Quaternary direct products for Point Group S10

Point Group S₁₀

Quaternary direct products

**A_g⊙A_g⊙**
⊙	A_g	E_1g*	E_2g*	A_u	E_1u*	E_2u*
A_g	A_g
E_1g*	E_1g	2A_g⊕E_2g
E_2g*	E_2g	E_1g⊕E_2g	2A_g⊕E_1g
A_u	A_u	E_1u	E_2u	A_g
E_1u*	E_1u	2A_u⊕E_2u	E_1u⊕E_2u	E_1g	2A_g⊕E_2g
E_2u*	E_2u	E_1u⊕E_2u	2A_u⊕E_1u	E_2g	E_1g⊕E_2g	2A_g⊕E_1g

**A_g⊙E_1g⊙**
⊙	E_1g*	E_2g*	A_u	E_1u*	E_2u*
E_1g*	3E_1g⊕E_2g
E_2g*	2A_g⊕E_1g⊕2E_2g	2A_g⊕2E_1g⊕E_2g
A_u	2A_u⊕E_2u	E_1u⊕E_2u	E_1g
E_1u*	3E_1u⊕E_2u	2A_u⊕E_1u⊕2E_2u	2A_g⊕E_2g	3E_1g⊕E_2g
E_2u*	2A_u⊕E_1u⊕2E_2u	2A_u⊕2E_1u⊕E_2u	E_1g⊕E_2g	2A_g⊕E_1g⊕2E_2g	2A_g⊕2E_1g⊕E_2g

**A_g⊙E_2g⊙**
⊙	E_2g*	A_u	E_1u*	E_2u*
E_2g*	E_1g⊕3E_2g
A_u	2A_u⊕E_1u	E_2g
E_1u*	2A_u⊕2E_1u⊕E_2u	E_1g⊕E_2g	2A_g⊕E_1g⊕2E_2g
E_2u*	E_1u⊕3E_2u	2A_g⊕E_1g	2A_g⊕2E_1g⊕E_2g	E_1g⊕3E_2g

**A_g⊙A_u⊙**
⊙	A_u	E_1u*	E_2u*
A_u	A_u
E_1u*	E_1u	2A_u⊕E_2u
E_2u*	E_2u	E_1u⊕E_2u	2A_u⊕E_1u

**A_g⊙E_1u⊙**
⊙	E_1u*	E_2u*
E_1u*	3E_1u⊕E_2u
E_2u*	2A_u⊕E_1u⊕2E_2u	2A_u⊕2E_1u⊕E_2u

**A_g⊙E_2u⊙**
⊙	E_2u*
E_2u*	E_1u⊕3E_2u

**E_1g⊙E_1g⊙**
⊙	E_1g*	E_2g*	A_u	E_1u*	E_2u*
E_1g*	6A_g⊕E_1g⊕4E_2g
E_2g*	2A_g⊕4E_1g⊕3E_2g	4A_g⊕3E_1g⊕3E_2g
A_u	3E_1u⊕E_2u	2A_u⊕E_1u⊕2E_2u	2A_g⊕E_2g
E_1u*	6A_u⊕E_1u⊕4E_2u	2A_u⊕4E_1u⊕3E_2u	3E_1g⊕E_2g	6A_g⊕E_1g⊕4E_2g
E_2u*	2A_u⊕4E_1u⊕3E_2u	4A_u⊕3E_1u⊕3E_2u	2A_g⊕E_1g⊕2E_2g	2A_g⊕4E_1g⊕3E_2g	4A_g⊕3E_1g⊕3E_2g

**E_1g⊙E_2g⊙**
⊙	E_2g*	A_u	E_1u*	E_2u*
E_2g*	2A_g⊕3E_1g⊕4E_2g
A_u	2A_u⊕2E_1u⊕E_2u	E_1g⊕E_2g
E_1u*	4A_u⊕3E_1u⊕3E_2u	2A_g⊕E_1g⊕2E_2g	2A_g⊕4E_1g⊕3E_2g
E_2u*	2A_u⊕3E_1u⊕4E_2u	2A_g⊕2E_1g⊕E_2g	4A_g⊕3E_1g⊕3E_2g	2A_g⊕3E_1g⊕4E_2g

**E_1g⊙A_u⊙**
⊙	A_u	E_1u*	E_2u*
A_u	E_1u
E_1u*	2A_u⊕E_2u	3E_1u⊕E_2u
E_2u*	E_1u⊕E_2u	2A_u⊕E_1u⊕2E_2u	2A_u⊕2E_1u⊕E_2u

**E_1g⊙E_1u⊙**
⊙	E_1u*	E_2u*
E_1u*	6A_u⊕E_1u⊕4E_2u
E_2u*	2A_u⊕4E_1u⊕3E_2u	4A_u⊕3E_1u⊕3E_2u

**E_1g⊙E_2u⊙**
⊙	E_2u*
E_2u*	2A_u⊕3E_1u⊕4E_2u

**E_2g⊙E_2g⊙**
⊙	E_2g*	A_u	E_1u*	E_2u*
E_2g*	6A_g⊕4E_1g⊕E_2g
A_u	E_1u⊕3E_2u	2A_g⊕E_1g
E_1u*	2A_u⊕3E_1u⊕4E_2u	2A_g⊕2E_1g⊕E_2g	4A_g⊕3E_1g⊕3E_2g
E_2u*	6A_u⊕4E_1u⊕E_2u	E_1g⊕3E_2g	2A_g⊕3E_1g⊕4E_2g	6A_g⊕4E_1g⊕E_2g

**E_2g⊙A_u⊙**
⊙	A_u	E_1u*	E_2u*
A_u	E_2u
E_1u*	E_1u⊕E_2u	2A_u⊕E_1u⊕2E_2u
E_2u*	2A_u⊕E_1u	2A_u⊕2E_1u⊕E_2u	E_1u⊕3E_2u

**E_2g⊙E_1u⊙**
⊙	E_1u*	E_2u*
E_1u*	2A_u⊕4E_1u⊕3E_2u
E_2u*	4A_u⊕3E_1u⊕3E_2u	2A_u⊕3E_1u⊕4E_2u

**E_2g⊙E_2u⊙**
⊙	E_2u*
E_2u*	6A_u⊕4E_1u⊕E_2u

**A_u⊙A_u⊙**
⊙	A_u	E_1u*	E_2u*
A_u	A_g
E_1u*	E_1g	2A_g⊕E_2g
E_2u*	E_2g	E_1g⊕E_2g	2A_g⊕E_1g

**A_u⊙E_1u⊙**
⊙	E_1u*	E_2u*
E_1u*	3E_1g⊕E_2g
E_2u*	2A_g⊕E_1g⊕2E_2g	2A_g⊕2E_1g⊕E_2g

**A_u⊙E_2u⊙**
⊙	E_2u*
E_2u*	E_1g⊕3E_2g

**E_1u⊙E_1u⊙**
⊙	E_1u*	E_2u*
E_1u*	6A_g⊕E_1g⊕4E_2g
E_2u*	2A_g⊕4E_1g⊕3E_2g	4A_g⊕3E_1g⊕3E_2g

**E_1u⊙E_2u⊙**
⊙	E_2u*
E_2u*	2A_g⊕3E_1g⊕4E_2g

**E_2u⊙E_2u⊙**
⊙	E_2u*
E_2u*	6A_g⊕4E_1g⊕E_2g