Finite Group Databasebeta

← Group #12256271

Character table — Group #12256271

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113
size1111222222222222222244444444444444444444444444444448888888888888888888888888888881616161616161616161616161616162020202020202020404040404040808080
order1222224455888810101010101024444881010101020202020202020202020202040404040404040402288101010101010101010102020202040404040404040404040404024410101010202020202020202016161616161616164416161616244
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111
χ511111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-11-1
χ611111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11
χ711111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-11-11
χ811111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-11-1
χ91111-1-1111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1111111111111111111-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11
χ101111-1-1111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1111111111111111111-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1
χ111111-1-1111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1
χ121111-1-1111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11
χ131111-1-111111111111111-11-1-11-1-1-1-1-1-11111-1-1-1-1111111111111111-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11-1-1
χ141111-1-111111111111111-11-1-11-1-1-1-1-1-11111-1-1-1-1111111111111111-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-111
χ151111-1-111111111111111-11-1-11-1-1-1-1-1-11111-1-1-1-1111111111111-1-11-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-111111-1-1-1-111111111-1-1-1-1-1-111-1-1-111
χ161111-1-111111111111111-11-1-11-1-1-1-1-1-11111-1-1-1-1111111111111-1-11-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-111111-1-1-1-11111-1-1-1-1111111-1-1111-1-1
χ172222222222-2-2-2-222222222222-2-22222222222222222-2-2-2-2-2-2-2-200-2-222000000002222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ182222222222-2-2-2-2222222-2-22-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20022-2-200000000-2-2222222-2-2-2-2222200000000000000000000000000000000
χ1922222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−522222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522222−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000000000
χ2022222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−522222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-222−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-21−521−521+521+521−521−521+521+521−521−521+521+5200000000000000000
χ2122222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−52-2-22-2-222−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222-2-21−521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+522-2-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+5200000000000000000
χ2222222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−52-2-22-2-222−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2-2-21−521+521−521−521−521−521+521+521+521+521−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52-2221−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000000000
χ2322222222−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−5222222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+5200-2-2−1+52−1−52ζ24−ζ56ζ24−ζ56−ζ24+ζ56−ζ24+ζ56−ζ8+ζ72−ζ8+ζ72ζ8−ζ72ζ8−ζ72−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+52000ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ7200000000000000000
χ2422222222−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−5222222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+5200-2-2−1+52−1−52−ζ24+ζ56−ζ24+ζ56ζ24−ζ56ζ24−ζ56ζ8−ζ72ζ8−ζ72−ζ8+ζ72−ζ8+ζ72−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+52000−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ7200000000000000000
χ2522222222−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52-2-22-2-2-2-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+5200221−521+52ζ24−ζ56ζ24−ζ56−ζ24+ζ56−ζ24+ζ56−ζ8+ζ72−ζ8+ζ72ζ8−ζ72ζ8−ζ721−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ7200000000000000000
χ2622222222−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52-2-22-2-2-2-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+5200221−521+52−ζ24+ζ56−ζ24+ζ56ζ24−ζ56ζ24−ζ56ζ8−ζ72ζ8−ζ72−ζ8+ζ72−ζ8+ζ721−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ7200000000000000000
χ2722222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+522222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522222−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000000000000
χ2822222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+522222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-222−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-21+521+521−521−521+521+521−521−521+521+521−521−5200000000000000000
χ2922222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+52-2-22-2-222−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5222-2-21+521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−522-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−5200000000000000000
χ3022222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+52-2-22-2-222−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-2-2-21+521−521+521+521+521+521−521−521−521−521+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52-2221+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000000000000
χ3122222222−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+5222222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−5200-2-2−1−52−1+52−ζ8+ζ72−ζ8+ζ72ζ8−ζ72ζ8−ζ72−ζ24+ζ56−ζ24+ζ56ζ24−ζ56ζ24−ζ56−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−52000−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ5600000000000000000
χ3222222222−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+5222222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−5200-2-2−1−52−1+52ζ8−ζ72ζ8−ζ72−ζ8+ζ72−ζ8+ζ72ζ24−ζ56ζ24−ζ56−ζ24+ζ56−ζ24+ζ56−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−52000ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ5600000000000000000
χ3322222222−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52-2-22-2-2-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−5200221+521−52−ζ8+ζ72−ζ8+ζ72ζ8−ζ72ζ8−ζ72−ζ24+ζ56−ζ24+ζ56ζ24−ζ56ζ24−ζ561+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52000−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ5600000000000000000
χ3422222222−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52-2-22-2-2-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−5200221+521−52ζ8−ζ72ζ8−ζ72−ζ8+ζ72−ζ8+ζ72ζ24−ζ56ζ24−ζ56−ζ24+ζ56−ζ24+ζ561+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52000ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ5600000000000000000
χ35222222-2-22200002222222-2-2-22002222-2-2-2-2-2-2-2-2-2-2-2-2000000000000220000000022-2-200000000000000000000000000022−2−222−2−2002−22−2000
χ36222222-2-22200002222222-2-2-22002222-2-2-2-2-2-2-2-2-2-2-2-2000000000000220000000022-2-2000000000000000000000000000−2−222−2−22200−22−22000
χ37222222-2-2220000222222-22-22-200222222222222-2-2-2-2000000000000-2-200000000-2-2-2-200000000000000000000000000022−2−222−2−200−22−22000
χ38222222-2-2220000222222-22-22-200222222222222-2-2-2-2000000000000-2-200000000-2-2-2-2000000000000000000000000000−2−222−2−222002−22−2000
χ392222-2-22222-2-2-2-22222222-2-22-222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2002-22200000000-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ402222-2-22222-2-2-2-2222222-22-2-2222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-200-22-2-20000000022-2-2-2-2-2-22222222200000000000000000000000000000000
χ412222-2-222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−522-2-22-2-2-21−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222-22−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521+521−521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52-2-221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−5200000000000000000
χ422222-2-222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−522-2-22-2-2-21−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2-22−1+52−1−521−521−521−521−521+521+521+521+521−521+521−521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−5222-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+5200000000000000000
χ432222-2-222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−52-22-2-22-2-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52222-21−521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52-22-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+5200000000000000000
χ442222-2-222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−52-22-2-22-2-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-22-21−521+521−521−521−521−521+521+521+521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+522-22−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200000000000000000
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Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.