Cyclic group:Z40

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This group, denoted C_{40}, \mathbb{Z}_{40}, or \mathbb{Z}/40\mathbb{Z}, is defined in the following equivalent ways:

GAP implementation

Group ID

This finite group has order 40 and has ID 2 among the groups of order 40 in GAP's SmallGroup library. For context, there are groups of order 40. 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(40,2);

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

IdGroup(G) = [40,2]

or just do:


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

Other descriptions

Description Functions used
CyclicGroup(40) CyclicGroup
DirectProduct(CyclicGroup(8),CyclicGroup(5)) CyclicGroup, DirectProduct