We determine the exact value of the η-constant and the multiwise Davenport constants for finite abelian groups of rank three having the form G ≃ C 2 ⊕ Cn 2 ⊕ Cn 3 with 2 | n 2 | n 3. Moreover, we determine the Erd˝ os– Ginzburg–Ziv constant of these groups under the assumption that n 2 /2 has Property D or n 2 = n 3 .