SmallGroup(32,8)
From Groupprops
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Definition
The group can be defined by means of the presentation (here, denotes the identity element):
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
GAP implementation
Group ID
This finite group has order 32 and has ID 8 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(32,8)
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(32,8);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [32,8]
or just do:
IdGroup(G)
to have GAP output the group ID, that we can then compare to what we want.