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Irreducible representations of the Point Group 222 (No. 6)

Table of characters

(1)
(2)
(3)
C1
C2
C3
C4
GM1
A1
GM1
1
1
1
1
GM3
B1
GM2
1
1
-1
-1
GM4
B3
GM3
1
-1
-1
1
GM2
B2
GM4
1
-1
1
-1
(1): Notation of the irreps according to Bradley CJ and Cracknell AP, (1972) The Mathematical Theory of Symmetry in Solids. Oxford: Clarendon Press.
(2): Notation of the irreps according to Bradley CJ and Cracknell AP, (1972) The Mathematical Theory of Symmetry in Solids. Oxford: Clarendon Press, based on Mulliken RS (1933) Phys. Rev. 43, 279-302.
(3): Notation of the irreps according to A. P. Cracknell, B. L. Davies, S. C. Miller and W. F. Love (1979) Kronecher Product Tables, 1, General Introduction and Tables of Irreducible Representations of Space groups. New York: IFI/Plenum, for the GM point.

Lists of symmetry operations in the conjugacy classes

C1: 1
C2: 2001
C3: 2010
C4: 2100

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)
1
(
1 0 0
0 1 0
0 0 1
)
1
1
1
1
1
2
(
-1 0 0
0 -1 0
0 0 1
)
2001
1
1
-1
-1
3
(
-1 0 0
0 1 0
0 0 -1
)
2010
1
-1
-1
1
4
(
1 0 0
0 -1 0
0 0 -1
)
2100
1
-1
1
-1
k-Subgroupsmag
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