Point Group Ih

Ternary direct products



Ag
Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
Ag Ag
T1g T1g Ag⊕T1g⊕Hg
T2g T2g Gg⊕Hg Ag⊕T2g⊕Hg
Gg Gg T2g⊕Gg⊕Hg T1g⊕Gg⊕Hg Ag⊕T1g⊕T2g⊕Gg⊕Hg
Hg Hg T1g⊕T2g⊕Gg⊕Hg T1g⊕T2g⊕Gg⊕Hg T1g⊕T2g⊕Gg⊕2Hg Ag⊕T1g⊕T2g⊕2Gg⊕2Hg
Au Au T1u T2u Gu Hu Ag
T1u T1u Au⊕T1u⊕Hu Gu⊕Hu T2u⊕Gu⊕Hu T1u⊕T2u⊕Gu⊕Hu T1g Ag⊕T1g⊕Hg
T2u T2u Gu⊕Hu Au⊕T2u⊕Hu T1u⊕Gu⊕Hu T1u⊕T2u⊕Gu⊕Hu T2g Gg⊕Hg Ag⊕T2g⊕Hg
Gu Gu T2u⊕Gu⊕Hu T1u⊕Gu⊕Hu Au⊕T1u⊕T2u⊕Gu⊕Hu T1u⊕T2u⊕Gu⊕2Hu Gg T2g⊕Gg⊕Hg T1g⊕Gg⊕Hg Ag⊕T1g⊕T2g⊕Gg⊕Hg
Hu Hu T1u⊕T2u⊕Gu⊕Hu T1u⊕T2u⊕Gu⊕Hu T1u⊕T2u⊕Gu⊕2Hu Au⊕T1u⊕T2u⊕2Gu⊕2Hu Hg T1g⊕T2g⊕Gg⊕Hg T1g⊕T2g⊕Gg⊕Hg T1g⊕T2g⊕Gg⊕2Hg Ag⊕T1g⊕T2g⊕2Gg⊕2Hg


T1g
T1g T2g Gg Hg Au T1u T2u Gu Hu
T1g Ag⊕3T1g⊕T2g⊕Gg⊕2Hg
T2g T1g⊕2T2g⊕2Gg⊕2Hg 2T1g⊕T2g⊕2Gg⊕2Hg
Gg T1g⊕2T2g⊕3Gg⊕3Hg Ag⊕2T1g⊕2T2g⊕2Gg⊕3Hg Ag⊕3T1g⊕2T2g⊕3Gg⊕4Hg
Hg Ag⊕2T1g⊕2T2g⊕3Gg⊕4Hg Ag⊕2T1g⊕2T2g⊕3Gg⊕4Hg Ag⊕3T1g⊕3T2g⊕4Gg⊕5Hg Ag⊕4T1g⊕4T2g⊕5Gg⊕6Hg
Au Au⊕T1u⊕Hu Gu⊕Hu T2u⊕Gu⊕Hu T1u⊕T2u⊕Gu⊕Hu T1g
T1u Au⊕3T1u⊕T2u⊕Gu⊕2Hu T1u⊕2T2u⊕2Gu⊕2Hu T1u⊕2T2u⊕3Gu⊕3Hu Au⊕2T1u⊕2T2u⊕3Gu⊕4Hu Ag⊕T1g⊕Hg Ag⊕3T1g⊕T2g⊕Gg⊕2Hg
T2u T1u⊕2T2u⊕2Gu⊕2Hu 2T1u⊕T2u⊕2Gu⊕2Hu Au⊕2T1u⊕2T2u⊕2Gu⊕3Hu Au⊕2T1u⊕2T2u⊕3Gu⊕4Hu Gg⊕Hg T1g⊕2T2g⊕2Gg⊕2Hg 2T1g⊕T2g⊕2Gg⊕2Hg
Gu T1u⊕2T2u⊕3Gu⊕3Hu Au⊕2T1u⊕2T2u⊕2Gu⊕3Hu Au⊕3T1u⊕2T2u⊕3Gu⊕4Hu Au⊕3T1u⊕3T2u⊕4Gu⊕5Hu T2g⊕Gg⊕Hg T1g⊕2T2g⊕3Gg⊕3Hg Ag⊕2T1g⊕2T2g⊕2Gg⊕3Hg Ag⊕3T1g⊕2T2g⊕3Gg⊕4Hg
Hu Au⊕2T1u⊕2T2u⊕3Gu⊕4Hu Au⊕2T1u⊕2T2u⊕3Gu⊕4Hu Au⊕3T1u⊕3T2u⊕4Gu⊕5Hu Au⊕4T1u⊕4T2u⊕5Gu⊕6Hu T1g⊕T2g⊕Gg⊕Hg Ag⊕2T1g⊕2T2g⊕3Gg⊕4Hg Ag⊕2T1g⊕2T2g⊕3Gg⊕4Hg Ag⊕3T1g⊕3T2g⊕4Gg⊕5Hg Ag⊕4T1g⊕4T2g⊕5Gg⊕6Hg


