Direct product of Z5 and GA(1,5)

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VIEW DEFINITIONS USING THIS AS EXAMPLE: All terms |Group properties |Subgroup properties|
VIEW FACTS USING THIS AS EXAMPLE: All facts |Group property non-implications |Subgroup property non-implications |Group metaproperty dissatisfactionsSubgroup metaproperty dissatisfactions

Definition

This group can be defined as the external direct product of the cyclic group:Z5 and the general affine group:GA(1,5).

GAP implementation

Group ID

This finite group has order 100 and has ID 9 among the groups of order 100 in GAP's SmallGroup library. For context, there are groups of order 100. It can thus be defined using GAP's SmallGroup function as:

SmallGroup(100,9)

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

gap> G := SmallGroup(100,9);

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

IdGroup(G) = [100,9]

or just do:

IdGroup(G)

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