1 0 0
)
(
0 1 0
0 0 1
-1 0 0
)
(
e-iπ/42/2 ei3π/42/2
eiπ/42/2 eiπ/42/2
)
(
e-i11π/122/2 eiπ/122/2
e-i5π/122/2 e-i5π/122/2
)
(
ei5π/122/2 e-i7π/122/2
ei11π/122/2 ei11π/122/2
)
(
ei3π/42/2 e-iπ/42/2
e-i3π/42/2 e-i3π/42/2
)
(
eiπ/122/2 e-i11π/122/2
ei7π/122/2 ei7π/122/2
)
(
e-i7π/122/2 ei5π/122/2
e-iπ/122/2 e-iπ/122/2
)
23
(
0 -1 0
0 0 1
1 0 0
)
(
(1+i)/2 -(1+i)/2
(1-i)/2 (1-i)/2
)
3-111
1
-1
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
(
0 -1 0
0 0 1
-1 0 0
)
(
0 1 0
0 0 -1
1 0 0
)
(
eiπ/42/2 e-i3π/42/2
e-iπ/42/2 e-iπ/42/2
)
(
e-i5π/122/2 ei7π/122/2
e-i11π/122/2 e-i11π/122/2
)
(
ei11π/122/2 e-iπ/122/2
ei5π/122/2 ei5π/122/2
)
(
e-i3π/42/2 eiπ/42/2
ei3π/42/2 ei3π/42/2
)
(
ei7π/122/2 e-i5π/122/2
eiπ/122/2 eiπ/122/2
)
(
e-iπ/122/2 ei11π/122/2
e-i7π/122/2 e-i7π/122/2
)
24
(
0 1 0
0 0 1
-1 0 0
)
(
(1-i)/2 (1-i)/2
-(1+i)/2 (1+i)/2
)
3-111
1
-1
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
(
0 1 0
0 0 -1
-1 0 0
)
(
0 -1 0
0 0 1
1 0 0
)
(
e-iπ/42/2 e-iπ/42/2
e-i3π/42/2 eiπ/42/2
)
(
e-i11π/122/2 e-i11π/122/2
ei7π/122/2 e-i5π/122/2
)
(
ei5π/122/2 ei5π/122/2
e-iπ/122/2 ei11π/122/2
)
(
ei3π/42/2 ei3π/42/2
eiπ/42/2 e-i3π/42/2
)
(
eiπ/122/2 eiπ/122/2
e-i5π/122/2 ei7π/122/2
)
(
e-i7π/122/2 e-i7π/122/2
ei11π/122/2 e-iπ/122/2
)
25
(
1 0 0
0 1 0
0 0 1
)
(
-1 0
0 -1
)
d1
1
1
1
1
1
1
(
1 0 0
0 1 0
0 0 1
)
(
1 0 0
0 1 0
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
)
26
(
-1 0 0
0 -1 0
0 0 1
)
(
i 0
0 -i
)
d2001
1
1
1
1
1
1
(
1 0 0
0 -1 0
0 0 -1
)
(
1 0 0
0 -1 0
0 0 -1
)
(
i 0
0 -i
)
(
i 0
0 -i
)
(
i 0
0 -i
)
(
i 0
0 -i
)
(
i 0
0 -i
)
(
i 0
0 -i
)
27
(
-1 0 0
0 1 0
0 0 -1
)
(
0 1
-1 0
)
d2010
1
1
1
1
1
1
(
-1 0 0
0 -1 0
0 0 1
)
(
-1 0 0
0 -1 0
0 0 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
)
28
(
1 0 0
0 -1 0
0 0 -1
)
(
0 i
i 0
)
d2100
1
1
1
1
1
1
(
-1 0 0
0 1 0
0 0 -1
)
(
-1 0 0
0 1 0
0 0 -1
)
(
0 i
i 0
)
(
0 i
i 0
)
(
0 i
i 0
)
(
0 i
i 0
)
(
0 i
i 0
)
(
0 i
i 0
)
29
(
0 0 1
1 0 0
0 1 0
)
(
-(1-i)/2 (1+i)/2
-(1-i)/2 -(1+i)/2
)
d3+111