T2g
T2g Gg Hg Au T1u T2u Gu Hu
T2g Ag⊕T1g⊕3T2g⊕Gg⊕2Hg
Gg 2T1g⊕T2g⊕3Gg⊕3Hg Ag⊕2T1g⊕3T2g⊕3Gg⊕4Hg
Hg Ag⊕2T1g⊕2T2g⊕3Gg⊕4Hg Ag⊕3T1g⊕3T2g⊕4Gg⊕5Hg Ag⊕4T1g⊕4T2g⊕5Gg⊕6Hg
Au Au⊕T2u⊕Hu T1u⊕Gu⊕Hu T1u⊕T2u⊕Gu⊕Hu T2g
T1u 2T1u⊕T2u⊕2Gu⊕2Hu Au⊕2T1u⊕2T2u⊕2Gu⊕3Hu Au⊕2T1u⊕2T2u⊕3Gu⊕4Hu Gg⊕Hg T1g⊕2T2g⊕2Gg⊕2Hg
T2u Au⊕T1u⊕3T2u⊕Gu⊕2Hu 2T1u⊕T2u⊕3Gu⊕3Hu Au⊕2T1u⊕2T2u⊕3Gu⊕4Hu Ag⊕T2g⊕Hg 2T1g⊕T2g⊕2Gg⊕2Hg Ag⊕T1g⊕3T2g⊕Gg⊕2Hg
Gu 2T1u⊕T2u⊕3Gu⊕3Hu Au⊕2T1u⊕3T2u⊕3Gu⊕4Hu Au⊕3T1u⊕3T2u⊕4Gu⊕5Hu T1g⊕Gg⊕Hg Ag⊕2T1g⊕2T2g⊕2Gg⊕3Hg 2T1g⊕T2g⊕3Gg⊕3Hg Ag⊕2T1g⊕3T2g⊕3Gg⊕4Hg
Hu Au⊕2T1u⊕2T2u⊕3Gu⊕4Hu Au⊕3T1u⊕3T2u⊕4Gu⊕5Hu Au⊕4T1u⊕4T2u⊕5Gu⊕6Hu T1g⊕T2g⊕Gg⊕Hg Ag⊕2T1g⊕2T2g⊕3Gg⊕4Hg Ag⊕2T1g⊕2T2g⊕3Gg⊕4Hg Ag⊕3T1g⊕3T2g⊕4Gg⊕5Hg Ag⊕4T1g⊕4T2g⊕5Gg⊕6Hg


Gg
Gg Hg Au T1u T2u Gu Hu
Gg Ag⊕3T1g⊕3T2g⊕5Gg⊕5Hg
Hg Ag⊕4T1g⊕4T2g⊕5Gg⊕7Hg 2Ag⊕5T1g⊕5T2g⊕7Gg⊕8Hg
Au Au⊕T1u⊕T2u⊕Gu⊕Hu T1u⊕T2u⊕Gu⊕2Hu Gg
T1u Au⊕3T1u⊕2T2u⊕3Gu⊕4Hu Au⊕3T1u⊕3T2u⊕4Gu⊕5Hu T2g⊕Gg⊕Hg T1g⊕2T2g⊕3Gg⊕3Hg
T2u Au⊕2T1u⊕3T2u⊕3Gu⊕4Hu Au⊕3T1u⊕3T2u⊕4Gu⊕5Hu T1g⊕Gg⊕Hg Ag⊕2T1g⊕2T2g⊕2Gg⊕3Hg 2T1g⊕T2g⊕3Gg⊕3Hg
Gu Au⊕3T1u⊕3T2u⊕5Gu⊕5Hu Au⊕4T1u⊕4T2u⊕5Gu⊕7Hu Ag⊕T1g⊕T2g⊕Gg⊕Hg Ag⊕3T1g⊕2T2g⊕3Gg⊕4Hg Ag⊕2T1g⊕3T2g⊕3Gg⊕4Hg Ag⊕3T1g⊕3T2g⊕5Gg⊕5Hg
Hu Au⊕4T1u⊕4T2u⊕5Gu⊕7Hu 2Au⊕5T1u⊕5T2u⊕7Gu⊕8Hu T1g⊕T2g⊕Gg⊕2Hg Ag⊕3T1g⊕3T2g⊕4Gg⊕5Hg Ag⊕3T1g⊕3T2g⊕4Gg⊕5Hg Ag⊕4T1g⊕4T2g⊕5Gg⊕7Hg 2Ag⊕5T1g⊕5T2g⊕7Gg⊕8Hg


