Direct product of D8 and Z7

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This group is defined as the external direct product of dihedral group:D8 and cyclic group:Z7.

GAP implementation

Group ID

This finite group has order 56 and has ID 9 among the groups of order 56 in GAP's SmallGroup library. For context, there are 13 groups of order 56. 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(56,9);

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

IdGroup(G) = [56,9]

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(DihedralGroup(8),CyclicGroup(7)) DirectProduct, DihedralGroup, CyclicGroup