Final answer:
For a shipment of radioactive material that is not a limited quantity and also a flammable solid, the primary Hazard Class is Division 4.1 (C), which indicates its primary risk as a flammable solid during transport.
Step-by-step explanation:
The primary Hazard Class for a shipment of radioactive material that is not a limited quantity but is also a flammable solid would be determined by the predominant risk during transport. According to the regulations for the transport of dangerous goods, the material's primary hazard dictates its classification. Radioactive materials are typically classified under Class 7, while flammable solids are classified under Division 4.1. In cases where the material poses multiple hazards, one must reference the Hazardous Materials Table provided by the appropriate regulatory body, such as the US Department of Transportation (DOT) or international guidelines like the International Air Transport Association (IATA) Dangerous Goods Regulations, to determine the primary hazard class for transportation purposes.
Given that the radioactive material is not in limited quantity and the query states that the material is also a flammable solid, it appears that the flammability aspect of the material could represent the principal danger during transport. Therefore, the correct answer would be C. Division 4.1, which is for flammable solids. Rationalizing this choice, the primary hazard during transport is the risk of fire, which would likely be considered of higher priority over the radioactive aspect in this context.