# Direct product of Dic12 and Z2

View a complete list of particular groups (this is a very huge list!)[SHOW MORE]

## Definition

This group is defined as the external direct product of the dicyclic group of order 12 and the cyclic group of order 2.

## Arithmetic functions

Function Value Similar groups Explanation for function value
order (number of elements, equivalently, cardinality or size of underlying set) 24 groups with same order
exponent of a group 12 groups with same order and exponent of a group | groups with same exponent of a group
Fitting length 2 groups with same order and Fitting length | groups with same Fitting length
Frattini length 2 groups with same order and Frattini length | groups with same Frattini length
derived length 2 groups with same order and derived length | groups with same derived length
minimum size of generating set 2 groups with same order and minimum size of generating set | groups with same minimum size of generating set

## GAP implementation

### Group ID

This finite group has order 24 and has ID 7 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(24,7)

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

gap> G := SmallGroup(24,7);

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

IdGroup(G) = [24,7]

or just do:

IdGroup(G)

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