Point Group C7h
Quaternary direct products
A'⊙A'⊙
⊙ |
A' |
E'1*
|
E'2*
|
E'3*
|
A'' |
E''1*
|
E''2*
|
E''3*
|
A' |
A' |
|
|
|
|
|
|
|
E'1*
|
E'1 |
2A'⊕E'2 |
|
|
|
|
|
|
E'2*
|
E'2 |
E'1⊕E'3 |
2A'⊕E'3 |
|
|
|
|
|
E'3*
|
E'3 |
E'2⊕E'3 |
E'1⊕E'2 |
2A'⊕E'1 |
|
|
|
|
A'' |
A'' |
E''1 |
E''2 |
E''3 |
A' |
|
|
|
E''1*
|
E''1 |
2A''⊕E''2 |
E''1⊕E''3 |
E''2⊕E''3 |
E'1 |
2A'⊕E'2 |
|
|
E''2*
|
E''2 |
E''1⊕E''3 |
2A''⊕E''3 |
E''1⊕E''2 |
E'2 |
E'1⊕E'3 |
2A'⊕E'3 |
|
E''3*
|
E''3 |
E''2⊕E''3 |
E''1⊕E''2 |
2A''⊕E''1 |
E'3 |
E'2⊕E'3 |
E'1⊕E'2 |
2A'⊕E'1 |
A'⊙E'1⊙
⊙ |
E'1*
|
E'2*
|
E'3*
|
A'' |
E''1*
|
E''2*
|
E''3*
|
E'1*
|
3E'1⊕E'3 |
|
|
|
|
|
|
E'2*
|
2A'⊕2E'2⊕E'3 |
2E'1⊕E'2⊕E'3 |
|
|
|
|
|
E'3*
|
E'1⊕E'2⊕2E'3 |
2A'⊕E'1⊕E'2⊕E'3 |
2A'⊕2E'1⊕E'2 |
|
|
|
|
A'' |
2A''⊕E''2 |
E''1⊕E''3 |
E''2⊕E''3 |
E'1 |
|
|
|
E''1*
|
3E''1⊕E''3 |
2A''⊕2E''2⊕E''3 |
E''1⊕E''2⊕2E''3 |
2A'⊕E'2 |
3E'1⊕E'3 |
|
|
E''2*
|
2A''⊕2E''2⊕E''3 |
2E''1⊕E''2⊕E''3 |
2A''⊕E''1⊕E''2⊕E''3 |
E'1⊕E'3 |
2A'⊕2E'2⊕E'3 |
2E'1⊕E'2⊕E'3 |
|
E''3*
|
E''1⊕E''2⊕2E''3 |
2A''⊕E''1⊕E''2⊕E''3 |
2A''⊕2E''1⊕E''2 |
E'2⊕E'3 |
E'1⊕E'2⊕2E'3 |
2A'⊕E'1⊕E'2⊕E'3 |
2A'⊕2E'1⊕E'2 |
A'⊙E'2⊙
⊙ |
E'2*
|
E'3*
|
A'' |
E''1*
|
E''2*
|
E''3*
|
E'2*
|
E'1⊕3E'2 |
|
|
|
|
|
E'3*
|
2A'⊕E'1⊕2E'3 |
E'1⊕2E'2⊕E'3 |
|
|
|
|
A'' |
2A''⊕E''3 |
E''1⊕E''2 |
E'2 |
|
|
|
E''1*
|
2E''1⊕E''2⊕E''3 |
2A''⊕E''1⊕E''2⊕E''3 |
E'1⊕E'3 |
2A'⊕2E'2⊕E'3 |
|
|
E''2*
|
E''1⊕3E''2 |
2A''⊕E''1⊕2E''3 |
2A'⊕E'3 |
2E'1⊕E'2⊕E'3 |
E'1⊕3E'2 |
|
E''3*
|
2A''⊕E''1⊕2E''3 |
E''1⊕2E''2⊕E''3 |
E'1⊕E'2 |
2A'⊕E'1⊕E'2⊕E'3 |
2A'⊕E'1⊕2E'3 |
E'1⊕2E'2⊕E'3 |
A'⊙E'3⊙
⊙ |
E'3*
|
A'' |
E''1*
|
E''2*
|
E''3*
|
E'3*
|
E'2⊕3E'3 |
