HA (holomorph of an abelian group): These are the primitive groups which are subgroups of the affine general linear group AGL(d,p), for some prime p and positive integer d ≥ 1. For such a group G to be primitive, it must contain the subgroup of all translations, and the stabilizer G0 in G of the zero vector must be an irreducible subgroup of GL(d,p). Primitive groups of type HA are characterized by having a unique minimal normal subgroup which is elementary abelian and acts regularly.
