Quaternary direct products for Point Group D5d

Point Group D_5d

Quaternary direct products

**A_1g⊙A_1g⊙**
⊙	A_1g	A_2g	E_1g	E_2g	A_1u	A_2u	E_1u	E_2u
A_1g	A_1g
A_2g	A_2g	A_1g
E_1g	E_1g	E_1g	A_1g⊕A_2g⊕E_2g
E_2g	E_2g	E_2g	E_1g⊕E_2g	A_1g⊕A_2g⊕E_1g
A_1u	A_1u	A_2u	E_1u	E_2u	A_1g
A_2u	A_2u	A_1u	E_1u	E_2u	A_2g	A_1g
E_1u	E_1u	E_1u	A_1u⊕A_2u⊕E_2u	E_1u⊕E_2u	E_1g	E_1g	A_1g⊕A_2g⊕E_2g
E_2u	E_2u	E_2u	E_1u⊕E_2u	A_1u⊕A_2u⊕E_1u	E_2g	E_2g	E_1g⊕E_2g	A_1g⊕A_2g⊕E_1g

**A_1g⊙A_2g⊙**
⊙	A_2g	E_1g	E_2g	A_1u	A_2u	E_1u	E_2u
A_2g	A_2g
E_1g	E_1g	A_1g⊕A_2g⊕E_2g
E_2g	E_2g	E_1g⊕E_2g	A_1g⊕A_2g⊕E_1g
A_1u	A_1u	E_1u	E_2u	A_2g
A_2u	A_2u	E_1u	E_2u	A_1g	A_2g
E_1u	E_1u	A_1u⊕A_2u⊕E_2u	E_1u⊕E_2u	E_1g	E_1g	A_1g⊕A_2g⊕E_2g
E_2u	E_2u	E_1u⊕E_2u	A_1u⊕A_2u⊕E_1u	E_2g	E_2g	E_1g⊕E_2g	A_1g⊕A_2g⊕E_1g

**A_1g⊙E_1g⊙**
⊙	E_1g	E_2g	A_1u	A_2u	E_1u	E_2u
E_1g	3E_1g⊕E_2g
E_2g	A_1g⊕A_2g⊕E_1g⊕2E_2g	A_1g⊕A_2g⊕2E_1g⊕E_2g
A_1u	A_1u⊕A_2u⊕E_2u	E_1u⊕E_2u	E_1g
A_2u	A_1u⊕A_2u⊕E_2u	E_1u⊕E_2u	E_1g	E_1g
E_1u	3E_1u⊕E_2u	A_1u⊕A_2u⊕E_1u⊕2E_2u	A_1g⊕A_2g⊕E_2g	A_1g⊕A_2g⊕E_2g	3E_1g⊕E_2g
E_2u	A_1u⊕A_2u⊕E_1u⊕2E_2u	A_1u⊕A_2u⊕2E_1u⊕E_2u	E_1g⊕E_2g	E_1g⊕E_2g	A_1g⊕A_2g⊕E_1g⊕2E_2g	A_1g⊕A_2g⊕2E_1g⊕E_2g

**A_1g⊙E_2g⊙**
⊙	E_2g	A_1u	A_2u	E_1u	E_2u
E_2g	E_1g⊕3E_2g
A_1u	A_1u⊕A_2u⊕E_1u	E_2g
A_2u	A_1u⊕A_2u⊕E_1u	E_2g	E_2g
E_1u	A_1u⊕A_2u⊕2E_1u⊕E_2u	E_1g⊕E_2g	E_1g⊕E_2g	A_1g⊕A_2g⊕E_1g⊕2E_2g
E_2u	E_1u⊕3E_2u	A_1g⊕A_2g⊕E_1g	A_1g⊕A_2g⊕E_1g	A_1g⊕A_2g⊕2E_1g⊕E_2g	E_1g⊕3E_2g

**A_1g⊙A_1u⊙**
⊙	A_1u	A_2u	E_1u	E_2u
A_1u	A_1u
A_2u	A_2u	A_1u
E_1u	E_1u	E_1u	A_1u⊕A_2u⊕E_2u
E_2u	E_2u	E_2u	E_1u⊕E_2u	A_1u⊕A_2u⊕E_1u

