This article is about a GAP function.
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
This function takes as input a positive integer and outputs a positive integer.
|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)|
|Something other than a positive integer||NoMethodFound error|| NumberSmallGroups(0)|
- 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 is the number of small groups of the given order.