E = SmallGroup(32,28) is the first example. It has two central subgroups A1 and A2 isomorphic to A ≅ 2 with quotient isomorphic to SmallGroup(16,3), but A1 and A2 are not conjugate in Aut(E).
Examples such as this are reasonably common in p-groups.
E = SmallGroup(32,28) is the first example. It has two central subgroups A1 and A2 isomorphic to A ≅ 2 with quotient isomorphic to SmallGroup(16,3), but A1 and A2 are not conjugate in Aut(E).
Examples such as this are reasonably common in p-groups.