Groups of order 42

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 $42$.

See also

Classification of groups of order two times a product of two distinct odd primes