**A_1g⊙A_2u⊙**
⊙	A_2u	E_1u	E_2u
A_2u	A_2u
E_1u	E_1u	A_1u⊕A_2u⊕E_2u
E_2u	E_2u	E_1u⊕E_2u	A_1u⊕A_2u⊕E_1u

**A_1g⊙E_1u⊙**
⊙	E_1u	E_2u
E_1u	3E_1u⊕E_2u
E_2u	A_1u⊕A_2u⊕E_1u⊕2E_2u	A_1u⊕A_2u⊕2E_1u⊕E_2u

**A_1g⊙E_2u⊙**
⊙	E_2u
E_2u	E_1u⊕3E_2u

**A_2g⊙A_2g⊙**
⊙	A_2g	E_1g	E_2g	A_1u	A_2u	E_1u	E_2u
A_2g	A_1g
E_1g	E_1g	A_1g⊕A_2g⊕E_2g
E_2g	E_2g	E_1g⊕E_2g	A_1g⊕A_2g⊕E_1g
A_1u	A_2u	E_1u	E_2u	A_1g
A_2u	A_1u	E_1u	E_2u	A_2g	A_1g
E_1u	E_1u	A_1u⊕A_2u⊕E_2u	E_1u⊕E_2u	E_1g	E_1g	A_1g⊕A_2g⊕E_2g
E_2u	E_2u	E_1u⊕E_2u	A_1u⊕A_2u⊕E_1u	E_2g	E_2g	E_1g⊕E_2g	A_1g⊕A_2g⊕E_1g

**A_2g⊙E_1g⊙**
⊙	E_1g	E_2g	A_1u	A_2u	E_1u	E_2u
E_1g	3E_1g⊕E_2g
E_2g	A_1g⊕A_2g⊕E_1g⊕2E_2g	A_1g⊕A_2g⊕2E_1g⊕E_2g
A_1u	A_1u⊕A_2u⊕E_2u	E_1u⊕E_2u	E_1g
A_2u	A_1u⊕A_2u⊕E_2u	E_1u⊕E_2u	E_1g	E_1g
E_1u	3E_1u⊕E_2u	A_1u⊕A_2u⊕E_1u⊕2E_2u	A_1g⊕A_2g⊕E_2g	A_1g⊕A_2g⊕E_2g	3E_1g⊕E_2g
E_2u	A_1u⊕A_2u⊕E_1u⊕2E_2u	A_1u⊕A_2u⊕2E_1u⊕E_2u	E_1g⊕E_2g	E_1g⊕E_2g	A_1g⊕A_2g⊕E_1g⊕2E_2g	A_1g⊕A_2g⊕2E_1g⊕E_2g

**A_2g⊙E_2g⊙**
⊙	E_2g	A_1u	A_2u	E_1u	E_2u
E_2g	E_1g⊕3E_2g
A_1u	A_1u⊕A_2u⊕E_1u	E_2g
A_2u	A_1u⊕A_2u⊕E_1u	E_2g	E_2g
E_1u	A_1u⊕A_2u⊕2E_1u⊕E_2u	E_1g⊕E_2g	E_1g⊕E_2g	A_1g⊕A_2g⊕E_1g⊕2E_2g
E_2u	E_1u⊕3E_2u	A_1g⊕A_2g⊕E_1g	A_1g⊕A_2g⊕E_1g	A_1g⊕A_2g⊕2E_1g⊕E_2g	E_1g⊕3E_2g

**A_2g⊙A_1u⊙**
⊙	A_1u	A_2u	E_1u	E_2u
A_1u	A_2u
A_2u	A_1u	A_2u
E_1u	E_1u	E_1u	A_1u⊕A_2u⊕E_2u
E_2u	E_2u	E_2u	E_1u⊕E_2u	A_1u⊕A_2u⊕E_1u

