PGL(2,5) is isomorphic to S5

Statement
The projective general linear group of degree two over field:F5, denoted $$PGL(2,5)$$, is isomorphic to symmetric group:S5.

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

 * 1) uses::PSL(2,5) is isomorphic to A5
 * 2) $$S_5$$ is the automorphism group of $$A_5$$
 * 3) $$PGL(2,p)$$ is the automorphism group of $$PSL(2,p)$$ for any prime $$p$$

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