Groups of order 102

From Groupprops

This article gives information about, and links to more details on, groups of order 102
See pages on algebraic structures of order 102 | See pages on groups of a particular order

Statistics at a glance

The number 102 has prime factors 2, 3, and 17. The prime factorization is:

One such way to classify groups of order 102 is therefore by the classification of groups of order 2pq.

Square-free implies solvability-forcing, so all groups of order 102 are finite solvable groups. Moreover, every Sylow subgroup is cyclic implies metacyclic, so all groups of order 102 are in fact metacyclic groups.

The list

There are 4 groups of order 102:

Group Second part of GAP ID Abelian Direct Product
direct product of dihedral group:D6 and cyclic group:Z16 1 no yes
direct product of dihedral group:D38 and cyclic group:Z3 2 no yes
dihedral group:D102 3 no no
cyclic group:Z102 4 yes yes