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**1. Homework Statement**

Prove that Z/3 X|

_{[tex]\alpha[/tex]}Z/4 is a non-abelian group of order 12 which it is not isomorphic to A

_{4}or to D

_{6}

X|

_{][tex]\alpha[/tex]}is supposed to be the sign for semi direct product.

**2. Homework Equations**

Z/3 X|

_{[tex]\alpha[/tex]}Z/4=<a,b / a

^{4}=b

^{3}=1, aba=a>

A

_{4}=<a,b / a

^{3}=b

^{2}=1, aba=ba

^{-1}b>

D

_{6}=<a,b / a

^{2}=b

^{2}=1, bab

^{-1}=a

^{-1}>

**3. The Attempt at a Solution**

I am just having issues wrapping my head around Z/3 X|

_{[tex]\alpha[/tex]}Z/4, I read somewhere that Z/3 X|

_{[tex]\alpha[/tex]}Z/4 = {x,y / x[tex]\in[/tex]Z/3 and y[tex]\in[/tex]Z/4} with the operation (x

_{1},y

_{1})(x

_{2},y

_{2})=....and thats where I am stuck.