|
|
|
|
A'' |
2A''⊕E''1 |
E'3 |
|
|
|
E''1*
|
2A''⊕2E''1⊕E''2 |
E'2⊕E'3 |
E'1⊕E'2⊕2E'3 |
|
|
E''2*
|
E''1⊕2E''2⊕E''3 |
E'1⊕E'2 |
2A'⊕E'1⊕E'2⊕E'3 |
2A'⊕E'1⊕2E'3 |
|
E''3*
|
E''2⊕3E''3 |
2A'⊕E'1 |
2A'⊕2E'1⊕E'2 |
E'1⊕2E'2⊕E'3 |
E'2⊕3E'3 |
A'⊙A''⊙
⊙ |
A'' |
E''1*
|
E''2*
|
E''3*
|
A'' |
A'' |
|
|
|
E''1*
|
E''1 |
2A''⊕E''2 |
|
|
E''2*
|
E''2 |
E''1⊕E''3 |
2A''⊕E''3 |
|
E''3*
|
E''3 |
E''2⊕E''3 |
E''1⊕E''2 |
2A''⊕E''1 |
A'⊙E''1⊙
⊙ |
E''1*
|
E''2*
|
E''3*
|
E''1*
|
3E''1⊕E''3 |
|
|
E''2*
|
2A''⊕2E''2⊕E''3 |
2E''1⊕E''2⊕E''3 |
|
E''3*
|
E''1⊕E''2⊕2E''3 |
2A''⊕E''1⊕E''2⊕E''3 |
2A''⊕2E''1⊕E''2 |
A'⊙E''2⊙
⊙ |
E''2*
|
E''3*
|
E''2*
|
E''1⊕3E''2 |
|
E''3*
|
2A''⊕E''1⊕2E''3 |
E''1⊕2E''2⊕E''3 |
A'⊙E''3⊙
⊙ |
E''3*
|
E''3*
|
E''2⊕3E''3 |
E'1⊙E'1⊙
⊙ |
E'1*
|
E'2*
|
E'3*
|
A'' |
E''1*
|
E''2*
|
E''3*
|
E'1*
|
6A'⊕4E'2⊕E'3 |
|
|
|
|
|
|
E'2*
|
4E'1⊕E'2⊕3E'3 |
4A'⊕E'1⊕3E'2⊕2E'3 |
|
|
|
|
|
E'3*
|
2A'⊕E'1⊕3E'2⊕3E'3 |
2A'⊕3E'1⊕2E'2⊕2E'3 |
4A'⊕3E'1⊕2E'2⊕E'3 |
|
|
|
|
A'' |
3E''1⊕E''3 |
2A''⊕2E''2⊕E''3 |
E''1⊕E''2⊕2E''3 |
2A'⊕E'2 |
|
|
|
E''1*
|
6A''⊕4E''2⊕E''3 |
4E''1⊕E''2⊕3E''3 |
2A''⊕E''1⊕3E''2⊕3E''3 |
3E'1⊕E'3 |
6A'⊕4E'2⊕E'3 |
|
|
E''2*
|
4E''1⊕E''2⊕3E''3 |
4A''⊕E''1⊕3E''2⊕2E''3 |
2A''⊕3E''1⊕2E''2⊕2E''3 |
2A'⊕2E'2⊕E'3 |
4E'1⊕E'2⊕3E'3 |
4A'⊕E'1⊕3E'2⊕2E'3 |
|
E''3*
|
2A''⊕E''1⊕3E''2⊕3E''3 |
2A''⊕3E''1⊕2E''2⊕2E''3 |
4A''⊕3E''1⊕2E''2⊕E''3 |
E'1⊕E'2⊕2E'3 |
2A'⊕E'1⊕3E'2⊕3E'3 |
2A'⊕3E'1⊕2E'2⊕2E'3 |
4A'⊕3E'1⊕2E'2⊕E'3 |
E'1⊙E'2⊙
⊙ |
E'2*
|
E'3*
|
A'' |
E''1*
|
E''2*
|
E''3*
|
E'2*
|
2A'⊕3E'1⊕E'2⊕3E'3 |
|
|
|
|
|
E'3*
|
2A'⊕2E'1⊕3E'2⊕2E'3 |
2A'⊕2E'1⊕2E'2⊕3E'3 |
|
|
|
|
A'' |
2E''1⊕E''2⊕E''3 |
2A''⊕E''1⊕E''2⊕E''3 |
E'1⊕E'3 |
|
|
|
E''1*
|
4A''⊕E''1⊕3E''2⊕2E''3 |
2A''⊕3E''1⊕2E''2⊕2E''3 |
2A'⊕2E'2⊕E'3 |
4E'1⊕E'2⊕3E'3 |
|
|
E''2*
|
2A''⊕3E''1⊕E''2⊕3E''3 |
2A''⊕2E''1⊕3E''2⊕2E''3 |
2E'1⊕E'2⊕E'3 |
4A'⊕E'1⊕3E'2⊕2E'3 |
2A'⊕3E'1⊕E'2⊕3E'3 |
|
E''3*
|
2A''⊕2E''1⊕3E''2⊕2E''3 |
2A''⊕2E''1⊕2E''2⊕3E''3 |
2A'⊕E'1⊕E'2⊕E'3 |
2A'⊕3E'1⊕2E'2⊕2E'3 |
2A'⊕2E'1⊕3E'2⊕2E'3 |
2A'⊕2E'1⊕2E'2⊕3E'3 |
E'1⊙E'3⊙
⊙ |
E'3*
|
A'' |
E''1*
|
E''2*
|
E''3*
|
E'3*
|
E'1⊕3E'2⊕4E'3 |
|
|
|
|
A'' |
2A''⊕2E''1⊕E''2 |
E'2⊕E'3 |
|
|
|
E''1*
|
4A''⊕3E''1⊕2E''2⊕E''3 |
E'1⊕E'2⊕2E'3 |
2A'⊕E'1⊕3E'2⊕3E'3 |
|
|
E''2*
|
2A''⊕2E''1⊕2E''2⊕3E''3 |
2A'⊕E'1⊕E'2⊕E'3 |
2A'⊕3E'1⊕2E'2⊕2E'3 |
2A'⊕2E'1⊕3E'2⊕2E'3 |
|
E''3*
|
E''1⊕3E''2⊕4E''3 |
2A'⊕2E'1⊕E'2 |
4A'⊕3E'1⊕2E'2⊕E'3 |
2A'⊕2E'1⊕2E'2⊕3E'3 |
E'1⊕3E'2⊕4E'3 |
E'1⊙A''⊙
⊙ |
A'' |
E''1*
|
E''2*
|
E''3*
|
A'' |
E''1 |
|
|
|
E''1*
|
2A''⊕E''2 |
3E''1⊕E''3 |
|
|
E''2*
|
E''1⊕E''3 |
2A''⊕2E''2⊕E''3 |
2E''1⊕E''2⊕E''3 |
|
E''3*
|
E''2⊕E''3 |
E''1⊕E''2⊕2E''3 |
2A''⊕E''1⊕E''2⊕E''3 |
2A''⊕2E''1⊕E''2 |
E'1⊙E''1⊙
⊙ |
E''1*
|
E''2*
|
E''3*
|
E''1*
|
6A''⊕4E''2⊕E''3 |
|
|
E''2*
|
4E''1⊕E''2⊕3E''3 |
4A''⊕E''1⊕3E''2⊕2E''3 |
|
E''3*
|
2A''⊕E''1⊕3E''2⊕3E''3 |
2A''⊕3E''1⊕2E''2⊕2E''3 |
4A''⊕3E''1⊕2E''2⊕E''3 |
E'1⊙E''2⊙
⊙ |
E''2*
|
E''3*
|
E''2*
|
2A''⊕3E''1⊕E''2⊕3E''3 |
|
E''3*
|
2A''⊕2E''1⊕3E''2⊕2E''3 |
2A''⊕2E''1⊕2E''2⊕3E''3 |
E'1⊙E''3⊙
⊙ |
E''3*
|
E''3*
|
E''1⊕3E''2⊕4E''3 |
E'2⊙E'2⊙
⊙ |
E'2*
|
E'3*
|
A'' |
E''1*
|
E''2*
|
E''3*
|
E'2*
|
6A'⊕E'1⊕4E'3 |
|
|
|
|
|
E'3*
|
3E'1⊕4E'2⊕E'3 |
4A'⊕2E'1⊕E'2⊕3E'3 |
|
|
|
|
A'' |
E''1⊕3E''2 |
2A''⊕E''1⊕2E''3 |
2A'⊕E'3 |
|
|
|
E''1*
|
2A''⊕3E''1⊕E''2⊕3E''3 |
2A''⊕2E''1⊕3E''2⊕2E''3 |