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
(
0 0 1
1 0 0
0 1 0
)
(
0 0 1
1 0 0
0 1 0
)
(
ei3π/42/2 eiπ/42/2
ei3π/42/2 e-i3π/42/2
)
(
e-i7π/122/2 ei11π/122/2
e-i7π/122/2 e-iπ/122/2
)
(
eiπ/122/2 e-i5π/122/2
eiπ/122/2 ei7π/122/2
)
(
ei3π/42/2 eiπ/42/2
ei3π/42/2 e-i3π/42/2
)
(
e-i7π/122/2 ei11π/122/2
e-i7π/122/2 e-iπ/122/2
)
(
eiπ/122/2 e-i5π/122/2
eiπ/122/2 ei7π/122/2
)
30
(
0 0 1
-1 0 0
0 -1 0
)
(
-(1+i)/2 (1-i)/2
-(1+i)/2 -(1-i)/2
)
d3+111
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
(
0 0 -1
1 0 0
0 -1 0
)
(
0 0 -1
1 0 0
0 -1 0
)
(
e-i3π/42/2 e-iπ/42/2
e-i3π/42/2 ei3π/42/2
)
(
e-iπ/122/2 ei5π/122/2
e-iπ/122/2 e-i7π/122/2
)
(
ei7π/122/2 e-i11π/122/2
ei7π/122/2 eiπ/122/2
)
(
e-i3π/42/2 e-iπ/42/2
e-i3π/42/2 ei3π/42/2
)
(
e-iπ/122/2 ei5π/122/2
e-iπ/122/2 e-i7π/122/2
)
(
ei7π/122/2 e-i11π/122/2
ei7π/122/2 eiπ/122/2
)
31
(
0 0 -1
-1 0 0
0 1 0
)
(
-(1+i)/2 -(1-i)/2
(1+i)/2 -(1-i)/2
)
d3+111
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
(
0 0 1
-1 0 0
0 -1 0
)
(
0 0 1
-1 0 0
0 -1 0
)
(
e-i3π/42/2 ei3π/42/2
eiπ/42/2 ei3π/42/2
)
(
e-iπ/122/2 e-i7π/122/2
ei11π/122/2 e-i7π/122/2
)
(
ei7π/122/2 eiπ/122/2
e-i5π/122/2 eiπ/122/2
)
(
e-i3π/42/2 ei3π/42/2
eiπ/42/2 ei3π/42/2
)
(
e-iπ/122/2 e-i7π/122/2
ei11π/122/2 e-i7π/122/2
)
(
ei7π/122/2 eiπ/122/2
e-i5π/122/2 eiπ/122/2
)
32
(
0 0 -1
1 0 0
0 -1 0
)
(
-(1-i)/2 -(1+i)/2
(1-i)/2 -(1+i)/2
)
d3+111
1
1
ei2π/3
ei2π/3
e-i2π/3
e-i2π/3
(
0 0 -1
-1 0 0
0 1 0
)
(
0 0 -1
-1 0 0
0 1 0
)
(
ei3π/42/2 e-i3π/42/2
e-iπ/42/2 e-i3π/42/2
)
(
e-i7π/122/2 e-iπ/122/2
ei5π/122/2 e-iπ/122/2
)
(
eiπ/122/2 ei7π/122/2
e-i11π/122/2 ei7π/122/2
)
(
ei3π/42/2 e-i3π/42/2
e-iπ/42/2 e-i3π/42/2
)
(
e-i7π/122/2 e-iπ/122/2
ei5π/122/2 e-iπ/122/2
)
(
eiπ/122/2 ei7π/122/2
e-i11π/122/2 ei7π/122/2
)
33
(
0 1 0
0 0 1
1 0 0
)
(
-(1+i)/2 -(1+i)/2
(1-i)/2 -(1-i)/2
)
d3-111
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
(
0 1 0
0 0 1
1 0 0
)
(
0 1 0
0 0 1
1 0 0
)
(
e-i3π/42/2 e-i3π/42/2
e-iπ/42/2 ei3π/42/2
)
(
ei7π/122/2 ei7π/122/2
e-i11π/122/2 eiπ/122/2
)
(
e-iπ/122/2 e-iπ/122/2
