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File:Symmetric group 4; Cayley table; numbers.svg

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Summary

Description
A submatrix containing all 24 elements

Cayley table of the symmetric group S4 showing all 24 permutations of 4 elements

There is also:
left action
last ⋅ first
This is:
right action
first ⋅ last

For left action (the usual way to compose functions) see: File:Symmetric group 4; Cayley table (left); numbers.svg

Even permutations are white:

Odd permutations are colored:

  • six transpositions (green)
  • six 4-cycles (orange)

Calculation of the matrix with Python: http://pastebin.com/BGkvfdgH

This SVG was created with Inkscape.
Date
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Author
Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".

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Date/TimeThumbnailDimensionsUserComment
current21:50, 10 May 2017Thumbnail for version as of 21:50, 10 May 2017744 × 744 (1.31 MB)Watchduckactive right matrices
11:08, 16 October 2014Thumbnail for version as of 11:08, 16 October 2014744 × 744 (1.32 MB)Wereldburger758Valid SVG now.
21:02, 2 March 2011Thumbnail for version as of 21:02, 2 March 2011744 × 744 (1.39 MB)Watchduckbackwards notation
16:01, 2 August 2010Thumbnail for version as of 16:01, 2 August 2010744 × 744 (1.7 MB)Watchduck{{Information |Description=Cayley table of the symmetric group S<sub>4</sub> All permutations of 4 elements, or the tetrahedron respectively |Source={{own}} |Date= |Author=[[User:Lipedia|Lipedia]

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