a:grpSp (Group Shape)

<p:grpSp xmlns:p="http://schemas.openxmlformats.org/presentationml/2006/main" xmlns:a="http://schemas.openxmlformats.org/drawingml/2006/main">
  <p:nvGrpSpPr>
    <p:cNvPr id="1" name="Group 1"/>
    <p:cNvGrpSpPr/>
    <p:nvPr/>
  </p:nvGrpSpPr>
  <p:grpSpPr>
    <a:xfrm>
      <a:off x="1000000" y="1000000"/>
      <a:ext cx="5000000" cy="3000000"/>
      <a:chOff x="0" y="0"/>
      <a:chExt cx="5000000" cy="3000000"/>
    </a:xfrm>
  </p:grpSpPr>
  <p:sp>
    <p:nvSpPr>
      <p:cNvPr id="2" name="Rectangle"/>
      <p:cNvSpPr/>
      <p:nvPr/>
    </p:nvSpPr>
    <p:spPr>
      <a:xfrm>
        <a:off x="1000000" y="1000000"/>
        <a:ext cx="2000000" cy="1000000"/>
      </a:xfrm>
      <a:prstGeom prst="rect">
        <a:avLst/>
      </a:prstGeom>
      <a:solidFill>
        <a:srgbClr val="0070C0"/>
      </a:solidFill>
    </p:spPr>
    <p:txBody>
      <a:bodyPr/>
      <a:lstStyle/>
      <a:p/>
    </p:txBody>
  </p:sp>
</p:grpSp>

using DocumentFormat.OpenXml.Presentation;
using DocumentFormat.OpenXml.Drawing;

var grpSp = new GroupShape();

// Non-visual group properties
var nvGrpSpPr = new NonVisualGroupShapeProperties();
nvGrpSpPr.Append(new NonVisualDrawingProperties { Id = 1, Name = "Group 1" });
nvGrpSpPr.Append(new NonVisualGroupShapeDrawingProperties());
nvGrpSpPr.Append(new GroupShapeNonVisualProperties());
grpSp.Append(nvGrpSpPr);

// Group shape properties with transform
var grpSpPr = new GroupShapeProperties();
var xfrm = new Transform2D();
xfrm.Append(new Offset { X = 1000000, Y = 1000000 });
xfrm.Append(new Extents { Cx = 5000000, Cy = 3000000 });
xfrm.Append(new ChildOffset { X = 0, Y = 0 });
xfrm.Append(new ChildExtents { Cx = 5000000, Cy = 3000000 });
grpSpPr.Append(xfrm);
grpSp.Append(grpSpPr);

// Add shape to group
var sp = new Shape();
var nvSpPr = new NonVisualShapeProperties();
nvSpPr.Append(new NonVisualDrawingProperties { Id = 2, Name = "Rectangle" });
nvSpPr.Append(new NonVisualShapeDrawingProperties());
nvSpPr.Append(new ShapeNonVisualProperties());
sp.Append(nvSpPr);

var spPr = new ShapeProperties();
var spXfrm = new Transform2D();
spXfrm.Append(new Offset { X = 1000000, Y = 1000000 });
spXfrm.Append(new Extents { Cx = 2000000, Cy = 1000000 });
spPr.Append(spXfrm);

var prstGeom = new PresetGeometry { Preset = ShapeTypeValues.Rectangle };
prstGeom.Append(new AdjustmentValueList());
spPr.Append(prstGeom);

var fill = new SolidFill();
fill.Append(new RgbColorModelHex { Val = "0070C0" });
spPr.Append(fill);
sp.Append(spPr);

var txBody = new TextBody();
txBody.Append(new BodyProperties());
txBody.Append(new ListStyle());
txBody.Append(new Paragraph());
sp.Append(txBody);

grpSp.Append(sp);

<p:grpSp xmlns:p="http://schemas.openxmlformats.org/presentationml/2006/main" xmlns:a="http://schemas.openxmlformats.org/drawingml/2006/main">
  <p:nvGrpSpPr>
    <p:cNvPr id="1" name="Parent Group"/>
    <p:cNvGrpSpPr/>
    <p:nvPr/>
  </p:nvGrpSpPr>
  <p:grpSpPr>
    <a:xfrm>
      <a:off x="0" y="0"/>
      <a:ext cx="10000000" cy="6000000"/>
      <a:chOff x="0" y="0"/>
      <a:chExt cx="10000000" cy="6000000"/>
    </a:xfrm>
  </p:grpSpPr>
  <!-- Can contain nested groups and shapes -->
  <p:grpSp>
    <p:nvGrpSpPr>
      <p:cNvPr id="2" name="Child Group"/>
      <p:cNvGrpSpPr/>
      <p:nvPr/>
    </p:nvGrpSpPr>
    <p:grpSpPr>
      <a:xfrm>
        <a:off x="1000000" y="1000000"/>
        <a:ext cx="4000000" cy="4000000"/>
        <a:chOff x="0" y="0"/>
        <a:chExt cx="4000000" cy="4000000"/>
      </a:xfrm>
    </p:grpSpPr>
  </p:grpSp>
</p:grpSp>

// Create parent group
var parentGrp = new GroupShape();
var parentNvGrpSpPr = new NonVisualGroupShapeProperties();
parentNvGrpSpPr.Append(new NonVisualDrawingProperties { Id = 1, Name = "Parent Group" });
parentNvGrpSpPr.Append(new NonVisualGroupShapeDrawingProperties());
parentNvGrpSpPr.Append(new GroupShapeNonVisualProperties());
parentGrp.Append(parentNvGrpSpPr);

var parentGrpSpPr = new GroupShapeProperties();
var parentXfrm = new Transform2D();
parentXfrm.Append(new Offset { X = 0, Y = 0 });
parentXfrm.Append(new Extents { Cx = 10000000, Cy = 6000000 });
parentXfrm.Append(new ChildOffset { X = 0, Y = 0 });
parentXfrm.Append(new ChildExtents { Cx = 10000000, Cy = 6000000 });
parentGrpSpPr.Append(parentXfrm);
parentGrp.Append(parentGrpSpPr);

// Create nested child group
var childGrp = new GroupShape();
var childNvGrpSpPr = new NonVisualGroupShapeProperties();
childNvGrpSpPr.Append(new NonVisualDrawingProperties { Id = 2, Name = "Child Group" });
childNvGrpSpPr.Append(new NonVisualGroupShapeDrawingProperties());
childNvGrpSpPr.Append(new GroupShapeNonVisualProperties());
childGrp.Append(childNvGrpSpPr);

var childGrpSpPr = new GroupShapeProperties();
var childXfrm = new Transform2D();
childXfrm.Append(new Offset { X = 1000000, Y = 1000000 });
childXfrm.Append(new Extents { Cx = 4000000, Cy = 4000000 });
childXfrm.Append(new ChildOffset { X = 0, Y = 0 });
childXfrm.Append(new ChildExtents { Cx = 4000000, Cy = 4000000 });
childGrpSpPr.Append(childXfrm);
childGrp.Append(childGrpSpPr);

parentGrp.Append(childGrp);