Parameters are accessed with C4DAtom::GetParameter()/ C4DAtom::SetParameter(). See Parameter IDs.
Parameter: Show Planes
SYMMETRYGENERATOR_DRAW
Parameter: Keep Hierarchy
SYMMETRYGENERATOR_KEEPHIERARCHY
Parameter: Weld Objects
SYMMETRYGENERATOR_WELD
Parameter: Type
SYMMETRYGENERATOR_TYPE
Parameter: X
SYMMETRYGENERATOR_PLANAR_AXIS_X
Parameter: Y
SYMMETRYGENERATOR_PLANAR_AXIS_Y
Parameter: Z
SYMMETRYGENERATOR_PLANAR_AXIS_Z
Parameter: Axis
SYMMETRYGENERATOR_RADIAL_AXIS
Parameter: Rotation Offset
SYMMETRYGENERATOR_RADIAL_ROTATIONOFFSET
Parameter: Slice Count
SYMMETRYGENERATOR_RADIAL_SLICECOUNT
Parameter: Mirror
SYMMETRYGENERATOR_RADIAL_MIRROR
Parameter: Source Slice
SYMMETRYGENERATOR_RADIAL_SOURCESLICE
Parameter: Cut Along Plane
SYMMETRYGENERATOR_CUTALONGPLANE
Parameter: Remove Outside
SYMMETRYGENERATOR_REMOVEOUTSIDE
Parameter: Tolerance
SYMMETRYGENERATOR_TOLERANCE
Parameter: Copy Settings to Hub
SYMMETRYGENERATOR_COPYTOHUB
Parameter: Copy Settings from Hub
SYMMETRYGENERATOR_COPYFROMHUB