Groups of order 66
This article gives information about, and links to more details on, groups of order 66
See pages on algebraic structures of order 66 | See pages on groups of a particular order
Statistics at a glance
The number 66 has prime factors 2, 3, and 11. The prime factorization is:
One such way to classify groups of order 66 is therefore by the classification of groups of order 2pq.
Square-free implies solvability-forcing, so all groups of order 66 are finite solvable groups. Moreover, every Sylow subgroup is cyclic implies metacyclic, so all groups of order 66 are in fact metacyclic groups.
The list
There are 4 groups of order 66:
| Group | Second part of GAP ID | Abelian | Direct Product |
|---|---|---|---|
| direct product of dihedral group:D6 and cyclic group:Z11 | 1 | no | yes |
| direct product of dihedral group:D22 and cyclic group:Z3 | 2 | no | yes |
| dihedral group:D66 | 3 | no | no |
| cyclic group:Z66 | 4 | yes | yes |