# SmallGroup(32,8)

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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
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## Definition

The group can be defined by means of the presentation (here, $1$ denotes the identity element): $\! G := \langle a,b,c \mid a^8 = b^2 = 1, c^2 = a^4, ab = ba^5, bc = cb, ac = cab^{-1} \rangle$

## 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 $G$:

gap> G := SmallGroup(32,8);

Conversely, to check whether a given group $G$ 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.