Ternary direct products for Point Group D8h

Point Group D_8h

Ternary direct products

**A_1g⊙**
⊙	A_1g	A_2g	B_1g	B_2g	E_1g	E_2g	E_3g	A_1u	A_2u	B_1u	B_2u	E_1u	E_2u	E_3u
A_1g	A_1g
A_2g	A_2g	A_1g
B_1g	B_1g	B_2g	A_1g
B_2g	B_2g	B_1g	A_2g	A_1g
E_1g	E_1g	E_1g	E_3g	E_3g	A_1g⊕A_2g⊕E_2g
E_2g	E_2g	E_2g	E_2g	E_2g	E_1g⊕E_3g	A_1g⊕A_2g⊕B_1g⊕B_2g
E_3g	E_3g	E_3g	E_1g	E_1g	B_1g⊕B_2g⊕E_2g	E_1g⊕E_3g	A_1g⊕A_2g⊕E_2g
A_1u	A_1u	A_2u	B_1u	B_2u	E_1u	E_2u	E_3u	A_1g
A_2u	A_2u	A_1u	B_2u	B_1u	E_1u	E_2u	E_3u	A_2g	A_1g
B_1u	B_1u	B_2u	A_1u	A_2u	E_3u	E_2u	E_1u	B_1g	B_2g	A_1g
B_2u	B_2u	B_1u	A_2u	A_1u	E_3u	E_2u	E_1u	B_2g	B_1g	A_2g	A_1g
E_1u	E_1u	E_1u	E_3u	E_3u	A_1u⊕A_2u⊕E_2u	E_1u⊕E_3u	B_1u⊕B_2u⊕E_2u	E_1g	E_1g	E_3g	E_3g	A_1g⊕A_2g⊕E_2g
E_2u	E_2u	E_2u	E_2u	E_2u	E_1u⊕E_3u	A_1u⊕A_2u⊕B_1u⊕B_2u	E_1u⊕E_3u	E_2g	E_2g	E_2g	E_2g	E_1g⊕E_3g	A_1g⊕A_2g⊕B_1g⊕B_2g
E_3u	E_3u	E_3u	E_1u	E_1u	B_1u⊕B_2u⊕E_2u	E_1u⊕E_3u	A_1u⊕A_2u⊕E_2u	E_3g	E_3g	E_1g	E_1g	B_1g⊕B_2g⊕E_2g	E_1g⊕E_3g	A_1g⊕A_2g⊕E_2g

**A_2g⊙**
⊙	A_2g	B_1g	B_2g	E_1g	E_2g	E_3g	A_1u	A_2u	B_1u	B_2u	E_1u	E_2u	E_3u
A_2g	A_2g
B_1g	B_1g	A_2g
B_2g	B_2g	A_1g	A_2g
E_1g	E_1g	E_3g	E_3g	A_1g⊕A_2g⊕E_2g
E_2g	E_2g	E_2g	E_2g	E_1g⊕E_3g	A_1g⊕A_2g⊕B_1g⊕B_2g
E_3g	E_3g	E_1g	E_1g	B_1g⊕B_2g⊕E_2g	E_1g⊕E_3g	A_1g⊕A_2g⊕E_2g
A_1u	A_1u	B_2u	B_1u	E_1u	E_2u	E_3u	A_2g
A_2u	A_2u	B_1u	B_2u	E_1u	E_2u	E_3u	A_1g	A_2g
B_1u	B_1u	A_2u	A_1u	E_3u	E_2u	E_1u	B_2g	B_1g	A_2g
B_2u	B_2u	A_1u	A_2u	E_3u	E_2u	E_1u	B_1g	B_2g	A_1g	A_2g
E_1u	E_1u	E_3u	E_3u	A_1u⊕A_2u⊕E_2u	E_1u⊕E_3u	B_1u⊕B_2u⊕E_2u	E_1g	E_1g	E_3g	E_3g	A_1g⊕A_2g⊕E_2g
E_2u	E_2u	E_2u	E_2u	E_1u⊕E_3u	A_1u⊕A_2u⊕B_1u⊕B_2u	E_1u⊕E_3u	E_2g	E_2g	E_2g	E_2g	E_1g⊕E_3g	A_1g⊕A_2g⊕B_1g⊕B_2g
E_3u	E_3u	E_1u	E_1u	B_1u⊕B_2u⊕E_2u	E_1u⊕E_3u	A_1u⊕A_2u⊕E_2u	E_3g	E_3g	E_1g	E_1g	B_1g⊕B_2g⊕E_2g	E_1g⊕E_3g	A_1g⊕A_2g⊕E_2g

