The term 'Palindromic Band' refers to the Swedish pop group ABBA, which is a four-letter palindrome. ABBA was one of the most successful musical groups of the 1970s and early 1980s, selling over 380 million records worldwide. They are best known for their hit songs such as 'Dancing Queen', 'Mamma Mia', and 'Take a Chance on Me'. ABBA's music has been featured in films, television shows, and musicals, and their influence can still be heard in modern pop music.