Quaternary direct products for Point Group D3d

Point Group D_3d

Quaternary direct products

**A_1g⊙A_1g⊙**
⊙	A_1g	A_2g	E_g	A_1u	A_2u	E_u
A_1g	A_1g
A_2g	A_2g	A_1g
E_g	E_g	E_g	A_1g⊕A_2g⊕E_g
A_1u	A_1u	A_2u	E_u	A_1g
A_2u	A_2u	A_1u	E_u	A_2g	A_1g
E_u	E_u	E_u	A_1u⊕A_2u⊕E_u	E_g	E_g	A_1g⊕A_2g⊕E_g

**A_1g⊙A_2g⊙**
⊙	A_2g	E_g	A_1u	A_2u	E_u
A_2g	A_2g
E_g	E_g	A_1g⊕A_2g⊕E_g
A_1u	A_1u	E_u	A_2g
A_2u	A_2u	E_u	A_1g	A_2g
E_u	E_u	A_1u⊕A_2u⊕E_u	E_g	E_g	A_1g⊕A_2g⊕E_g

**A_1g⊙E_g⊙**
⊙	E_g	A_1u	A_2u	E_u
E_g	A_1g⊕A_2g⊕3E_g
A_1u	A_1u⊕A_2u⊕E_u	E_g
A_2u	A_1u⊕A_2u⊕E_u	E_g	E_g
E_u	A_1u⊕A_2u⊕3E_u	A_1g⊕A_2g⊕E_g	A_1g⊕A_2g⊕E_g	A_1g⊕A_2g⊕3E_g

**A_1g⊙A_1u⊙**
⊙	A_1u	A_2u	E_u
A_1u	A_1u
A_2u	A_2u	A_1u
E_u	E_u	E_u	A_1u⊕A_2u⊕E_u

**A_1g⊙A_2u⊙**
⊙	A_2u	E_u
A_2u	A_2u
E_u	E_u	A_1u⊕A_2u⊕E_u

**A_1g⊙E_u⊙**
⊙	E_u
E_u	A_1u⊕A_2u⊕3E_u

**A_2g⊙A_2g⊙**
⊙	A_2g	E_g	A_1u	A_2u	E_u
A_2g	A_1g
E_g	E_g	A_1g⊕A_2g⊕E_g
A_1u	A_2u	E_u	A_1g
A_2u	A_1u	E_u	A_2g	A_1g
E_u	E_u	A_1u⊕A_2u⊕E_u	E_g	E_g	A_1g⊕A_2g⊕E_g

**A_2g⊙E_g⊙**
⊙	E_g	A_1u	A_2u	E_u
E_g	A_1g⊕A_2g⊕3E_g
A_1u	A_1u⊕A_2u⊕E_u	E_g
A_2u	A_1u⊕A_2u⊕E_u	E_g	E_g
E_u	A_1u⊕A_2u⊕3E_u	A_1g⊕A_2g⊕E_g	A_1g⊕A_2g⊕E_g	A_1g⊕A_2g⊕3E_g

**A_2g⊙A_1u⊙**
⊙	A_1u	A_2u	E_u
A_1u	A_2u
A_2u	A_1u	A_2u
E_u	E_u	E_u	A_1u⊕A_2u⊕E_u

**A_2g⊙A_2u⊙**
⊙	A_2u	E_u
A_2u	A_1u
E_u	E_u	A_1u⊕A_2u⊕E_u

**A_2g⊙E_u⊙**
⊙	E_u
E_u	A_1u⊕A_2u⊕3E_u

**E_g⊙E_g⊙**
⊙	E_g	A_1u	A_2u	E_u
E_g	3A_1g⊕3A_2g⊕5E_g
A_1u	A_1u⊕A_2u⊕3E_u	A_1g⊕A_2g⊕E_g
A_2u	A_1u⊕A_2u⊕3E_u	A_1g⊕A_2g⊕E_g	A_1g⊕A_2g⊕E_g
E_u	3A_1u⊕3A_2u⊕5E_u	A_1g⊕A_2g⊕3E_g	A_1g⊕A_2g⊕3E_g	3A_1g⊕3A_2g⊕5E_g

**E_g⊙A_1u⊙**
⊙	A_1u	A_2u	E_u
A_1u	E_u
A_2u	E_u	E_u
E_u	A_1u⊕A_2u⊕E_u	A_1u⊕A_2u⊕E_u	A_1u⊕A_2u⊕3E_u

**E_g⊙A_2u⊙**
⊙	A_2u	E_u
A_2u	E_u
E_u	A_1u⊕A_2u⊕E_u	A_1u⊕A_2u⊕3E_u

**E_g⊙E_u⊙**
⊙	E_u
E_u	3A_1u⊕3A_2u⊕5E_u

**A_1u⊙A_1u⊙**
⊙	A_1u	A_2u	E_u
A_1u	A_1g
A_2u	A_2g	A_1g
E_u	E_g	E_g	A_1g⊕A_2g⊕E_g

**A_1u⊙A_2u⊙**
⊙	A_2u	E_u
A_2u	A_2g
E_u	E_g	A_1g⊕A_2g⊕E_g

**A_1u⊙E_u⊙**
⊙	E_u
E_u	A_1g⊕A_2g⊕3E_g

**A_2u⊙A_2u⊙**
⊙	A_2u	E_u
A_2u	A_1g
E_u	E_g	A_1g⊕A_2g⊕E_g

**A_2u⊙E_u⊙**
⊙	E_u
E_u	A_1g⊕A_2g⊕3E_g

**E_u⊙E_u⊙**
⊙	E_u
E_u	3A_1g⊕3A_2g⊕5E_g