How to Wrap the Points of a 3D Clustering Plot?

 Show[ListPointPlot3D[data1, PlotTheme -> "Business", 
  PlotStyle -> {AbsolutePointSize[3]}], 
 Table[{HighlightMesh[ConvexHullMesh[data1[[i]]], 
    Style[2, ColorData[97, i], Opacity[0.2]]]}, {i, 3}]]

Yu could use BoundingRegion with the "FastEllipsoid" as second argument:

Graphics3D[{
  Transpose[{
    ColorData[97] /@ Range[3],
    Point /@ data1
    }],
  Opacity[0.25],
  Transpose[{
    ColorData[97] /@ Range[3], 
    BoundingRegion[#, "FastEllipsoid"] & /@ data1
    }]
  },
 Lighting -> "Neutral"
 ]

See also the documenttion of BoundingRegion for further bounding shapes.