ei5π/122/2 e-i7π/122/2
)
(
e-i3π/42/2 e-i3π/42/2
e-iπ/42/2 ei3π/42/2
)
(
ei7π/122/2 ei7π/122/2
e-i11π/122/2 eiπ/122/2
)
(
e-iπ/122/2 e-iπ/122/2
ei5π/122/2 e-i7π/122/2
)
34
(
0 -1 0
0 0 1
-1 0 0
)
(
-(1-i)/2 (1-i)/2
-(1+i)/2 -(1+i)/2
)
d3-111
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
(
0 -1 0
0 0 -1
1 0 0
)
(
0 -1 0
0 0 -1
1 0 0
)
(
ei3π/42/2 e-iπ/42/2
e-i3π/42/2 e-i3π/42/2
)
(
eiπ/122/2 e-i11π/122/2
ei7π/122/2 ei7π/122/2
)
(
e-i7π/122/2 ei5π/122/2
e-iπ/122/2 e-iπ/122/2
)
(
ei3π/42/2 e-iπ/42/2
e-i3π/42/2 e-i3π/42/2
)
(
eiπ/122/2 e-i11π/122/2
ei7π/122/2 ei7π/122/2
)
(
e-i7π/122/2 ei5π/122/2
e-iπ/122/2 e-iπ/122/2
)
35
(
0 1 0
0 0 -1
-1 0 0
)
(
-(1+i)/2 (1+i)/2
-(1-i)/2 -(1-i)/2
)
d3-111
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
(
0 -1 0
0 0 1
-1 0 0
)
(
0 -1 0
0 0 1
-1 0 0
)
(
e-i3π/42/2 eiπ/42/2
ei3π/42/2 ei3π/42/2
)
(
ei7π/122/2 e-i5π/122/2
eiπ/122/2 eiπ/122/2
)
(
e-iπ/122/2 ei11π/122/2
e-i7π/122/2 e-i7π/122/2
)
(
e-i3π/42/2 eiπ/42/2
ei3π/42/2 ei3π/42/2
)
(
ei7π/122/2 e-i5π/122/2
eiπ/122/2 eiπ/122/2
)
(
e-iπ/122/2 ei11π/122/2
e-i7π/122/2 e-i7π/122/2
)
36
(
0 -1 0
0 0 -1
1 0 0
)
(
-(1-i)/2 -(1-i)/2
(1+i)/2 -(1+i)/2
)
d3-111
1
1
e-i2π/3
e-i2π/3
ei2π/3
ei2π/3
(
0 1 0
0 0 -1
-1 0 0
)
(
0 1 0
0 0 -1
-1 0 0
)
(
ei3π/42/2 ei3π/42/2
eiπ/42/2 e-i3π/42/2
)
(
eiπ/122/2 eiπ/122/2
e-i5π/122/2 ei7π/122/2
)
(
e-i7π/122/2 e-i7π/122/2
ei11π/122/2 e-iπ/122/2
)
(
ei3π/42/2 ei3π/42/2
eiπ/42/2 e-i3π/42/2
)
(
eiπ/122/2 eiπ/122/2
e-i5π/122/2 ei7π/122/2
)
(
e-i7π/122/2 e-i7π/122/2
ei11π/122/2 e-iπ/122/2
)
37
(
-1 0 0
0 -1 0
0 0 -1
)
(
-1 0
0 -1
)
d1
1
-1
1
-1
1
-1
(
1 0 0
0 1 0
0 0 1
)
(
-1 0 0
0 -1 0
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
)
38
(
1 0 0
0 1 0
0 0 -1
)
(
i 0
0 -i
)
dm001
1
-1
1
-1
1
-1
(
1 0 0
0 -1 0
0 0 -1
)
(
-1 0 0
0 1 0
0 0 1
)
(
i 0
0 -i
)
(
i 0
0 -i
)
(
i 0
0 -i
)
(
-i 0
0 i
)
(
-i 0
0 i
)
(
-i 0
0 i
)
39
(
1 0 0
0 -1 0
0 0 1
)
(
0 1
-1 0
)
dm010
1
-1
1
-1
1
-1
(
-1 0 0
0 -1 0
0 0 1
)
(
1 0 0
0 1 0
0 0 -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
