GAP:NumberSmallGroups
From Groupprops
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
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 is the number of small groups of the given order.