Automorphism group of alternating group:A6

From Groupprops
Revision as of 02:28, 2 November 2011 by Vipul (talk | contribs) (Created page with "{{particular group}} ==Definition== This group is defined in the following equivalent ways: # It is the automorphism group of alternating group:A6. # It is the [[autom...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
View a complete list of particular groups (this is a very huge list!)[SHOW MORE]

Definition

This group is defined in the following equivalent ways:

  1. It is the automorphism group of alternating group:A6.
  2. It is the automorphism group of symmetric group:S6.

GAP implementation

Group ID

This finite group has order 1440 and has ID 5841 among the groups of order 1440 in GAP's SmallGroup library. For context, there are 5,958 groups of order 1440. It can thus be defined using GAP's SmallGroup function as:

SmallGroup(1440,5841)

For instance, we can use the following assignment in GAP to create the group and name it G:

gap> G := SmallGroup(1440,5841);

Conversely, to check whether a given group G is in fact the group we want, we can use GAP's IdGroup function:

IdGroup(G) = [1440,5841]

or just do:

IdGroup(G)

to have GAP output the group ID, that we can then compare to what we want.


Other descriptions

Description Functions used
AutomorphismGroup(AlternatingGroup(6)) AutomorphismGroup, AlternatingGroup
AutomorphismGroup(SymmetricGroup(6)) AutomorphismGroup, SymmetricGroup