)
40
(
-1 0 0
0 1 0
0 0 1
)
(
0 i
i 0
)
dm100
1
-1
1
-1
1
-1
(
-1 0 0
0 1 0
0 0 -1
)
(
1 0 0
0 -1 0
0 0 1
)
(
0 i
i 0
)
(
0 i
i 0
)
(
0 i
i 0
)
(
0 -i
-i 0
)
(
0 -i
-i 0
)
(
0 -i
-i 0
)
41
(
0 0 -1
-1 0 0
0 -1 0
)
(
-(1-i)/2 (1+i)/2
-(1-i)/2 -(1+i)/2
)
d3+111
1
-1
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
(
0 0 1
1 0 0
0 1 0
)
(
0 0 -1
-1 0 0
0 -1 0
)
(
ei3π/42/2 eiπ/42/2
ei3π/42/2 e-i3π/42/2
)
(
e-i7π/122/2 ei11π/122/2
e-i7π/122/2 e-iπ/122/2
)
(
eiπ/122/2 e-i5π/122/2
eiπ/122/2 ei7π/122/2
)
(
e-iπ/42/2 e-i3π/42/2
e-iπ/42/2 eiπ/42/2
)
(
ei5π/122/2 e-iπ/122/2
ei5π/122/2 ei11π/122/2
)
(
e-i11π/122/2 ei7π/122/2
e-i11π/122/2 e-i5π/122/2
)
42
(
0 0 -1
1 0 0
0 1 0
)
(
-(1+i)/2 (1-i)/2
-(1+i)/2 -(1-i)/2
)
d3+111
1
-1
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
(
0 0 -1
1 0 0
0 -1 0
)
(
0 0 1
-1 0 0
0 1 0
)
(
e-i3π/42/2 e-iπ/42/2
e-i3π/42/2 ei3π/42/2
)
(
e-iπ/122/2 ei5π/122/2
e-iπ/122/2 e-i7π/122/2
)
(
ei7π/122/2 e-i11π/122/2
ei7π/122/2 eiπ/122/2
)
(
eiπ/42/2 ei3π/42/2
eiπ/42/2 e-iπ/42/2
)
(
ei11π/122/2 e-i7π/122/2
ei11π/122/2 ei5π/122/2
)
(
e-i5π/122/2 eiπ/122/2
e-i5π/122/2 e-i11π/122/2
)
43
(
0 0 1
1 0 0
0 -1 0
)
(
-(1+i)/2 -(1-i)/2
(1+i)/2 -(1-i)/2
)
d3+111
1
-1
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
(
0 0 1
-1 0 0
0 -1 0
)
(
0 0 -1
1 0 0
0 1 0
)
(
e-i3π/42/2 ei3π/42/2
eiπ/42/2 ei3π/42/2
)
(
e-iπ/122/2 e-i7π/122/2
ei11π/122/2 e-i7π/122/2
)
(
ei7π/122/2 eiπ/122/2
e-i5π/122/2 eiπ/122/2
)
(
eiπ/42/2 e-iπ/42/2
e-i3π/42/2 e-iπ/42/2
)
(
ei11π/122/2 ei5π/122/2
e-iπ/122/2 ei5π/122/2
)
(
e-i5π/122/2 e-i11π/122/2
ei7π/122/2 e-i11π/122/2
)
44
(
0 0 1
-1 0 0
0 1 0
)
(
-(1-i)/2 -(1+i)/2
(1-i)/2 -(1+i)/2
)
d3+111
1
-1
ei2π/3
e-iπ/3
e-i2π/3
eiπ/3
(
0 0 -1
-1 0 0
0 1 0
)
(
0 0 1
1 0 0
0 -1 0
)
(
ei3π/42/2 e-i3π/42/2
e-iπ/42/2 e-i3π/42/2
)
(
e-i7π/122/2 e-iπ/122/2
ei5π/122/2 e-iπ/122/2
)
(
eiπ/122/2 ei7π/122/2
e-i11π/122/2 ei7π/122/2
)
(
e-iπ/42/2 eiπ/42/2
ei3π/42/2 eiπ/42/2
)
(
ei5π/122/2 ei11π/122/2
e-i7π/122/2 ei11π/122/2
)
(
