Prove/Disprove that $A_4\cong D_3×\mathbb Z_2$:
I can't seem to find a way to disprove it (Something in my mind it telling me it can't be true). But the order of both is 12, both are non cyclic, non abelian.
Can I simply say that the order of an element in $D_3$ is 3 and combined with $\mathbb Z_2$ it will have order 6, when in $A_4$ the maximum order of an element is 3?
2)Another Question:
Consider the set $H$:={$e,(24)(13),(14)(23),(34)(12)$ }
Is $H\cong \mathbb Z_4$? Prove it's normal in $S_4$
I don't know how to show/disprove isomorphism (I think it's false). It is normal because it's a union of conjugacy classes and the $geg^{-1}=e\in S_4$