# Dicyclic group:Dic24

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## Definition

This group is defined as the dicyclic group of order $24$ (hence, degree $6$). In other words, it has the presentation:

$\langle a,b,c \mid a^6 = b^2 = c^2 = abc \rangle$.

## Arithmetic functions

Function Value Explanation
order 24
exponent 12
derived length 2

## GAP implementation

### Group ID

This finite group has order 24 and has ID 4 among the groups of order 24 in GAP's SmallGroup library. For context, there are 15 groups of order 24. It can thus be defined using GAP's SmallGroup function as:

SmallGroup(24,4)

For instance, we can use the following assignment in GAP to create the group and name it $G$:

gap> G := SmallGroup(24,4);

Conversely, to check whether a given group $G$ is in fact the group we want, we can use GAP's IdGroup function:

IdGroup(G) = [24,4]

or just do:

IdGroup(G)

to have GAP output the group ID, that we can then compare to what we want.