Groups of order 75
This article gives information about, and links to more details on, groups of order 75
See pages on algebraic structures of order 75 | See pages on groups of a particular order
Statistics at a glance
75 has prime factorisation .
| Quantity | Value | Explanation |
|---|---|---|
| Total number of groups | 3 | |
| Number of abelian groups | 2 | equals the number of unordered integer partitions of 1 times the number of unordered integer partitions of 2. See classification of finite abelian groups and structure theorem for finitely generated abelian groups. |
The list
| Group | GAP ID (second part) | Abelian? |
|---|---|---|
| cyclic group:Z75 | 1 | Yes |
| semidirect product of (direct product of Z5 and Z5) and Z3 | 2 | No |
| direct product of Z5 and Z15 | 3 | Yes |
Minimal order attaining number
is the smallest number such that there are precisely groups of that order up to isomorphism. That is, the value of the minimal order attaining function at is .
