Groups of order 1152

This article gives information about, and links to more details on, groups of order 1152
See pages on algebraic structures of order 1152 | See pages on groups of a particular order

GAP implementation

The order 1152 is part of GAP's SmallGroup library. Hence, any group of order 1152 can be constructed using the SmallGroup function by specifying its group ID. Also, IdGroup is available, so the group ID of any group of this order can be queried.

Further, the collection of all groups of order 1152 can be accessed as a list using GAP's AllSmallGroups function.

Here is GAP's summary information about how it stores groups of this order, accessed using GAP's SmallGroupsInformation function:

gap> SmallGroupsInformation(1152);

  There are 157877 groups of order 1152.
  There are sorted using Sylow subgroups.
     1 - 2328 are nilpotent with Sylow 3-subgroup c9.
     2329 - 4656 are nilpotent with Sylow 3-subgroup 3^2.
     4657 - 153312 are non-nilpotent with normal Sylow 3-subgroup.
     153313 - 157877 have no normal Sylow 3-subgroup.

  This size belongs to layer 6 of the SmallGroups library.
  IdSmallGroup is available for this size.