Groups of order 125
This article gives information about, and links to more details on, groups of order 125
See pages on algebraic structures of order 125| See pages on groups of a particular order
Statistics at a glance
To understand these in a broader context, see
groups of order 5^n|groups of prime-cube order
|Total number of groups||5||See classification of groups of prime-cube order|
|Number of abelian groups||3||Equals the number of unordered integer partitions of , which is the exponent term in . See classification of finite abelian groups and structure theorem for finitely generated abelian groups.|
|Number of groups of nilpotency class exactly two||2|
The order 125 is part of GAP's SmallGroup library. Hence, any group of order 125 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 125 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(125); There are 5 groups of order 125. 1 is of type c125. 2 is of type 5x25. 3 is of type 5^2:5. 4 is of type 25:5. 5 is of type 5^3. 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.