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).