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Direct product of S3 and Z4


Arithmetic functions

GAP implementation

Group ID

This finite group has order 24 and has ID 5 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:


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

gap> G := SmallGroup(24,5);

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

IdGroup(G) = [24,5]

or just do:


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

Short descriptions

Description Functions used Mathematical comments
DirectProduct(SymmetricGroup(3),CyclicGroup(4)) SymmetricGroup, CyclicGroup