Groups of order 312: Difference between revisions

Latest revision as of 21:16, 29 November 2023

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 $1 3^{1}$ ) = $3 \times 1 \times 1 = 3$ . See classification of finite abelian groups and structure theorem for finitely generated abelian groups.

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 | Total number of groups up to isomorphism|| [[count::61]] ||
 |-
-| Number of [[abelian group]]s (i.e., [[finite abelian group]]s) up to isomorphism|| {{abelian count|3}} || (number of abelian groups of order <math>2^3</math>) times (number of abelian groups of order <math>3^1</math>) times (number of abelian groups of order <math>7^1</math>) = <math>3 \times 1 \times 1 = 3</math>. {{abelian count explanation}}
+| Number of [[abelian group]]s (i.e., [[finite abelian group]]s) up to isomorphism|| {{abelian count|3}} || (number of abelian groups of order <math>2^3</math>) times (number of abelian groups of order <math>3^1</math>) times (number of abelian groups of order <math>13^1</math>) = <math>3 \times 1 \times 1 = 3</math>. {{abelian count explanation}}
 |}