Let G be a group. The orbits of the natural action of \({{\,\mathrm{Aut}\,}}(G)\) on G are called automorphism orbits of G, and the number of automorphism orbits of G is denoted by \(\omega (G)\). Let G be a virtually nilpotent group such that \(\omega (G)< \infty \). We prove that \(G = K \rtimes H\) where H is a torsion subgroup and K is a torsion-free nilpotent radicable characteristic subgroup of G. Moreover, we prove that \(G^{'}= D \times {{\,\mathrm{Tor}\,}}(G^{'})\) where D is a torsion-free nilpotent radicable characteristic subgroup. In particular, if the maximum normal torsion subgroup \(\tau (G)\) of G is trivial, then \(G^{'}\) is nilpotent.

令G为一组。\（{{\，\ mathrm {Aut} \，}}（G）\）在G上的自然动作的轨道称为G的自同构轨道，而G的自同构轨道的数目由\（\ Ω（G）\）。令G是一个几乎为零的组，使得\（\ omega（G）<\ infty \）。我们证明\（G = K \ rtimes H \），其中H是G的扭转子群，K是G的无扭转幂等可辐照特征子群。此外，我们证明\（G ^ {'} = D \ times {{\，\ mathrm {Tor} \，}}（G ^ {'}）\）其中D是无扭转幂等可装配特征子组。特别地，如果最大正常挠子群\（\ tau蛋白（G）\）的ģ是微不足道的，然后\（G ^ {'} \）是幂零。