Let's assume that there exists simple non-Abelian group $G$ of order $120$. How can I show that $G$ is isomorphic to some subgroup of $A_6$?
[Math] Non-Abelian simple group of order $120$
finite-groupsgroup-theorysimple-groups
finite-groupsgroup-theorysimple-groups
Let's assume that there exists simple non-Abelian group $G$ of order $120$. How can I show that $G$ is isomorphic to some subgroup of $A_6$?
Best Answer
Hint: How many Sylow 5-subgroups will $G$ have? Do you know of a way $G$ acts on them?