Groups of order 30

Statistics at a glance
The number 30 has prime factors 2, 3, and 5. The prime factorization is:

$$30 = 2^1 \cdot 3^1 \cdot 5^1$$

Square-free implies solvability-forcing, so all groups of order 30 are finite solvable groups. Moreover, every Sylow subgroup is cyclic implies metacyclic, so all groups of order 30 are in fact metacyclic groups.

GAP implementation
gap> SmallGroupsInformation(30);

There are 4 groups of order 30. 1 is of type S3x5. 2 is of type D10x3. 3 - 3 are of types 3:2+5:2. 4 is of type c30.

The groups whose order factorises in at most 3 primes have been classified by O. Hoelder. This classification is used in the SmallGroups library.

This size belongs to layer 1 of the SmallGroups library. IdSmallGroup is available for this size.