= Affine primitive permutation group
{title2=$G=\mathbb F_p^d\rtimes H,\quad H\le GL_d(p)\text{ irreducible}$}
An elementary abelian regular minimal normal subgroup acts as translations of a vector space. Its point stabilizer acts faithfully and irreducibly on that space; invariant subspaces would be blocks. The full affine normalizer is $AGL_d(p)$. In degree sixteen it lies inside $A_{16}$: nonzero translations swap eight pairs, and elementary linear transvections swap four pairs. Thus it is not a maximal subgroup of $S_{16}$.
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