In　social　network　applications,　individual　opinion　is　often　influenced　by　groups,　and　most　decisions　usually　reflect　the　majority＇s　opinions.　This　imposes　the　group　influence　maximization　(GIM)　problem　that　selects　$k$　initial　nodes,　where　each　node　belongs　to　multiple　groups　for　a　given　social　network　and　each　group　has　a　weight,　to　maximize　the　weight　of　the　eventually　activated　groups.　The　GIM　problem　is　apparently　NP-hard,　given　the　NP-hardness　of　the　influence　maximization　(IM)　problem　that　does　not　consider　groups.　Focusing　on　activating　groups　rather　than　individuals,　this　paper　proposes　the　complementary　maximum　coverage　(CMC)　algorithm,　which　greedily　and　iteratively　removes　the　node　with　the　approximate　least　group　influence　until　at　most　$k$　nodes　remain.　Although　the　evaluation　of　the　current　group　influence　against　each　node　is　only　approximate,　it　nevertheless　ensures　the　success　of　activating　an　approximate　maximum　number　of　groups.　Moreover,　we　also　propose　the　improved　reverse　influence　sampling　(IRIS)　algorithm　through　fine-tuning　of　the　renowned　reverse　influence　sampling　algorithm　for　GIM.　Finally,　we　carry　out　experiments　to　evaluate　CMC　and　IRIS,　demonstrating　that　they　both　outperform　the　baseline　algorithms　respective　of　their　average　number　of　activated　groups　under　the　independent　cascade　(IC)　model.