Small groups

This interactive webpage allows you to investigate left and right cosets of subgroups in various small finite groups.

Select the group from the list. The Cayley table will appear on the left.
Select the subgroup from the list. Press `Show subgroup' to highlight the elements of the subgroup in the top row and leftmost column of the Cayley table.
To show a left coset, select the generator in the leftmost column.
To show a right coset, select the generator in the top row.
If you click on the button 'Show left cosets', respectively 'Show right cosets', the left, respectively right, cosets will be shown using different colours for the cosets. In addition the table will be reordered so that the coset elements are grouped together. This means that the shape of any factor group will be apparent.
A Cayley table of second group can be shown by choosing the group wanted from the list labelled second group and clicking on the button 'Show second group'. The elements of this group are coloured.