# PGL(2,5) is isomorphic to S5

From Groupprops

This article gives a proof/explanation of the equivalence of multiple definitions for the term symmetric group:S5

View a complete list of pages giving proofs of equivalence of definitions

## Statement

The projective general linear group of degree two over field:F5, denoted , is isomorphic to symmetric group:S5.

## Related facts

### Similar facts

- PSL(2,5) is isomorphic to A5
- PGammaL(2,4) is isomorphic to S5
- PSL(2,4) is isomorphic to A5
- PGL(2,3) is isomorphic to S4
- PSL(2,3) is isomorphic to A4
- PSL(2,9) is isomorphic to A6

## Facts used

- PSL(2,5) is isomorphic to A5
- is the automorphism group of
- is the automorphism group of for any prime

## Proof

The proof follows directly by combining Facts (1)-(3).