Groups of order 1536

Statistics at a glance
The number 1536 has prime factorization $$1536 = 3 \cdot 2^9$$. Because the order has only two distinct prime factors, and order has only two prime factors implies solvable, all groups of this order are solvable groups.

GAP implementation
gap> SmallGroupsInformation(1536);

There are 408641062 groups of order 1536. 1 - 10494213 are the nilpotent groups. 10494214 - 408526597 have a normal Sylow 3-subgroup. 408526598 - 408544625 have a normal Sylow 2-subgroup. 408544626 - 408641062 have no normal Sylow subgroup.

This size belongs to layer 8 of the SmallGroups library. IdSmallGroup is not available for this size.