Some pages on groups.

- Cayley Diagrams
**Small Groups**giving Cayley diagrams for all groups with fewer than 32 elements:**on the plane**with the arcs crossing as necessary;**SVG**version of above which looks better, but renders more slowly, and does not work with older browsers**on the torus**;**SVG**version of above which looks better, but renders more slowly, and does not work with older browsers- on the plane but excluding direct products, and using orange triangles to denote central extensions.

- Platonic Solids giving Cayley diagrams drawn on symmetrical polyhedra
- Plane Tilings giving Cayley diagrams drawn on the Euclidean plane
- Infinite "Two-Ended" Groups giving Cayley diagrams for a very few infinite groups
- Double Cayley diagrams, showing groups and their automorphism groups in the same diagram:
- Cayley diagrams listed by the genus of the surface they are presented on:
- the sphere,
- the torus,
- the genus-2 surface,
- the genus-3 surface.

- the Pauli group
- PSL(2,7) ≅ GL(3,2)
- Some thoughts about Cayley diagrams

- group extensions, with
- Examples showing all 14 ways to build a group of order 8

- ways of building larger groups from small ones, with sub-pages
- Semi-direct products
- Toll-bean Extensions introducing the symbols and ↑
- Valid and Invalid Cayley Diagrams

- some groups acting on the colour cube: S4, S4 × C2, SO(3).
- miscellaneous short pages
- Puzzles
- Puzzle of the Day
- A puzzle involving permutations

Here are a few links to pages about groups.

**Index page for regular maps**
in surfaces of orientable genera 0, 1, 2, 3, 4; and non-orientable genera 1, 4, 5, 6.

Some old pages on regular maps on surfaces of various genus: