Groups of order 138

This article gives information about, and links to more details on, groups of order 138
See pages on algebraic structures of order 138 | See pages on groups of a particular order

Statistics at a glance

The number 138 has prime factors 2, 3, and 23. The prime factorization is:

$138=2^{1}\cdot 3^{1}\cdot 23^{1}$

One such way to classify groups of order 138 is therefore by the classification of groups of order 2pq.

Square-free implies solvability-forcing, so all groups of order 138 are finite solvable groups. Moreover, every Sylow subgroup is cyclic implies metacyclic, so all groups of order 138 are in fact metacyclic groups.

The list

There are 4 groups of order 138:

Group	Second part of GAP ID	Abelian	Direct Product
direct product of dihedral group:D6 and cyclic group:Z23	1	no	yes
direct product of dihedral group:D46 and cyclic group:Z3	2	no	yes
dihedral group:D138	3	no	no
cyclic group:Z138	4	yes	yes