# Contents

## Idea

The Fano plane is the projective plane over the finite field $\mathbf{F}_2$ with two elements. It is denoted either $\mathbb{F}_2\mathbb{P}^2$, $\mathbb{P}^2_{\mathbb{F}_2}$ (in algebraic geometry), or $PG(2,2)$ (in finite geometry). It is often pictured as at right, but there are many different representations.

## Properties

### Automorphisms

The automorphism group $PGL(3,\mathbb{F}_2)$ is isomorphic to the projective special linear group $PSL(2,\mathbb{F}_7)$.

## References

Last revised on December 2, 2016 at 04:57:32. See the history of this page for a list of all contributions to it.