2E'1⊕E'2⊕E'3 |
4A'⊕E'1⊕3E'2⊕2E'3 |
|
|
E''2*
|
6A''⊕E''1⊕4E''3 |
3E''1⊕4E''2⊕E''3 |
E'1⊕3E'2 |
2A'⊕3E'1⊕E'2⊕3E'3 |
6A'⊕E'1⊕4E'3 |
|
E''3*
|
3E''1⊕4E''2⊕E''3 |
4A''⊕2E''1⊕E''2⊕3E''3 |
2A'⊕E'1⊕2E'3 |
2A'⊕2E'1⊕3E'2⊕2E'3 |
3E'1⊕4E'2⊕E'3 |
4A'⊕2E'1⊕E'2⊕3E'3 |
E'2⊙E'3⊙
⊙ |
E'3*
|
A'' |
E''1*
|
E''2*
|
E''3*
|
E'3*
|
2A'⊕3E'1⊕3E'2⊕E'3 |
|
|
|
|
A'' |
E''1⊕2E''2⊕E''3 |
E'1⊕E'2 |
|
|
|
E''1*
|
2A''⊕2E''1⊕2E''2⊕3E''3 |
2A'⊕E'1⊕E'2⊕E'3 |
2A'⊕3E'1⊕2E'2⊕2E'3 |
|
|
E''2*
|
4A''⊕2E''1⊕E''2⊕3E''3 |
2A'⊕E'1⊕2E'3 |
2A'⊕2E'1⊕3E'2⊕2E'3 |
3E'1⊕4E'2⊕E'3 |
|
E''3*
|
2A''⊕3E''1⊕3E''2⊕E''3 |
E'1⊕2E'2⊕E'3 |
2A'⊕2E'1⊕2E'2⊕3E'3 |
4A'⊕2E'1⊕E'2⊕3E'3 |
2A'⊕3E'1⊕3E'2⊕E'3 |
E'2⊙A''⊙
⊙ |
A'' |
E''1*
|
E''2*
|
E''3*
|
A'' |
E''2 |
|
|
|
E''1*
|
E''1⊕E''3 |
2A''⊕2E''2⊕E''3 |
|
|
E''2*
|
2A''⊕E''3 |
2E''1⊕E''2⊕E''3 |
E''1⊕3E''2 |
|
E''3*
|
E''1⊕E''2 |
2A''⊕E''1⊕E''2⊕E''3 |
2A''⊕E''1⊕2E''3 |
E''1⊕2E''2⊕E''3 |
E'2⊙E''1⊙
⊙ |
E''1*
|
E''2*
|
E''3*
|
E''1*
|
4E''1⊕E''2⊕3E''3 |
|
|
E''2*
|
4A''⊕E''1⊕3E''2⊕2E''3 |
2A''⊕3E''1⊕E''2⊕3E''3 |
|
E''3*
|
2A''⊕3E''1⊕2E''2⊕2E''3 |
2A''⊕2E''1⊕3E''2⊕2E''3 |
2A''⊕2E''1⊕2E''2⊕3E''3 |
E'2⊙E''2⊙
⊙ |
E''2*
|
E''3*
|
E''2*
|
6A''⊕E''1⊕4E''3 |
|
E''3*
|
3E''1⊕4E''2⊕E''3 |
4A''⊕2E''1⊕E''2⊕3E''3 |
E'2⊙E''3⊙
⊙ |
E''3*
|
E''3*
|
2A''⊕3E''1⊕3E''2⊕E''3 |
E'3⊙E'3⊙
⊙ |
E'3*
|
A'' |
E''1*
|
E''2*
|
E''3*
|
E'3*
|
6A'⊕4E'1⊕E'2 |
|
|
|
|
A'' |
E''2⊕3E''3 |
2A'⊕E'1 |
|
|
|
E''1*
|
E''1⊕3E''2⊕4E''3 |
2A'⊕2E'1⊕E'2 |
4A'⊕3E'1⊕2E'2⊕E'3 |
|
|
E''2*
|
2A''⊕3E''1⊕3E''2⊕E''3 |
E'1⊕2E'2⊕E'3 |
2A'⊕2E'1⊕2E'2⊕3E'3 |
4A'⊕2E'1⊕E'2⊕3E'3 |
|
E''3*
|
6A''⊕4E''1⊕E''2 |
E'2⊕3E'3 |
E'1⊕3E'2⊕4E'3 |
2A'⊕3E'1⊕3E'2⊕E'3 |
