Cyclic group:Z36

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This group can be defined in the following equivalent ways:

  1. It is the cyclic group, and specifically finite cyclic group, of order 36.
  2. It is the external direct product of cyclic group:Z4 and cyclic group:Z9.

GAP implementation

Group ID

This finite group has order 36 and has ID 2 among the groups of order 36 in GAP's SmallGroup library. For context, there are groups of order 36. 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(36,2);

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

IdGroup(G) = [36,2]

or just do:


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

Other descriptions

Descriptions Functions used
CyclicGroup(36) CyclicGroup
DirectProduct(CyclicGroup(4),CyclicGroup(9)) DirectProduct, CyclicGroup