**B_1g⊙**
⊙	B_1g	B_2g	E_1g	E_2g	E_3g	A_1u	A_2u	B_1u	B_2u	E_1u	E_2u	E_3u
B_1g	B_1g
B_2g	B_2g	B_1g
E_1g	E_1g	E_1g	B_1g⊕B_2g⊕E_2g
E_2g	E_2g	E_2g	E_1g⊕E_3g	A_1g⊕A_2g⊕B_1g⊕B_2g
E_3g	E_3g	E_3g	A_1g⊕A_2g⊕E_2g	E_1g⊕E_3g	B_1g⊕B_2g⊕E_2g
A_1u	A_1u	A_2u	E_3u	E_2u	E_1u	B_1g
A_2u	A_2u	A_1u	E_3u	E_2u	E_1u	B_2g	B_1g
B_1u	B_1u	B_2u	E_1u	E_2u	E_3u	A_1g	A_2g	B_1g
B_2u	B_2u	B_1u	E_1u	E_2u	E_3u	A_2g	A_1g	B_2g	B_1g
E_1u	E_1u	E_1u	B_1u⊕B_2u⊕E_2u	E_1u⊕E_3u	A_1u⊕A_2u⊕E_2u	E_3g	E_3g	E_1g	E_1g	B_1g⊕B_2g⊕E_2g
E_2u	E_2u	E_2u	E_1u⊕E_3u	A_1u⊕A_2u⊕B_1u⊕B_2u	E_1u⊕E_3u	E_2g	E_2g	E_2g	E_2g	E_1g⊕E_3g	A_1g⊕A_2g⊕B_1g⊕B_2g
E_3u	E_3u	E_3u	A_1u⊕A_2u⊕E_2u	E_1u⊕E_3u	B_1u⊕B_2u⊕E_2u	E_1g	E_1g	E_3g	E_3g	A_1g⊕A_2g⊕E_2g	E_1g⊕E_3g	B_1g⊕B_2g⊕E_2g

**B_2g⊙**
⊙	B_2g	E_1g	E_2g	E_3g	A_1u	A_2u	B_1u	B_2u	E_1u	E_2u	E_3u
B_2g	B_2g
E_1g	E_1g	B_1g⊕B_2g⊕E_2g
E_2g	E_2g	E_1g⊕E_3g	A_1g⊕A_2g⊕B_1g⊕B_2g
E_3g	E_3g	A_1g⊕A_2g⊕E_2g	E_1g⊕E_3g	B_1g⊕B_2g⊕E_2g
A_1u	A_1u	E_3u	E_2u	E_1u	B_2g
A_2u	A_2u	E_3u	E_2u	E_1u	B_1g	B_2g
B_1u	B_1u	E_1u	E_2u	E_3u	A_2g	A_1g	B_2g
B_2u	B_2u	E_1u	E_2u	E_3u	A_1g	A_2g	B_1g	B_2g
E_1u	E_1u	B_1u⊕B_2u⊕E_2u	E_1u⊕E_3u	A_1u⊕A_2u⊕E_2u	E_3g	E_3g	E_1g	E_1g	B_1g⊕B_2g⊕E_2g
E_2u	E_2u	E_1u⊕E_3u	A_1u⊕A_2u⊕B_1u⊕B_2u	E_1u⊕E_3u	E_2g	E_2g	E_2g	E_2g	E_1g⊕E_3g	A_1g⊕A_2g⊕B_1g⊕B_2g
E_3u	E_3u	A_1u⊕A_2u⊕E_2u	E_1u⊕E_3u	B_1u⊕B_2u⊕E_2u	E_1g	E_1g	E_3g	E_3g	A_1g⊕A_2g⊕E_2g	E_1g⊕E_3g	B_1g⊕B_2g⊕E_2g

