Visualization software for the abstract algebra classroom

Release 3.6.1 fixes bug in normalizer calculation

Group Library

All groups up to order 20 plus noteworthy groups of higher order

Visualization Options

Cayley diagrams, multiplication tables, cycle graphs, and other visualizations available


Create sheets to see relationships among groups, or have Group Explorer create them for you


Developed by Nathan Carter and Ray Ellis

Source code repository

Bug reports/feature requests

Citing Group Explorer 3.0


All those listed above, plus:


The textbook Visual Group Theory introduces the subject using almost exclusively visual means, and is a great companion to this software.


There is a 2005 article on the use of Group Explorer 1.5.8 in the classroom, but it has not been updated for the new version.