Direct product of M16 and Z3

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This group is defined as the external direct product of the following two groups: M16 and cyclic group:Z3.

GAP implementation

Group ID

This finite group has order 48 and has ID 24 among the groups of order 48 in GAP's SmallGroup library. For context, there are groups of order 48. 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(48,24);

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

IdGroup(G) = [48,24]

or just do:


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

Other descriptions

Description Functions used
DirectProduct(SmallGroup(16,6),CyclicGroup(3)) DirectProduct, SmallGroup, CyclicGroup