Groups of order 170
This article gives information about, and links to more details on, groups of order 170
See pages on algebraic structures of order 170 | See pages on groups of a particular order
Statistics at a glance
The number 170 has prime factors 2, 5, and 17. The prime factorization is:
One such way to classify groups of order 170 is therefore by the classification of groups of order 2pq.
Square-free implies solvability-forcing, so all groups of order 170 are finite solvable groups. Moreover, every Sylow subgroup is cyclic implies metacyclic, so all groups of order 170 are in fact metacyclic groups.
The list
There are 4 groups of order 170:
| Group | Second part of GAP ID | Abelian | Direct Product |
|---|---|---|---|
| direct product of dihedral group:D10 and cyclic group:Z17 | 1 | no | yes |
| direct product of dihedral group:D34 and cyclic group:Z5 | 2 | no | yes |
| dihedral group:D170 | 3 | no | no |
| cyclic group:Z170 | 4 | yes | yes |