Direct product of Dic12 and Z2
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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
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 
:
gap> G := SmallGroup(24,7);
Conversely, to check whether a given group 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.