**E_1g⊙**
⊙	E_1g	E_2g	E_3g	A_1u	A_2u	B_1u	B_2u	E_1u	E_2u	E_3u
E_1g	3E_1g⊕E_3g
E_2g	A_1g⊕A_2g⊕B_1g⊕B_2g⊕2E_2g	2E_1g⊕2E_3g
E_3g	E_1g⊕3E_3g	A_1g⊕A_2g⊕B_1g⊕B_2g⊕2E_2g	3E_1g⊕E_3g
A_1u	A_1u⊕A_2u⊕E_2u	E_1u⊕E_3u	B_1u⊕B_2u⊕E_2u	E_1g
A_2u	A_1u⊕A_2u⊕E_2u	E_1u⊕E_3u	B_1u⊕B_2u⊕E_2u	E_1g	E_1g
B_1u	B_1u⊕B_2u⊕E_2u	E_1u⊕E_3u	A_1u⊕A_2u⊕E_2u	E_3g	E_3g	E_1g
B_2u	B_1u⊕B_2u⊕E_2u	E_1u⊕E_3u	A_1u⊕A_2u⊕E_2u	E_3g	E_3g	E_1g	E_1g
E_1u	3E_1u⊕E_3u	A_1u⊕A_2u⊕B_1u⊕B_2u⊕2E_2u	E_1u⊕3E_3u	A_1g⊕A_2g⊕E_2g	A_1g⊕A_2g⊕E_2g	B_1g⊕B_2g⊕E_2g	B_1g⊕B_2g⊕E_2g	3E_1g⊕E_3g
E_2u	A_1u⊕A_2u⊕B_1u⊕B_2u⊕2E_2u	2E_1u⊕2E_3u	A_1u⊕A_2u⊕B_1u⊕B_2u⊕2E_2u	E_1g⊕E_3g	E_1g⊕E_3g	E_1g⊕E_3g	E_1g⊕E_3g	A_1g⊕A_2g⊕B_1g⊕B_2g⊕2E_2g	2E_1g⊕2E_3g
E_3u	E_1u⊕3E_3u	A_1u⊕A_2u⊕B_1u⊕B_2u⊕2E_2u	3E_1u⊕E_3u	B_1g⊕B_2g⊕E_2g	B_1g⊕B_2g⊕E_2g	A_1g⊕A_2g⊕E_2g	A_1g⊕A_2g⊕E_2g	E_1g⊕3E_3g	A_1g⊕A_2g⊕B_1g⊕B_2g⊕2E_2g	3E_1g⊕E_3g

**E_2g⊙**
⊙	E_2g	E_3g	A_1u	A_2u	B_1u	B_2u	E_1u	E_2u	E_3u
E_2g	4E_2g
E_3g	2E_1g⊕2E_3g	A_1g⊕A_2g⊕B_1g⊕B_2g⊕2E_2g
A_1u	A_1u⊕A_2u⊕B_1u⊕B_2u	E_1u⊕E_3u	E_2g
A_2u	A_1u⊕A_2u⊕B_1u⊕B_2u	E_1u⊕E_3u	E_2g	E_2g
B_1u	A_1u⊕A_2u⊕B_1u⊕B_2u	E_1u⊕E_3u	E_2g	E_2g	E_2g
B_2u	A_1u⊕A_2u⊕B_1u⊕B_2u	E_1u⊕E_3u	E_2g	E_2g	E_2g	E_2g
E_1u	2E_1u⊕2E_3u	A_1u⊕A_2u⊕B_1u⊕B_2u⊕2E_2u	E_1g⊕E_3g	E_1g⊕E_3g	E_1g⊕E_3g	E_1g⊕E_3g	A_1g⊕A_2g⊕B_1g⊕B_2g⊕2E_2g
E_2u	4E_2u	2E_1u⊕2E_3u	A_1g⊕A_2g⊕B_1g⊕B_2g	A_1g⊕A_2g⊕B_1g⊕B_2g	A_1g⊕A_2g⊕B_1g⊕B_2g	A_1g⊕A_2g⊕B_1g⊕B_2g	2E_1g⊕2E_3g	4E_2g
E_3u	2E_1u⊕2E_3u	A_1u⊕A_2u⊕B_1u⊕B_2u⊕2E_2u	E_1g⊕E_3g	E_1g⊕E_3g	E_1g⊕E_3g	E_1g⊕E_3g	A_1g⊕A_2g⊕B_1g⊕B_2g⊕2E_2g	2E_1g⊕2E_3g	A_1g⊕A_2g⊕B_1g⊕B_2g⊕2E_2g

