# Non-Abelian group of Order 12

1. Dec 19, 2008

### nobody56

1. The problem statement, all variables and given/known data
Prove that Z/3 X|$$\alpha$$ Z/4 is a non-abelian group of order 12 which it is not isomorphic to A4 or to D6

X|]$$\alpha$$ is supposed to be the sign for semi direct product.

2. Relevant equations

Z/3 X|$$\alpha$$ Z/4=<a,b / a4=b3=1, aba=a>
A4=<a,b / a3=b2=1, aba=ba-1b>
D6=<a,b / a2=b2=1, bab-1=a-1>

3. The attempt at a solution

I am just having issues wrapping my head around Z/3 X|$$\alpha$$ Z/4, I read somewhere that Z/3 X|$$\alpha$$ Z/4 = {x,y / x$$\in$$Z/3 and y$$\in$$Z/4} with the operation (x1,y1)(x2,y2)=....and thats where I am stuck.