Groups of order 42: Difference between revisions

Latest revision as of 23:00, 9 December 2023

This article gives information about, and links to more details on, groups of order 42
See pages on algebraic structures of order 42 | See pages on groups of a particular order

The list

There are, up to isomorphism, six groups of order 42, indicated in the table below:

Group	GAP ID (second part)	Abelian?
General affine group:GA(1,7), also known as F7	1	No
direct product of Z2 and the semidirect product of Z7 and Z3	2	No
direct product of S3 and Z7	3	No
direct product of D14 and Z3	4	No
dihedral group:D42	5	No
cyclic group:Z42	6	Yes

Minimal order attaining number

$42$ is the smallest number such that there are precisely $6$ groups of that order up to isomorphism. That is, the value of the minimal order attaining function at $6$ is $42$ .

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 {{groups of order|42}}
-There are 6 groups of order 42, namely the abelian group Z42, and the non-abelian groups D21, S3×Z7, Z2×Z7⋊Z3, D7×Z3, F7
+==The list==
+There are, up to isomorphism, six groups of order 42, indicated in the table below:
+{| class="sortable" border="1"
+! Group !! GAP ID (second part) !! Abelian?
+|-
+| [[General affine group:GA(1,7)|General affine group:GA(1,7), also known as F7]] || 1 || No
+|-
+| [[direct product of Z2 and the semidirect product of Z7 and Z3 ]] || 2 || No
+|-
+| [[direct product of S3 and Z7]] || 3 || No
+|-
+| [[direct product of D14 and Z3]] || 4 || No
+|-
+| [[dihedral group:D42]] || 5 || No
+|-
+| [[cyclic group:Z42]] || 6 || Yes
+|}
+==Minimal order attaining number==
+<math>42</math> is the smallest number such that there are precisely <math>6</math> groups of that order up to isomorphism. That is, the value of the [[minimal order attaining function]] at <math>6</math> is <math>42</math>.
+==See also==
+[[Classification of groups of order two times a product of two distinct odd primes]]