**A_2g⊙A_2u⊙**
⊙	A_2u	E_1u	E_2u
A_2u	A_1u
E_1u	E_1u	A_1u⊕A_2u⊕E_2u
E_2u	E_2u	E_1u⊕E_2u	A_1u⊕A_2u⊕E_1u

**A_2g⊙E_1u⊙**
⊙	E_1u	E_2u
E_1u	3E_1u⊕E_2u
E_2u	A_1u⊕A_2u⊕E_1u⊕2E_2u	A_1u⊕A_2u⊕2E_1u⊕E_2u

**A_2g⊙E_2u⊙**
⊙	E_2u
E_2u	E_1u⊕3E_2u

**E_1g⊙E_1g⊙**
⊙	E_1g	E_2g	A_1u	A_2u	E_1u	E_2u
E_1g	3A_1g⊕3A_2g⊕E_1g⊕4E_2g
E_2g	A_1g⊕A_2g⊕4E_1g⊕3E_2g	2A_1g⊕2A_2g⊕3E_1g⊕3E_2g
A_1u	3E_1u⊕E_2u	A_1u⊕A_2u⊕E_1u⊕2E_2u	A_1g⊕A_2g⊕E_2g
A_2u	3E_1u⊕E_2u	A_1u⊕A_2u⊕E_1u⊕2E_2u	A_1g⊕A_2g⊕E_2g	A_1g⊕A_2g⊕E_2g
E_1u	3A_1u⊕3A_2u⊕E_1u⊕4E_2u	A_1u⊕A_2u⊕4E_1u⊕3E_2u	3E_1g⊕E_2g	3E_1g⊕E_2g	3A_1g⊕3A_2g⊕E_1g⊕4E_2g
E_2u	A_1u⊕A_2u⊕4E_1u⊕3E_2u	2A_1u⊕2A_2u⊕3E_1u⊕3E_2u	A_1g⊕A_2g⊕E_1g⊕2E_2g	A_1g⊕A_2g⊕E_1g⊕2E_2g	A_1g⊕A_2g⊕4E_1g⊕3E_2g	2A_1g⊕2A_2g⊕3E_1g⊕3E_2g

**E_1g⊙E_2g⊙**
⊙	E_2g	A_1u	A_2u	E_1u	E_2u
E_2g	A_1g⊕A_2g⊕3E_1g⊕4E_2g
A_1u	A_1u⊕A_2u⊕2E_1u⊕E_2u	E_1g⊕E_2g
A_2u	A_1u⊕A_2u⊕2E_1u⊕E_2u	E_1g⊕E_2g	E_1g⊕E_2g
E_1u	2A_1u⊕2A_2u⊕3E_1u⊕3E_2u	A_1g⊕A_2g⊕E_1g⊕2E_2g	A_1g⊕A_2g⊕E_1g⊕2E_2g	A_1g⊕A_2g⊕4E_1g⊕3E_2g
E_2u	A_1u⊕A_2u⊕3E_1u⊕4E_2u	A_1g⊕A_2g⊕2E_1g⊕E_2g	A_1g⊕A_2g⊕2E_1g⊕E_2g	2A_1g⊕2A_2g⊕3E_1g⊕3E_2g	A_1g⊕A_2g⊕3E_1g⊕4E_2g

**E_1g⊙A_1u⊙**
⊙	A_1u	A_2u	E_1u	E_2u
A_1u	E_1u
A_2u	E_1u	E_1u
E_1u	A_1u⊕A_2u⊕E_2u	A_1u⊕A_2u⊕E_2u	3E_1u⊕E_2u
E_2u	E_1u⊕E_2u	E_1u⊕E_2u	A_1u⊕A_2u⊕E_1u⊕2E_2u	A_1u⊕A_2u⊕2E_1u⊕E_2u

**E_1g⊙A_2u⊙**
⊙	A_2u	E_1u	E_2u
A_2u	E_1u
E_1u	A_1u⊕A_2u⊕E_2u	3E_1u⊕E_2u
E_2u	E_1u⊕E_2u	A_1u⊕A_2u⊕E_1u⊕2E_2u	A_1u⊕A_2u⊕2E_1u⊕E_2u

**E_1g⊙E_1u⊙**
⊙	E_1u	E_2u
E_1u	3A_1u⊕3A_2u⊕E_1u⊕4E_2u
E_2u	A_1u⊕A_2u⊕4E_1u⊕3E_2u	2A_1u⊕2A_2u⊕3E_1u⊕3E_2u

**E_1g⊙E_2u⊙**
⊙	E_2u
E_2u	A_1u⊕A_2u⊕3E_1u⊕4E_2u

**E_2g⊙E_2g⊙**
⊙	E_2g	A_1u	A_2u	E_1u	E_2u
E_2g	3A_1g⊕3A_2g⊕4E_1g⊕E_2g
A_1u	E_1u⊕3E_2u	A_1g⊕A_2g⊕E_1g
A_2u	E_1u⊕3E_2u	A_1g⊕A_2g⊕E_1g	A_1g⊕A_2g⊕E_1g
E_1u	A_1u⊕A_2u⊕3E_1u⊕4E_2u	A_1g⊕A_2g⊕2E_1g⊕E_2g	A_1g⊕A_2g⊕2E_1g⊕E_2g	2A_1g⊕2A_2g⊕3E_1g⊕3E_2g
E_2u	3A_1u⊕3A_2u⊕4E_1u⊕E_2u	E_1g⊕3E_2g	E_1g⊕3E_2g	A_1g⊕A_2g⊕3E_1g⊕4E_2g	3A_1g⊕3A_2g⊕4E_1g⊕E_2g

