GAP:SmallGroupsInformation
From Groupprops
This article is about a GAP function.
Definition
Function type
This function takes as input a nonnegative integer and outputs verbal information.
Behavior
| Nature of input | Output | Example inputs |
|---|---|---|
| A positive integer for which there is information in GAP's SmallGroup library | Verbal information on the number of groups of the order, as well as a partial description of what groups have what group IDs. | SmallGroupsInformation(8) SmallGroupsInformation(343) |
| A positive integer for which there is no information in GAP's SmallGroup library | Message: The groups of size <size> are not available. | SmallGroupsInformation(1024) SmallGroupsInformation(6561) |
Related functions
- GAP:NumberSmallGroups to return the number of groups of a given order, if the order is part of GAP's SmallGroup library.
- GAP:SmallGroup to construct a group with a given GAP ID (which includes both the order and a number specifying the position among the groups of that order). This is available for only those groups in the SmallGroup library.
- GAP:IdGroup to determine the GAP ID of a given group. This is available for groups in the SmallGroup library with the exception of some orders (512 and 1536, and some prime powers above 2000).
- GAP:AllSmallGroups to construct a list of all groups of a given order, appearing in the sequence of their GAP IDs.
- GAP:OneSmallGroup to pick out one group of a given order (the one with second part of GAP ID equal to 1).
