GAP:NumberSmallGroups

Contents

INTERNAL AD: Don't have GAP but want to find the number of groups of a given order? Just type in "groups of order a" (where a is replaced by the order) and the total number of groups of the order is available as summary information near the beginning of the page, under "Statistics at a glance" -- see for instance groups of order 16

Definition

Function type

This function takes as input a positive integer and outputs a positive integer.

Behavior

Nature of input Output Example inputs and corresponding outputs
A positive integer for which there is information in GAP's SmallGroup library The number of groups of order equal to the input NumberSmallGroups(8) gives output 5
NumberSmallGroups(256) gives output 56092
A positive integer for which there is no information in GAP's SmallGroup library Message: The groups of size <size> are not available. NumberSmallGroups(1024)
NumberSmallGroups(6561)
Something other than a positive integer NoMethodFound error NumberSmallGroups(0)
NumberSmallGroups(-1)

Related functions

• GAP:SmallGroupsInformation gives more detailed information about the groups of a given order.
• GAP:AllSmallGroups constructs a list of all groups of a given order.
• GAP:SmallGroup constructs a group based on its GAP ID (order and a number specifying position among the groups of that order).
• GAP:IdGroup determines the GAP ID of a group.
• GAP:IdsOfAllSmallGroups returns a list [1 .. m] where $m$ is the number of small groups of the given order.