the United Kingdom
The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom or UK or Britain is a country located off the northwestern coast of Europe
the union jack
the Flag of the United Kingdom: red, white, and blue flag in which are combined the Crosses of St. George (England), St. Andrew (Scotland), and St. Patrick (Ireland). It was commonly called the Union Jack by the late 17th century, and that name became official in the late 19th century. The Union Jack is flown on land for government, at sea as a flag for the Royal Navy.
The Commonwealth of Nations, generally known as the Commonwealth, is a free association of 54 sovereign states, mostly former territories of the British Empire, who have chosen to maintain ties of friendship and practical cooperation and who acknowledge the British monarch as symbolic head of their association
the British Empire refers to a group of dependencies, colonies, protectorates, mandates and other territories that over three centuries was brought under the sovereignty of the crown of Great Britain and the administration of the British government.