Parameters are accessed with C4DAtom::GetParameter()/ C4DAtom::SetParameter(). See Parameter IDs.
Parameter: Show Planes
SYMMETRYGENERATOR_DRAWParameter: Keep Hierarchy
SYMMETRYGENERATOR_KEEPHIERARCHYParameter: Weld Objects
SYMMETRYGENERATOR_WELDParameter: Type
SYMMETRYGENERATOR_TYPEParameter: X
SYMMETRYGENERATOR_PLANAR_AXIS_XParameter: Y
SYMMETRYGENERATOR_PLANAR_AXIS_YParameter: Z
SYMMETRYGENERATOR_PLANAR_AXIS_ZParameter: Axis
SYMMETRYGENERATOR_RADIAL_AXISParameter: Rotation Offset
SYMMETRYGENERATOR_RADIAL_ROTATIONOFFSETParameter: Slice Count
SYMMETRYGENERATOR_RADIAL_SLICECOUNTParameter: Mirror
SYMMETRYGENERATOR_RADIAL_MIRRORParameter: Source Slice
SYMMETRYGENERATOR_RADIAL_SOURCESLICEParameter: Cut Along Plane
SYMMETRYGENERATOR_CUTALONGPLANEParameter: Remove Outside
SYMMETRYGENERATOR_REMOVEOUTSIDEParameter: Tolerance
SYMMETRYGENERATOR_TOLERANCEParameter: Copy Settings to Hub
SYMMETRYGENERATOR_COPYTOHUBParameter: Copy Settings from Hub
SYMMETRYGENERATOR_COPYFROMHUB