Which political party famously used the swastika symbol on its flag in the twentieth century?

Introduction / Context:
This question is from twentieth-century world history and politics. It asks about the infamous use of the swastika symbol on the flag of a political party that played a central role in the events leading to the Second World War and the Holocaust.

Given Data / Assumptions:
• The time period is the twentieth century. • The party is associated with Germany and Adolf Hitler. • The swastika, though an ancient symbol in many cultures, became strongly linked with this party's ideology in Europe.

Concept / Approach:
The National Socialist German Workers' Party, commonly known as the Nazi Party, adopted a red flag with a white circle and a black swastika as its emblem. This symbol became closely associated with Nazi ideology, racial policies and aggressive expansionism. Therefore, the correct answer identifies the Nazi Party as the political organisation that used the swastika on its flag.

Step-by-Step Solution:
Step 1: Recall that Adolf Hitler led the National Socialist Party in Germany. Step 2: Visualise the Nazi flag: red background, white disc, black swastika. Step 3: Compare the names of the political parties given in the options. Step 4: Identify the full name "National Socialist Party of Germany" as describing the Nazi Party. Step 5: Select this option as the correct answer.

Verification / Alternative check:
Historical photographs, films and textbooks all show the Nazi flag with the swastika symbol. No other major twentieth-century political party used the swastika in such a prominent and systematic way on national flags, banners and armbands. This confirms that the National Socialist Party of Germany is the accurate choice.

Why Other Options Are Wrong:
Option Communist Party of China: Uses the hammer and sickle symbol, not a swastika, on its flags and emblems. Option Republican Party of the United States of America: Uses an elephant symbol; it never adopted the swastika. Option Liberal Democratic Party of Japan: A mainstream political party in Japan with no swastika emblem. Option Indian National Congress: India's main freedom movement party, historically associated with the spinning wheel and later the tricolour, not the swastika as a party flag.

Common Pitfalls:
Students must clearly distinguish between the swastika as a sacred symbol in Indian and other Asian cultures and the tilted black swastika used by the Nazi Party in Germany. In exam questions about modern political history, the reference almost always points to the Nazi Party, not to traditional cultural uses of the symbol.

Final Answer:
Hence, the political party that famously used the swastika symbol on its flag in the twentieth century was the National Socialist Party of Germany (Nazi Party).