Finite Group Databasebeta

← Group #13031934

Character table — Group #13031934

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222244444444444445555555555558888881010101010101010101010101616161616161616162020202020202020202020202020202020202020202020202020203232404040404040
order12224444444445888810101044448888888844202020202244888888882020202020404040404444488888888888888888888882020248888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111-1-1-1-1iiii−i−i−i−i111111-1-1-1-1ii−i−iii−i−i111111111-1-1-1-1-1-1-1-1-1iiiii−i−i−i−i−iiiii−i−i−i−i11-1-1i−ii−i
χ4111111111111111111111-1-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−iii−i−iii111111111-1-1-1-1-1-1-1-1-1−i−i−i−i−iiiiii−i−i−i−iiiii11-1-1−ii−ii
χ511111111111111-1-1-1-1111111111111111-1-1111111111111111111111-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111-1-1-1-1111-1-1-1-1iiii−i−i−i−i-1-11111-1-1-1-1ii−i−iii−i−i11111-1-1-1-1-1-1-1-1-11111iiiii−i−i−i−i−i−i−i−i−iiiii-1-111−ii−ii
χ811111111111111-1-1-1-1111-1-1-1-1−i−i−i−iiiii-1-11111-1-1-1-1−i−iii−i−iii11111-1-1-1-1-1-1-1-1-11111−i−i−i−i−iiiiiiiiii−i−i−i−i-1-111i−ii−i
χ9111111111-1-1-1-111111111111111111111-1-11111111111111111-1-11-1-11111-1-11-1-111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1
χ10111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-11111-1-11-1-11111-11111-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ11111111111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i-1-11111-1-1-1-1ii−i−iii−i−i-1-11-1-1111111-111-1-1-1-1i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111−ii−ii
χ12111111111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii-1-11111-1-1-1-1−i−iii−i−iii-1-11-1-1111111-111-1-1-1-1−iiiiii−i−i−i−i−i−i−i−iiiii-1-111i−ii−i
χ13111111111-1-1-1-11-1-1-1-1111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111
χ14111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11111-11111111111111111-1-1-1-1
χ15111111111-1-1-1-11-1-1-1-1111-1-1-1-1iiii−i−i−i−i111111-1-1-1-1ii−i−iii−i−i-1-11-1-1-1-1-1-111-1111111i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1i−ii−i
χ16111111111-1-1-1-11-1-1-1-1111-1-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−iii−i−iii-1-11-1-1-1-1-1-111-1111111−iiiiii−i−i−i−iiiii−i−i−i−i11-1-1−ii−ii
χ171111-1-111-111-1-1111-1-11111111111111111-11-1-11-1-111-1-1-1-11111-1-1-11111-1-1-1-1-11111-1-1-111-1-1-111-1-111-1-111-1-11-11-111-1-1
χ181111-1-111-111-1-1111-1-11111111-1-1-1-1-1-1-1-11-11-1-11-1-1111111-1-1-1-1-1-1-11111-1-1-1-1-11111-1-11-1-1111-1-111-1-111-1-1111-11-1-1-111
χ191111-1-111-111-1-1111-1-1111-1-1-1-1iiii−i−i−i−i1-11-1-1111-1-1−i−iiiii−i−i-1-1-11111-1-1111-1-1-1-111−iii−i−ii−i−iiiii−i−i−i−iii1-1-11i−i−ii
χ201111-1-111-111-1-1111-1-1111-1-1-1-1−i−i−i−iiiii1-11-1-1111-1-1ii−i−i−i−iii-1-1-11111-1-1111-1-1-1-111i−i−iii−iii−i−i−i−iiiii−i−i1-1-11−iii−i
χ211111-1-111-111-1-11-1-111111111111111111-111-1-11-1-111-1-1-1-11111-1-1-111-1-111-1-1-111-1-111-111-1-1-111-1-1-1-111-1-111-11-11-1-111
χ221111-1-111-111-1-11-1-1111111111-1-1-1-1-1-1-1-1-111-1-11-1-1111111-1-1-1-1-1-1-111-1-111-1-1-111-1-1111-1-1111-1-11111-1-111-1-1-11-1111-1-1
