Gallery of images generated by Group Explorer

Three views of A₅

The dodecahedron, whose group of symmetries is A5	A buckyball (soccerball) Cayley diagram with cosets of a cyclic subgroup of order 5 highlighted by color	A truncated dodecahedron Calyey diagram

 

Four views of S₄

A truncated cube Cayley diagram, with cosets of an order-3 subgroup highlighted by color	A truncated octahedron Cayley diagram	A rhombicuboctahedron Cayley diagram	A Cayely diagram made from three order-2 generators (one of the least symmetric Cayley diagrams to be found)

 

Highlighting and Reorganization

The tutorial pages on Editing Cayley Diagrams and Editing Multiplication Tables each have an example of reorganizing the view to exemplify normality of a subgroup.  The results of such techniques appear in the following two views of the normality of the Klein-4 group within A₄.  We recommend reading those tutorials to fully appreciate the following two pictures.

An organization of the Cayley diagram for the alternating group A4 that demonstrates the normality of the Klein-4 subgroup V4	An organization of the multiplication table for the alternating group A4 that demonstrates the normality of the Klein-4 subgroup V4

 

Other interesting images

Group element names appear as node labels in this cylindrical Cayley diagram of S3 x Z2	Group element names appear as node labels and cosets of the subgroup <f> highlighed by color in this Cayley diagram of S3	Cosets of the subgroup <r> are chunked together in this alternate organization of the Cayley diagram for S3	A normal Sylow 3-subgroup is highlighted in yellow in this rectangular solid Cayley diagram for S3 x Z3