6A'⊕4E'1⊕E'2 |
E'3⊙A''⊙
⊙ |
A'' |
E''1*
|
E''2*
|
E''3*
|
A'' |
E''3 |
|
|
|
E''1*
|
E''2⊕E''3 |
E''1⊕E''2⊕2E''3 |
|
|
E''2*
|
E''1⊕E''2 |
2A''⊕E''1⊕E''2⊕E''3 |
2A''⊕E''1⊕2E''3 |
|
E''3*
|
2A''⊕E''1 |
2A''⊕2E''1⊕E''2 |
E''1⊕2E''2⊕E''3 |
E''2⊕3E''3 |
E'3⊙E''1⊙
⊙ |
E''1*
|
E''2*
|
E''3*
|
E''1*
|
2A''⊕E''1⊕3E''2⊕3E''3 |
|
|
E''2*
|
2A''⊕3E''1⊕2E''2⊕2E''3 |
2A''⊕2E''1⊕3E''2⊕2E''3 |
|
E''3*
|
4A''⊕3E''1⊕2E''2⊕E''3 |
2A''⊕2E''1⊕2E''2⊕3E''3 |
E''1⊕3E''2⊕4E''3 |
E'3⊙E''2⊙
⊙ |
E''2*
|
E''3*
|
E''2*
|
3E''1⊕4E''2⊕E''3 |
|
E''3*
|
4A''⊕2E''1⊕E''2⊕3E''3 |
2A''⊕3E''1⊕3E''2⊕E''3 |
E'3⊙E''3⊙
⊙ |
E''3*
|
E''3*
|
6A''⊕4E''1⊕E''2 |
A''⊙A''⊙
⊙ |
A'' |
E''1*
|
E''2*
|
E''3*
|
A'' |
A' |
|
|
|
E''1*
|
E'1 |
2A'⊕E'2 |
|
|
E''2*
|
E'2 |
E'1⊕E'3 |
2A'⊕E'3 |
|
E''3*
|
E'3 |
E'2⊕E'3 |
E'1⊕E'2 |
2A'⊕E'1 |
A''⊙E''1⊙
⊙ |
E''1*
|
E''2*
|
E''3*
|
E''1*
|
3E'1⊕E'3 |
|
|
E''2*
|
2A'⊕2E'2⊕E'3 |
2E'1⊕E'2⊕E'3 |
|
E''3*
|
E'1⊕E'2⊕2E'3 |
2A'⊕E'1⊕E'2⊕E'3 |
2A'⊕2E'1⊕E'2 |
A''⊙E''2⊙
⊙ |
E''2*
|
E''3*
|
E''2*
|
E'1⊕3E'2 |
|
E''3*
|
2A'⊕E'1⊕2E'3 |
E'1⊕2E'2⊕E'3 |
A''⊙E''3⊙
⊙ |
E''3*
|
E''3*
|
E'2⊕3E'3 |
E''1⊙E''1⊙
⊙ |
E''1*
|
E''2*
|
E''3*
|
E''1*
|
6A'⊕4E'2⊕E'3 |
|
|
E''2*
|
4E'1⊕E'2⊕3E'3 |
4A'⊕E'1⊕3E'2⊕2E'3 |
|
E''3*
|
2A'⊕E'1⊕3E'2⊕3E'3 |
2A'⊕3E'1⊕2E'2⊕2E'3 |
4A'⊕3E'1⊕2E'2⊕E'3 |
E''1⊙E''2⊙
⊙ |
E''2*
|
E''3*
|
E''2*
|
2A'⊕3E'1⊕E'2⊕3E'3 |
|
E''3*
|
2A'⊕2E'1⊕3E'2⊕2E'3 |
2A'⊕2E'1⊕2E'2⊕3E'3 |
E''1⊙E''3⊙
⊙ |
E''3*
|
E''3*
|
E'1⊕3E'2⊕4E'3 |
E''2⊙E''2⊙
⊙ |
E''2*
|
E''3*
|
E''2*
|
6A'⊕E'1⊕4E'3 |
|
E''3*
|
3E'1⊕4E'2⊕E'3 |
4A'⊕2E'1⊕E'2⊕3E'3 |
E''2⊙E''3⊙
⊙ |
E''3*
|
E''3*
|
2A'⊕3E'1⊕3E'2⊕E'3 |
E''3⊙E''3⊙
⊙ |
E''3*
|
E''3*
|
6A'⊕4E'1⊕E'2 |