Hg
Hg Au T1u T2u Gu Hu
Hg 2Ag⊕6T1g⊕6T2g⊕8Gg⊕11Hg
Au Au⊕T1u⊕T2u⊕2Gu⊕2Hu Hg
T1u Au⊕4T1u⊕4T2u⊕5Gu⊕6Hu T1g⊕T2g⊕Gg⊕Hg Ag⊕2T1g⊕2T2g⊕3Gg⊕4Hg
T2u Au⊕4T1u⊕4T2u⊕5Gu⊕6Hu T1g⊕T2g⊕Gg⊕Hg Ag⊕2T1g⊕2T2g⊕3Gg⊕4Hg Ag⊕2T1g⊕2T2g⊕3Gg⊕4Hg
Gu 2Au⊕5T1u⊕5T2u⊕7Gu⊕8Hu T1g⊕T2g⊕Gg⊕2Hg Ag⊕3T1g⊕3T2g⊕4Gg⊕5Hg Ag⊕3T1g⊕3T2g⊕4Gg⊕5Hg Ag⊕4T1g⊕4T2g⊕5Gg⊕7Hg
Hu 2Au⊕6T1u⊕6T2u⊕8Gu⊕11Hu Ag⊕T1g⊕T2g⊕2Gg⊕2Hg Ag⊕4T1g⊕4T2g⊕5Gg⊕6Hg Ag⊕4T1g⊕4T2g⊕5Gg⊕6Hg 2Ag⊕5T1g⊕5T2g⊕7Gg⊕8Hg 2Ag⊕6T1g⊕6T2g⊕8Gg⊕11Hg


Au
Au T1u T2u Gu Hu
Au Au
T1u T1u Au⊕T1u⊕Hu
T2u T2u Gu⊕Hu Au⊕T2u⊕Hu
Gu Gu T2u⊕Gu⊕Hu T1u⊕Gu⊕Hu Au⊕T1u⊕T2u⊕Gu⊕Hu
Hu Hu T1u⊕T2u⊕Gu⊕Hu T1u⊕T2u⊕Gu⊕Hu T1u⊕T2u⊕Gu⊕2Hu Au⊕T1u⊕T2u⊕2Gu⊕2Hu


T1u
T1u T2u Gu Hu
T1u Au⊕3T1u⊕T2u⊕Gu⊕2Hu
T2u T1u⊕2T2u⊕2Gu⊕2Hu 2T1u⊕T2u⊕2Gu⊕2Hu
Gu T1u⊕2T2u⊕3Gu⊕3Hu Au⊕2T1u⊕2T2u⊕2Gu⊕3Hu Au⊕3T1u⊕2T2u⊕3Gu⊕4Hu
Hu Au⊕2T1u⊕2T2u⊕3Gu⊕4Hu Au⊕2T1u⊕2T2u⊕3Gu⊕4Hu Au⊕3T1u⊕3T2u⊕4Gu⊕5Hu Au⊕4T1u⊕4T2u⊕5Gu⊕6Hu


T2u
T2u Gu Hu
T2u Au⊕T1u⊕3T2u⊕Gu⊕2Hu
Gu 2T1u⊕T2u⊕3Gu⊕3Hu Au⊕2T1u⊕3T2u⊕3Gu⊕4Hu
Hu Au⊕2T1u⊕2T2u⊕3Gu⊕4Hu Au⊕3T1u⊕3T2u⊕4Gu⊕5Hu Au⊕4T1u⊕4T2u⊕5Gu⊕6Hu


Gu
Gu Hu
Gu Au⊕3T1u⊕3T2u⊕5Gu⊕5Hu
Hu Au⊕4T1u⊕4T2u⊕5Gu⊕7Hu 2Au⊕5T1u⊕5T2u⊕7Gu⊕8Hu


Hu
Hu
Hu 2Au⊕6T1u⊕6T2u⊕8Gu⊕11Hu