Point Group Oh

Ternary direct products



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


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


Eg
Eg T1g T2g A1u A2u Eu T1u T2u
Eg A1g⊕A2g⊕3Eg
T1g 2T1g⊕2T2g A1g⊕A2g⊕2Eg⊕2T1g⊕2T2g
T2g 2T1g⊕2T2g A1g⊕A2g⊕2Eg⊕2T1g⊕2T2g A1g⊕A2g⊕2Eg⊕2T1g⊕2T2g
A1u A1u⊕A2u⊕Eu T1u⊕T2u T1u⊕T2u Eg
A2u A1u⊕A2u⊕Eu T1u⊕T2u T1u⊕T2u Eg Eg
Eu A1u⊕A2u⊕3Eu 2T1u⊕2T2u 2T1u⊕2T2u A1g⊕A2g⊕Eg A1g⊕A2g⊕Eg A1g⊕A2g⊕3Eg
T1u 2T1u⊕2T2u A1u⊕A2u⊕2Eu⊕2T1u⊕2T2u A1u⊕A2u⊕2Eu⊕2T1u⊕2T2u T1g⊕T2g T1g⊕T2g 2T1g⊕2T2g A1g⊕A2g⊕2Eg⊕2T1g⊕2T2g
T2u 2T1u⊕2T2u A1u⊕A2u⊕2Eu⊕2T1u⊕2T2u A1u⊕A2u⊕2Eu⊕2T1u⊕2T2u T1g⊕T2g T1g⊕T2g 2T1g⊕2T2g A1g⊕A2g⊕2Eg⊕2T1g⊕2T2g A1g⊕A2g⊕2Eg⊕2T1g⊕2T2g


T1g
T1g T2g A1u A2u Eu T1u T2u
T1g A1g⊕A2g⊕2Eg⊕4T1g⊕3T2g
T2g A1g⊕A2g⊕2Eg⊕3T1g⊕4T2g A1g⊕A2g⊕2Eg⊕4T1g⊕3T2g
A1u A1u⊕Eu⊕T1u⊕T2u A2u⊕Eu⊕T1u⊕T2u T1g
A2u A2u⊕Eu⊕T1u⊕T2u A1u⊕Eu⊕T1u⊕T2u T2g T1g
Eu A1u⊕A2u⊕2Eu⊕2T1u⊕2T2u A1u⊕A2u⊕2Eu⊕2T1u⊕2T2u T1g⊕T2g T1g⊕T2g 2T1g⊕2T2g
T1u A1u⊕A2u⊕2Eu⊕4T1u⊕3T2u A1u⊕A2u⊕2Eu⊕3T1u⊕4T2u A1g⊕Eg⊕T1g⊕T2g A2g⊕Eg⊕T1g⊕T2g A1g⊕A2g⊕2Eg⊕2T1g⊕2T2g A1g⊕A2g⊕2Eg⊕4T1g⊕3T2g
T2u A1u⊕A2u⊕2Eu⊕3T1u⊕4T2u A1u⊕A2u⊕2Eu⊕4T1u⊕3T2u A2g⊕Eg⊕T1g⊕T2g A1g⊕Eg⊕T1g⊕T2g A1g⊕A2g⊕2Eg⊕2T1g⊕2T2g A1g⊕A2g⊕2Eg⊕3T1g⊕4T2g A1g⊕A2g⊕2Eg⊕4T1g⊕3T2g


T2g
T2g A1u A2u Eu T1u T2u
T2g A1g⊕A2g⊕2Eg⊕3T1g⊕4T2g
A1u A1u⊕Eu⊕T1u⊕T2u T2g
A2u A2u⊕Eu⊕T1u⊕T2u T1g T2g
Eu A1u⊕A2u⊕2Eu⊕2T1u⊕2T2u T1g⊕T2g T1g⊕T2g 2T1g⊕2T2g
T1u A1u⊕A2u⊕2Eu⊕4T1u⊕3T2u A2g⊕Eg⊕T1g⊕T2g A1g⊕Eg⊕T1g⊕T2g A1g⊕A2g⊕2Eg⊕2T1g⊕2T2g A1g⊕A2g⊕2Eg⊕3T1g⊕4T2g
T2u A1u⊕A2u⊕2Eu⊕3T1u⊕4T2u A1g⊕Eg⊕T1g⊕T2g A2g⊕Eg⊕T1g⊕T2g A1g⊕A2g⊕2Eg⊕2T1g⊕2T2g A1g⊕A2g⊕2Eg⊕4T1g⊕3T2g A1g⊕A2g⊕2Eg⊕3T1g⊕4T2g


A1u
A1u A2u Eu T1u T2u
A1u A1u
A2u A2u A1u
Eu Eu Eu A1u⊕A2u⊕Eu
T1u T1u T2u T1u⊕T2u A1u⊕Eu⊕T1u⊕T2u
T2u T2u T1u T1u⊕T2u A2u⊕Eu⊕T1u⊕T2u A1u⊕Eu⊕T1u⊕T2u


A2u
A2u Eu T1u T2u
A2u A2u
Eu Eu A1u⊕A2u⊕Eu
T1u T1u T1u⊕T2u A2u⊕Eu⊕T1u⊕T2u
T2u T2u T1u⊕T2u A1u⊕Eu⊕T1u⊕T2u A2u⊕Eu⊕T1u⊕T2u


Eu
Eu T1u T2u
Eu A1u⊕A2u⊕3Eu
T1u 2T1u⊕2T2u A1u⊕A2u⊕2Eu⊕2T1u⊕2T2u
T2u 2T1u⊕2T2u A1u⊕A2u⊕2Eu⊕2T1u⊕2T2u A1u⊕A2u⊕2Eu⊕2T1u⊕2T2u


T1u
T1u T2u
T1u A1u⊕A2u⊕2Eu⊕4T1u⊕3T2u
T2u A1u⊕A2u⊕2Eu⊕3T1u⊕4T2u A1u⊕A2u⊕2Eu⊕4T1u⊕3T2u


T2u
T2u
T2u A1u⊕A2u⊕2Eu⊕3T1u⊕4T2u