Quaternary direct products for Point Group D4

Point Group D₄

Quaternary direct products

**A₁⊙A₁⊙**
⊙	A₁	A₂	B₁	B₂	E
A₁	A₁
A₂	A₂	A₁
B₁	B₁	B₂	A₁
B₂	B₂	B₁	A₂	A₁
E	E	E	E	E	A₁⊕A₂⊕B₁⊕B₂

**A₁⊙A₂⊙**
⊙	A₂	B₁	B₂	E
A₂	A₂
B₁	B₁	A₂
B₂	B₂	A₁	A₂
E	E	E	E	A₁⊕A₂⊕B₁⊕B₂

**A₁⊙B₁⊙**
⊙	B₁	B₂	E
B₁	B₁
B₂	B₂	B₁
E	E	E	A₁⊕A₂⊕B₁⊕B₂

**A₁⊙B₂⊙**
⊙	B₂	E
B₂	B₂
E	E	A₁⊕A₂⊕B₁⊕B₂

**A₁⊙E⊙**
⊙	E
E	4E

**A₂⊙A₂⊙**
⊙	A₂	B₁	B₂	E
A₂	A₁
B₁	B₂	A₁
B₂	B₁	A₂	A₁
E	E	E	E	A₁⊕A₂⊕B₁⊕B₂

**A₂⊙B₁⊙**
⊙	B₁	B₂	E
B₁	B₂
B₂	B₁	B₂
E	E	E	A₁⊕A₂⊕B₁⊕B₂

**A₂⊙B₂⊙**
⊙	B₂	E
B₂	B₁
E	E	A₁⊕A₂⊕B₁⊕B₂

**A₂⊙E⊙**
⊙	E
E	4E

**B₁⊙B₁⊙**
⊙	B₁	B₂	E
B₁	A₁
B₂	A₂	A₁
E	E	E	A₁⊕A₂⊕B₁⊕B₂

**B₁⊙B₂⊙**
⊙	B₂	E
B₂	A₂
E	E	A₁⊕A₂⊕B₁⊕B₂

**B₁⊙E⊙**
⊙	E
E	4E

**B₂⊙B₂⊙**
⊙	B₂	E
B₂	A₁
E	E	A₁⊕A₂⊕B₁⊕B₂

**B₂⊙E⊙**
⊙	E
E	4E

**E⊙E⊙**
⊙	E
E	4A₁⊕4A₂⊕4B₁⊕4B₂