Groups of order 35

This article gives information about, and links to more details on, groups of order 35
See pages on algebraic structures of order 35 | See pages on groups of a particular order

Up to isomorphism, there is a unique group of order $35$, namely cyclic group:Z35.

The fact of uniqueness follows from the classification of groups of order a product of two distinct primes. Since $35=5\cdot 7$ and $5$ does not divide $(7-1)$, the number $35$ falls in the one isomorphism class case.

Another way of viewing this is that $35$ is a cyclicity-forcing number, i.e., any group of order $35$ is cyclic. See the classification of cyclicity-forcing numbers to see the necessary and sufficient condition for a natural number to be cyclicity-forcing.