Conjugacy Class

Author

Eric W. Weisstein
January 31, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GroupTheory/ConjugacyClass.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/ConjugacyClass.html.

©2006 Wolfram Research, Inc. except for portions noted otherwise

(Subscript[D, 3])Example

letters=Prepend[CharacterRange["A","E"],"1"];
pg=DihedralGroup[3][[{1,5,4,6,2,3}]];
prules=Thread[pg->letters];

GroupMultiplicationTable[pg,prules]

Sort/@(ConjugacyClasses[pg]/.prules)

((GroupTimes[GroupInverse[#],"A",#]/.(Reverse/@prules))/.prules)&/@Rest[letters]

((GroupTimes[GroupInverse[#],"D",#]/.(Reverse/@prules))/.prules)&/@Rest[letters]