Onto Homomorphism: G/H Isomorphic to K

[Punkyc7]

If G/H is \cong K show there exist an homomorphism which is ont λ:G \rightarrow K with the kernel of λ=HI am having a hard time figuring out what this should be. I have a feeling it is easy if you know how to look at it.

I have been trying the First Isomorphism Theorem but I can't seem to get.

Any help would e greatly appreciated.

 

[jbunniii]

You have an isomorphism \phi : G/H \rightarrow K. Can you find a surjective homomorphism \theta : G \rightarrow G/H which has ker \theta = H? What happens when you compose \theta with \phi?