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Orientation XYZ

Symmetry Operations

In the Oh Point Group, with orientation XYZ there are the following symmetry operations

Operator Orientation
E {0,0,0} ,
C3 {1,1,1} , {1,1,1} , {1,1,1} , {1,1,1} , {1,1,1} , {1,1,1} , {1,1,1} , {1,1,1} ,
C2 {1,1,0} , {1,1,0} , {1,0,1} , {1,0,1} , {0,1,1} , {0,1,1} ,
C4 {0,0,1} , {0,1,0} , {1,0,0} , {0,0,1} , {0,1,0} , {1,0,0} ,
C2 {0,0,1} , {0,1,0} , {1,0,0} ,
i {0,0,0} ,
S4 {0,0,1} , {0,1,0} , {1,0,0} , {0,0,1} , {0,1,0} , {1,0,0} ,
S6 {1,1,1} , {1,1,1} , {1,1,1} , {1,1,1} , {1,1,1} , {1,1,1} , {1,1,1} , {1,1,1} ,
σh {1,0,0} , {0,1,0} , {0,0,1} ,
σd {1,1,0} , {1,1,0} , {1,0,1} , {1,0,1} , {0,1,1} , {0,1,1} ,

Character Table

E(1) C3(8) C2(6) C4(6) C2(3) i(1) S4(6) S6(8) σh(3) σd(6)
A1g 1 1 1 1 1 1 1 1 1 1
A2g 1 1 1 1 1 1 1 1 1 1
Eg 2 1 0 0 2 2 0 1 2 0
T1g 3 0 1 1 1 3 1 0 1 1
T2g 3 0 1 1 1 3 1 0 1 1
A1u 1 1 1 1 1 1 1 1 1 1
A2u 1 1 1 1 1 1 1 1 1 1
Eu 2 1 0 0 2 2 0 1 2 0
T1u 3 0 1 1 1 3 1 0 1 1
T2u 3 0 1 1 1 3 1 0 1 1

Product Table

A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
A1g A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
A2g A2g A1g Eg T2g T1g A2u A1u Eu T2u T1u
Eg Eg Eg A1g+A2g+Eg T1g+T2g T1g+T2g Eu Eu A1u+A2u+Eu T1u+T2u T1u+T2u
T1g T1g T2g T1g+T2g A1g+Eg+T1g+T2g A2g+Eg+T1g+T2g T1u T2u T1u+T2u A1u+Eu+T1u+T2u A2u+Eu+T1u+T2u
T2g T2g T1g T1g+T2g A2g+Eg+T1g+T2g A1g+Eg+T1g+T2g T2u T1u T1u+T2u A2u+Eu+T1u+T2u A1u+Eu+T1u+T2u
A1u A1u A2u Eu T1u T2u A1g A2g Eg T1g T2g
A2u A2u A1u Eu T2u T1u A2g A1g Eg T2g T1g
Eu Eu Eu A1u+A2u+Eu T1u+T2u T1u+T2u Eg Eg A1g+A2g+Eg T1g+T2g T1g+T2g
T1u T1u T2u T1u+T2u A1u+Eu+T1u+T2u A2u+Eu+T1u+T2u T1g T2g T1g+T2g A1g+Eg+T1g+T2g A2g+Eg+T1g+T2g
T2u T2u T1u T1u+T2u A2u+Eu+T1u+T2u A1u+Eu+T1u+T2u T2g T1g T1g+T2g A2g+Eg+T1g+T2g A1g+Eg+T1g+T2g

Other Orientations

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