Groups of order 154

This article gives information about, and links to more details on, groups of order 154
See pages on algebraic structures of order 154 | See pages on groups of a particular order

Statistics at a glance

The number 154 has prime factors 2, 7, and 11. The prime factorization is:

$154=2^{1}\cdot 7^{1}\cdot 11^{1}$

One such way to classify groups of order 154 is therefore by the classification of groups of order 2pq.

Square-free implies solvability-forcing, so all groups of order 154 are finite solvable groups. Moreover, every Sylow subgroup is cyclic implies metacyclic, so all groups of order 154 are in fact metacyclic groups.

The list

There are 4 groups of order 154:

Group	Second part of GAP ID	Abelian	Direct Product
direct product of dihedral group:D14 and cyclic group:Z11	1	no	yes
direct product of dihedral group:D22 and cyclic group:Z7	2	no	yes
dihedral group:D154	3	no	no
cyclic group:Z154	4	yes	yes