Bilbao Crystallographic Server Representations

## 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: 2001, d2001 C3: m010, dm010 C4: m100, dm100 C5: d1

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