This　paper　studies　the　continuous　time　scaled　group　consensus　problems　for　linear　time-invariant　multi-agent　systems　over　randomly　switching　topologies.　The　switching　is　controlled　by　a　time-homogeneous　Markov　process,　where　the　state　in　the　process　corresponds　to　a　possible　interaction　topology　among　agents.　It　is　proved　that　the　influence　of　switching　topology　on　scaled　group　consensus　is　determined　by　the　union　topology　related　to　state　in　the　Markov　process.　Using　algebra　theory,　graph　theory　and　Lyapunov　theory　as　tools,　sufficient　conditions　for　scaled　group　consensus　over　the　control　protocol　are　obtained.　Finally,　the　theoretical　results　are　verified　by　simulation　examples.　©　2022,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.