Quotient groups, isomorphisms, kernels

Let G be the group { | a, b, c are in with p a prime}

Then let K = { | b in }

The map P: G --> x is defined by

P( ) = (a, c)

(A). Prove the quotient group G/K is isomorphic to x

(B). Find the orders |g|, |K|, and |G/K|

my thoughts -

(A) I've already shown that K is normal in G, and I know this would be true if K were the kernel of P, but I don't know how to show that.

(B), I'm not sure -- is it |G|= 3| |, |K|=| |, and |G/K| = 2| |?

Thank you so much for any help!