Bilbao Crystallographic Server arrow Representations


Irreducible representations of the Point Group mmm (No. 8)

Table of characters

(1)
(2)
(3)
C1
C2
C3
C4
C5
C6
C7
C8
GM1+
Ag
GM1+
1
1
1
1
1
1
1
1
GM1-
Au
GM1-
1
1
1
1
-1
-1
-1
-1
GM3+
B1g
GM2+
1
1
-1
-1
1
1
-1
-1
GM3-
B1u
GM2-
1
1
-1
-1
-1
-1
1
1
GM4+
B3g
GM3+
1
-1
-1
1
1
-1
-1
1
GM4-
B3u
GM3-
1
-1
-1
1
-1
1
1
-1
GM2+
B2g
GM4+
1
-1
1
-1
1
-1
1
-1
GM2-
B2u
GM4-
1
-1
1
-1
-1
1
-1
1
(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 H. T. Stokes, B. J. Campbell, and R. Cordes (2013) Acta Cryst. A. 69, 388-395 for the GM point.

Lists of symmetry operations in the conjugacy classes

C1: 1
C2: 2001
C3: 2010
C4: 2100
C5: -1
C6: m001
C7: m010
C8: m100

Matrices of the representations of the group

N
General position
Seitz Symbol
GM1+(1)
GM1-(1)
GM2+(1)
GM2-(1)
GM3+(1)
GM3-(1)
GM4+(1)
GM4-(1)
1
(
1 0 0
0 1 0
0 0 1
)
1
1
1
1
1
1
1
1
1
2
(
-1 0 0
0 -1 0
0 0 1
)
2001
1
1
1
1
-1
-1
-1
-1
3
(
-1 0 0
0 1 0
0 0 -1
)
2010
1
1
-1
-1
-1
-1
1
1
4
(
1 0 0
0 -1 0
0 0 -1
)
2100
1
1
-1
-1
1
1
-1
-1
5
(
-1 0 0
0 -1 0
0 0 -1
)
1
1
-1
1
-1
1
-1
1
-1
6
(
1 0 0
0 1 0
0 0 -1
)
m001
1
-1
1
-1
-1
1
-1
1
7
(
1 0 0
0 -1 0
0 0 1
)
m010
1
-1
-1
1
-1
1
1
-1
8
(
-1 0 0
0 1 0
0 0 1
)
m100
1
-1
-1
1
1
-1
-1
1
k-Subgroupsmag
Bilbao Crystallographic Server
http://www.cryst.ehu.es
For comments, please mail to
administrador.bcs@ehu.eus