**E_2g⊙A_1u⊙**
⊙	A_1u	A_2u	E_1u	E_2u
A_1u	E_2u
A_2u	E_2u	E_2u
E_1u	E_1u⊕E_2u	E_1u⊕E_2u	A_1u⊕A_2u⊕E_1u⊕2E_2u
E_2u	A_1u⊕A_2u⊕E_1u	A_1u⊕A_2u⊕E_1u	A_1u⊕A_2u⊕2E_1u⊕E_2u	E_1u⊕3E_2u

**E_2g⊙A_2u⊙**
⊙	A_2u	E_1u	E_2u
A_2u	E_2u
E_1u	E_1u⊕E_2u	A_1u⊕A_2u⊕E_1u⊕2E_2u
E_2u	A_1u⊕A_2u⊕E_1u	A_1u⊕A_2u⊕2E_1u⊕E_2u	E_1u⊕3E_2u

**E_2g⊙E_1u⊙**
⊙	E_1u	E_2u
E_1u	A_1u⊕A_2u⊕4E_1u⊕3E_2u
E_2u	2A_1u⊕2A_2u⊕3E_1u⊕3E_2u	A_1u⊕A_2u⊕3E_1u⊕4E_2u

**E_2g⊙E_2u⊙**
⊙	E_2u
E_2u	3A_1u⊕3A_2u⊕4E_1u⊕E_2u

**A_1u⊙A_1u⊙**
⊙	A_1u	A_2u	E_1u	E_2u
A_1u	A_1g
A_2u	A_2g	A_1g
E_1u	E_1g	E_1g	A_1g⊕A_2g⊕E_2g
E_2u	E_2g	E_2g	E_1g⊕E_2g	A_1g⊕A_2g⊕E_1g

**A_1u⊙A_2u⊙**
⊙	A_2u	E_1u	E_2u
A_2u	A_2g
E_1u	E_1g	A_1g⊕A_2g⊕E_2g
E_2u	E_2g	E_1g⊕E_2g	A_1g⊕A_2g⊕E_1g

**A_1u⊙E_1u⊙**
⊙	E_1u	E_2u
E_1u	3E_1g⊕E_2g
E_2u	A_1g⊕A_2g⊕E_1g⊕2E_2g	A_1g⊕A_2g⊕2E_1g⊕E_2g

**A_1u⊙E_2u⊙**
⊙	E_2u
E_2u	E_1g⊕3E_2g

**A_2u⊙A_2u⊙**
⊙	A_2u	E_1u	E_2u
A_2u	A_1g
E_1u	E_1g	A_1g⊕A_2g⊕E_2g
E_2u	E_2g	E_1g⊕E_2g	A_1g⊕A_2g⊕E_1g

**A_2u⊙E_1u⊙**
⊙	E_1u	E_2u
E_1u	3E_1g⊕E_2g
E_2u	A_1g⊕A_2g⊕E_1g⊕2E_2g	A_1g⊕A_2g⊕2E_1g⊕E_2g

**A_2u⊙E_2u⊙**
⊙	E_2u
E_2u	E_1g⊕3E_2g

**E_1u⊙E_1u⊙**
⊙	E_1u	E_2u
E_1u	3A_1g⊕3A_2g⊕E_1g⊕4E_2g
E_2u	A_1g⊕A_2g⊕4E_1g⊕3E_2g	2A_1g⊕2A_2g⊕3E_1g⊕3E_2g

**E_1u⊙E_2u⊙**
⊙	E_2u
E_2u	A_1g⊕A_2g⊕3E_1g⊕4E_2g

**E_2u⊙E_2u⊙**
⊙	E_2u
E_2u	3A_1g⊕3A_2g⊕4E_1g⊕E_2g