Groups of order 312

This article gives information about, and links to more details on, groups of order 312
See pages on algebraic structures of order 312 | See pages on groups of a particular order

Statistics at a glance

Factorization and useful forms

The number 312 has prime factors 2, 3, and 13, with prime factorization:

$312=2^3\cdot 3\cdot 13=8\cdot 3\cdot 13$

Group counts

Quantity	Value	List/comment
Total number of groups up to isomorphism	61
Number of abelian groups (i.e., finite abelian groups) up to isomorphism	3	(number of abelian groups of order $2^3$) times (number of abelian groups of order $3^1$) times (number of abelian groups of order $7^1$) = $3\times 1\times 1=3$. See classification of finite abelian groups and structure theorem for finitely generated abelian groups.