SmallGroup(32,7)
From Groupprops
This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
View a complete list of particular groups (this is a very huge list!)[SHOW MORE]
Contents
Definition
PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]Position in classifications
Get more information about groups of the same order at Groups of order 32#The list
Type of classification | Position/number in classification |
---|---|
GAP ID | ![]() ![]() |
Hall-Senior number | 47 among groups of order 32 |
Hall-Senior symbol | ![]() |
Arithmetic functions
Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 32#Arithmetic functions
Group properties
Property | Satisfied? | Explanation | Comment |
---|---|---|---|
group of prime power order | Yes | ||
nilpotent group | Yes | prime power order implies nilpotent | |
supersolvable group | Yes | via nilpotent: finite nilpotent implies supersolvable | |
solvable group | Yes | via nilpotent: nilpotent implies solvable | |
abelian group | No |
GAP implementation
Group ID
This finite group has order 32 and has ID 7 among the groups of order 32 in GAP's SmallGroup library. For context, there are 51 groups of order 32. It can thus be defined using GAP's SmallGroup function as:
SmallGroup(32,7)
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(32,7);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [32,7]
or just do:
IdGroup(G)
to have GAP output the group ID, that we can then compare to what we want.