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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 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
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
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