GAP:SmallGroupsInformation

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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).