**E_3g⊙**
⊙	E_3g	A_1u	A_2u	B_1u	B_2u	E_1u	E_2u	E_3u
E_3g	E_1g⊕3E_3g
A_1u	A_1u⊕A_2u⊕E_2u	E_3g
A_2u	A_1u⊕A_2u⊕E_2u	E_3g	E_3g
B_1u	B_1u⊕B_2u⊕E_2u	E_1g	E_1g	E_3g
B_2u	B_1u⊕B_2u⊕E_2u	E_1g	E_1g	E_3g	E_3g
E_1u	3E_1u⊕E_3u	B_1g⊕B_2g⊕E_2g	B_1g⊕B_2g⊕E_2g	A_1g⊕A_2g⊕E_2g	A_1g⊕A_2g⊕E_2g	E_1g⊕3E_3g
E_2u	A_1u⊕A_2u⊕B_1u⊕B_2u⊕2E_2u	E_1g⊕E_3g	E_1g⊕E_3g	E_1g⊕E_3g	E_1g⊕E_3g	A_1g⊕A_2g⊕B_1g⊕B_2g⊕2E_2g	2E_1g⊕2E_3g
E_3u	E_1u⊕3E_3u	A_1g⊕A_2g⊕E_2g	A_1g⊕A_2g⊕E_2g	B_1g⊕B_2g⊕E_2g	B_1g⊕B_2g⊕E_2g	3E_1g⊕E_3g	A_1g⊕A_2g⊕B_1g⊕B_2g⊕2E_2g	E_1g⊕3E_3g

**A_1u⊙**
⊙	A_1u	A_2u	B_1u	B_2u	E_1u	E_2u	E_3u
A_1u	A_1u
A_2u	A_2u	A_1u
B_1u	B_1u	B_2u	A_1u
B_2u	B_2u	B_1u	A_2u	A_1u
E_1u	E_1u	E_1u	E_3u	E_3u	A_1u⊕A_2u⊕E_2u
E_2u	E_2u	E_2u	E_2u	E_2u	E_1u⊕E_3u	A_1u⊕A_2u⊕B_1u⊕B_2u
E_3u	E_3u	E_3u	E_1u	E_1u	B_1u⊕B_2u⊕E_2u	E_1u⊕E_3u	A_1u⊕A_2u⊕E_2u

**A_2u⊙**
⊙	A_2u	B_1u	B_2u	E_1u	E_2u	E_3u
A_2u	A_2u
B_1u	B_1u	A_2u
B_2u	B_2u	A_1u	A_2u
E_1u	E_1u	E_3u	E_3u	A_1u⊕A_2u⊕E_2u
E_2u	E_2u	E_2u	E_2u	E_1u⊕E_3u	A_1u⊕A_2u⊕B_1u⊕B_2u
E_3u	E_3u	E_1u	E_1u	B_1u⊕B_2u⊕E_2u	E_1u⊕E_3u	A_1u⊕A_2u⊕E_2u

**B_1u⊙**
⊙	B_1u	B_2u	E_1u	E_2u	E_3u
B_1u	B_1u
B_2u	B_2u	B_1u
E_1u	E_1u	E_1u	B_1u⊕B_2u⊕E_2u
E_2u	E_2u	E_2u	E_1u⊕E_3u	A_1u⊕A_2u⊕B_1u⊕B_2u
E_3u	E_3u	E_3u	A_1u⊕A_2u⊕E_2u	E_1u⊕E_3u	B_1u⊕B_2u⊕E_2u

**B_2u⊙**
⊙	B_2u	E_1u	E_2u	E_3u
B_2u	B_2u
E_1u	E_1u	B_1u⊕B_2u⊕E_2u
E_2u	E_2u	E_1u⊕E_3u	A_1u⊕A_2u⊕B_1u⊕B_2u
E_3u	E_3u	A_1u⊕A_2u⊕E_2u	E_1u⊕E_3u	B_1u⊕B_2u⊕E_2u

**E_1u⊙**
⊙	E_1u	E_2u	E_3u
E_1u	3E_1u⊕E_3u
E_2u	A_1u⊕A_2u⊕B_1u⊕B_2u⊕2E_2u	2E_1u⊕2E_3u
E_3u	E_1u⊕3E_3u	A_1u⊕A_2u⊕B_1u⊕B_2u⊕2E_2u	3E_1u⊕E_3u

**E_2u⊙**
⊙	E_2u	E_3u
E_2u	4E_2u
E_3u	2E_1u⊕2E_3u	A_1u⊕A_2u⊕B_1u⊕B_2u⊕2E_2u

**E_3u⊙**
⊙	E_3u
E_3u	E_1u⊕3E_3u