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Irreducible representations of the Double Point Group mm2 (No. 7)

Table of characters

(1)
(2)
(3)
C1
C2
C3
C4
C5
GM1
A1
GM1
1
1
1
1
1
GM3
A2
GM2
1
1
-1
-1
1
GM4
B2
GM3
1
-1
-1
1
1
GM2
B1
GM4
1
-1
1
-1
1
GM5
E
GM5
2
0
0
0
-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: 2001d2001
C3: m010dm010
C4: m100dm100
C5d1

Matrices of the representations of the group

The number in parentheses 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)
GM2(1)
GM3(1)
GM4(1)
GM5(-1)
1
(
1 0 0
0 1 0
0 0 1
)
(
1 0
0 1
)
1
1
1
1
1
(
1 0
0 1
)
2
(
-1 0 0
0 -1 0
0 0 1
)
(
-i 0
0 i
)
2001
1
1
-1
-1
(
0 -1
1 0
)
3
(
1 0 0
0 -1 0
0 0 1
)
(
0 -1
1 0
)
m010
1
-1
-1
1
(
0 -i
-i 0
)
4
(
-1 0 0
0 1 0
0 0 1
)
(
0 -i
-i 0
)
m100
1
-1
1
-1
(
-i 0
0 i
)
5
(
1 0 0
0 1 0
0 0 1
)
(
-1 0
0 -1
)
d1
1
1
1
1
(
-1 0
0 -1
)
6
(
-1 0 0
0 -1 0
0 0 1
)
(
i 0
0 -i
)
d2001
1
1
-1
-1
(
0 1
-1 0
)
7
(
1 0 0
0 -1 0
0 0 1
)
(
0 1
-1 0
)
dm010
1
-1
-1
1
(
0 i
i 0
)
8
(
-1 0 0
0 1 0
0 0 1
)
(
0 i
i 0
)
dm100
1
-1
1
-1
(
i 0
0 -i
)
k-Subgroupsmag
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