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 |