Interactive explorations of finite group structure. Click a cell in the Cayley table to highlight the row and column that compose to it. Colours correspond to conjugacy classes.
The dihedral group D3 acts on an equilateral triangle by rotations and reflections. Click the buttons to apply transformations and watch the labelled vertices move.
Enter a permutation as a list of images. The diagram shows the cycle decomposition: elements on the same loop form one cycle.
Enter images: “2 3 1 4” means 1→2, 2→3, 3→1, 4→4