Quaternary direct products for Point Group I

Point Group I

Quaternary direct products

**A⊙A⊙**
⊙	A	T₁	T₂	G	H
A	A
T₁	T₁	A⊕T₁⊕H
T₂	T₂	G⊕H	A⊕T₂⊕H
G	G	T₂⊕G⊕H	T₁⊕G⊕H	A⊕T₁⊕T₂⊕G⊕H
H	H	T₁⊕T₂⊕G⊕H	T₁⊕T₂⊕G⊕H	T₁⊕T₂⊕G⊕2H	A⊕T₁⊕T₂⊕2G⊕2H

**A⊙T₁⊙**
⊙	T₁	T₂	G	H
T₁	A⊕3T₁⊕T₂⊕G⊕2H
T₂	T₁⊕2T₂⊕2G⊕2H	2T₁⊕T₂⊕2G⊕2H
G	T₁⊕2T₂⊕3G⊕3H	A⊕2T₁⊕2T₂⊕2G⊕3H	A⊕3T₁⊕2T₂⊕3G⊕4H
H	A⊕2T₁⊕2T₂⊕3G⊕4H	A⊕2T₁⊕2T₂⊕3G⊕4H	A⊕3T₁⊕3T₂⊕4G⊕5H	A⊕4T₁⊕4T₂⊕5G⊕6H

**A⊙T₂⊙**
⊙	T₂	G	H
T₂	A⊕T₁⊕3T₂⊕G⊕2H
G	2T₁⊕T₂⊕3G⊕3H	A⊕2T₁⊕3T₂⊕3G⊕4H
H	A⊕2T₁⊕2T₂⊕3G⊕4H	A⊕3T₁⊕3T₂⊕4G⊕5H	A⊕4T₁⊕4T₂⊕5G⊕6H

**A⊙G⊙**
⊙	G	H
G	A⊕3T₁⊕3T₂⊕5G⊕5H
H	A⊕4T₁⊕4T₂⊕5G⊕7H	2A⊕5T₁⊕5T₂⊕7G⊕8H

**A⊙H⊙**
⊙	H
H	2A⊕6T₁⊕6T₂⊕8G⊕11H

**T₁⊙T₁⊙**
⊙	T₁	T₂	G	H
T₁	3A⊕6T₁⊕3T₂⊕4G⊕7H
T₂	A⊕3T₁⊕4T₂⊕6G⊕7H	2A⊕4T₁⊕4T₂⊕5G⊕7H
G	A⊕4T₁⊕6T₂⊕8G⊕9H	2A⊕6T₁⊕5T₂⊕7G⊕9H	3A⊕8T₁⊕7T₂⊕9G⊕12H
H	2A⊕7T₁⊕7T₂⊕9G⊕11H	2A⊕7T₁⊕7T₂⊕9G⊕11H	3A⊕9T₁⊕9T₂⊕12G⊕15H	4A⊕11T₁⊕11T₂⊕15G⊕19H

**T₁⊙T₂⊙**
⊙	T₂	G	H
T₂	A⊕4T₁⊕3T₂⊕6G⊕7H
G	2A⊕5T₁⊕6T₂⊕7G⊕9H	2A⊕7T₁⊕7T₂⊕10G⊕12H
H	2A⊕7T₁⊕7T₂⊕9G⊕11H	3A⊕9T₁⊕9T₂⊕12G⊕15H	4A⊕11T₁⊕11T₂⊕15G⊕19H

**T₁⊙G⊙**
⊙	G	H
G	3A⊕9T₁⊕10T₂⊕13G⊕16H
H	4A⊕12T₁⊕12T₂⊕16G⊕20H	5A⊕15T₁⊕15T₂⊕20G⊕25H

**T₁⊙H⊙**
⊙	H
H	6A⊕19T₁⊕19T₂⊕25G⊕31H

**T₂⊙T₂⊙**
⊙	T₂	G	H
T₂	3A⊕3T₁⊕6T₂⊕4G⊕7H
G	A⊕6T₁⊕4T₂⊕8G⊕9H	3A⊕7T₁⊕8T₂⊕9G⊕12H
H	2A⊕7T₁⊕7T₂⊕9G⊕11H	3A⊕9T₁⊕9T₂⊕12G⊕15H	4A⊕11T₁⊕11T₂⊕15G⊕19H

**T₂⊙G⊙**
⊙	G	H
G	3A⊕10T₁⊕9T₂⊕13G⊕16H
H	4A⊕12T₁⊕12T₂⊕16G⊕20H	5A⊕15T₁⊕15T₂⊕20G⊕25H

**T₂⊙H⊙**
⊙	H
H	6A⊕19T₁⊕19T₂⊕25G⊕31H

**G⊙G⊙**
⊙	G	H
G	5A⊕13T₁⊕13T₂⊕17G⊕21H
H	5A⊕16T₁⊕16T₂⊕21G⊕27H	7A⊕20T₁⊕20T₂⊕27G⊕33H

**G⊙H⊙**
⊙	H
H	8A⊕25T₁⊕25T₂⊕33G⊕42H

**H⊙H⊙**
⊙	H
H	11A⊕31T₁⊕31T₂⊕42G⊕52H