e-i11π/122/2 e-i5π/122/2
eiπ/122/2 e-i5π/122/2
)
45
(
0 -1 0
0 0 -1
-1 0 0
)
(
-(1+i)/2 -(1+i)/2
(1-i)/2 -(1-i)/2
)
d3-111
1
-1
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
(
0 1 0
0 0 1
1 0 0
)
(
0 -1 0
0 0 -1
-1 0 0
)
(
e-i3π/42/2 e-i3π/42/2
e-iπ/42/2 ei3π/42/2
)
(
ei7π/122/2 ei7π/122/2
e-i11π/122/2 eiπ/122/2
)
(
e-iπ/122/2 e-iπ/122/2
ei5π/122/2 e-i7π/122/2
)
(
eiπ/42/2 eiπ/42/2
ei3π/42/2 e-iπ/42/2
)
(
e-i5π/122/2 e-i5π/122/2
eiπ/122/2 e-i11π/122/2
)
(
ei11π/122/2 ei11π/122/2
e-i7π/122/2 ei5π/122/2
)
46
(
0 1 0
0 0 -1
1 0 0
)
(
-(1-i)/2 (1-i)/2
-(1+i)/2 -(1+i)/2
)
d3-111
1
-1
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
(
0 -1 0
0 0 -1
1 0 0
)
(
0 1 0
0 0 1
-1 0 0
)
(
ei3π/42/2 e-iπ/42/2
e-i3π/42/2 e-i3π/42/2
)
(
eiπ/122/2 e-i11π/122/2
ei7π/122/2 ei7π/122/2
)
(
e-i7π/122/2 ei5π/122/2
e-iπ/122/2 e-iπ/122/2
)
(
e-iπ/42/2 ei3π/42/2
eiπ/42/2 eiπ/42/2
)
(
e-i11π/122/2 eiπ/122/2
e-i5π/122/2 e-i5π/122/2
)
(
ei5π/122/2 e-i7π/122/2
ei11π/122/2 ei11π/122/2
)
47
(
0 -1 0
0 0 1
1 0 0
)
(
-(1+i)/2 (1+i)/2
-(1-i)/2 -(1-i)/2
)
d3-111
1
-1
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
(
0 -1 0
0 0 1
-1 0 0
)
(
0 1 0
0 0 -1
1 0 0
)
(
e-i3π/42/2 eiπ/42/2
ei3π/42/2 ei3π/42/2
)
(
ei7π/122/2 e-i5π/122/2
eiπ/122/2 eiπ/122/2
)
(
e-iπ/122/2 ei11π/122/2
e-i7π/122/2 e-i7π/122/2
)
(
eiπ/42/2 e-i3π/42/2
e-iπ/42/2 e-iπ/42/2
)
(
e-i5π/122/2 ei7π/122/2
e-i11π/122/2 e-i11π/122/2
)
(
ei11π/122/2 e-iπ/122/2
ei5π/122/2 ei5π/122/2
)
48
(
0 1 0
0 0 1
-1 0 0
)
(
-(1-i)/2 -(1-i)/2
(1+i)/2 -(1+i)/2
)
d3-111
1
-1
e-i2π/3
eiπ/3
ei2π/3
e-iπ/3
(
0 1 0
0 0 -1
-1 0 0
)
(
0 -1 0
0 0 1
1 0 0
)
(
ei3π/42/2 ei3π/42/2
eiπ/42/2 e-i3π/42/2
)
(
eiπ/122/2 eiπ/122/2
e-i5π/122/2 ei7π/122/2
)
(
e-i7π/122/2 e-i7π/122/2
ei11π/122/2 e-iπ/122/2
)
(
e-iπ/42/2 e-iπ/42/2
e-i3π/42/2 eiπ/42/2
)
(
e-i11π/122/2 e-i11π/122/2
ei7π/122/2 e-i5π/122/2
)
(
ei5π/122/2 ei5π/122/2
e-iπ/122/2 ei11π/122/2
)
k-Subgroupsmag
Bilbao Crystallographic Server
http://www.cryst.ehu.es
For comments, please mail to
administrador.bcs@ehu.eus