= Solution
Every affine transformation factors as
$$
(A,b)=(I,b)(A,0),
$$
so $G=NH$. A translation fixing zero has zero translation vector, so $H\cap N=\{(I,0)\}$. Together with normality from part (c), these are the internal <semidirect product> conditions. Thus
$$
\boxed{G\cong(F^n,+)\rtimes\operatorname{GL}_n(F).}
$$
The reconstruction data are the additive <group> $F^n$, the linear <group> $\operatorname{GL}_n(F)$, and its standard action $A:c\mapsto Ac$ on translations. In pair notation $(b,A)$, the product is $(b,A)(d,C)=(b+Ad,AC)$, equivalent to the formula in part (b).
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