χ231111-1-111-111-1-11-1-111111-1-1-1-1iiii−i−i−i−i-111-1-1111-1-1−i−iiiii−i−i-1-1-111-1-111111-1-111-1-1−iii−i−ii−i−iii−i−iiiii−i−i-111-1−iii−i
χ241111-1-111-111-1-11-1-111111-1-1-1-1−i−i−i−iiiii-111-1-1111-1-1ii−i−i−i−iii-1-1-111-1-111111-1-111-1-1i−i−iii−iii−i−iii−i−i−i−iii-111-1i−i−ii
χ251111-1-111-1-1-111111-1-1111111111111111-111-1-11-1-111-1-1-1-1111111-1-1-111-1-111-1-1-111-1-1-1-1-111-1-1-11111-1-111-1-1-11-11-1-111
χ261111-1-111-1-1-111111-1-11111111-1-1-1-1-1-1-1-1-111-1-11-1-1111111-1-1-1-111-1-1-111-1-111-1-1-111-1-1111-1-1111-1-1-1-111-1-111-11-1111-1-1
χ271111-1-111-1-1-111111-1-1111-1-1-1-1iiii−i−i−i−i-111-1-1111-1-1−i−iiiii−i−i11-1-1-111-1-1-1-1111-1-111−i−i−iiiiii−i−iii−i−i−i−iii-111-1−iii−i
χ281111-1-111-1-1-111111-1-1111-1-1-1-1−i−i−i−iiiii-111-1-1111-1-1ii−i−i−i−iii11-1-1-111-1-1-1-1111-1-111iii−i−i−i−i−iii−i−iiiii−i−i-111-1i−i−ii
χ291111-1-111-1-1-1111-1-1111111111111111111-11-1-11-1-111-1-1-1-1111111-1-1-1-1-11111-1-1-1-1-111-1-1-111-1-1-111-1-111-1-1111-11-111-1-1
χ301111-1-111-1-1-1111-1-1111111111-1-1-1-1-1-1-1-11-11-1-11-1-1111111-1-1-1-111-1-1-1-1-11111-1-1-1-1-111111-1-1111-1-111-1-111-1-11-11-1-1-111
χ311111-1-111-1-1-1111-1-111111-1-1-1-1iiii−i−i−i−i1-11-1-1111-1-1−i−iiiii−i−i11-1-1-1-1-111-1-111111-1-1−i−i−iiiiii−i−i−i−iiiii−i−i1-1-11i−i−ii
χ321111-1-111-1-1-1111-1-111111-1-1-1-1−i−i−i−iiiii1-11-1-1111-1-1ii−i−i−i−iii11-1-1-1-1-111-1-111111-1-1iii−i−i−i−i−iiiii−i−i−i−iii1-1-11−iii−i
χ33222222-2-2-200002000022222222222222200-222-222-2-22222-2-2-2-200-200000000-2000000-20000-200000000000000000000
χ34222222-2-2-20000200002222222-2-2-2-2-2-2-2-200-222-222-2-2-2-2-2-2222200-200000000-200000020000200000000000000000000
χ35222222-2-2-2000020000222-2-2-2-22i2i2i2i−2i−2i−2i−2i00-222-2-2-2222i2i−2i−2i−2i−2i2i2i00-2000000002000000−2i00002i00000000000000000000
χ36222222-2-2-2000020000222-2-2-2-2−2i−2i−2i−2i2i2i2i2i00-222-2-2-222−2i−2i2i2i2i2i−2i−2i00-20000000020000002i0000−2i00000000000000000000
χ372222-2-2-2-2200002000022222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200200000000200000020000200000000000000000000
χ382222-2-2-2-220000200002222222-2-2-2-2-2-2-2-200-2-2-2-2-2-2-2-222222222002000000002000000-20000-200000000000000000000
χ392222-2-2-2-22000020000222-2-2-2-22i2i2i2i−2i−2i−2i−2i00-2-2-2-22222−2i−2i2i2i−2i−2i2i2i00200000000-20000002i0000−2i00000000000000000000
χ402222-2-2-2-22000020000222-2-2-2-2−2i−2i−2i−2i2i2i2i2i00-2-2-2-222222i2i−2i−2i2i2i−2i−2i00200000000-2000000−2i00002i00000000000000000000
χ412-22-22i−2i00000002i2−i22−2-2-222i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30002i−2i02-2002ζ3−2ζ32ζ−2ζ000000000i2−i22−2000002−2i2−i200000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ422-22-22i−2i00000002i2−i22−2-2-222i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30002i−2i02-200−2ζ32ζ3−2ζ2ζ000000000i2−i22−2000002−2i2−i20000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ432-22-22i−2i00000002i2−i22−2-2-22−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0002i−2i0-2200−2ζ2ζ−2ζ32ζ3000000000i2−i22−200000−22−i2i200000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000
χ442-22-22i−2i00000002i2−i22−2-2-22−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0002i−2i0-22002ζ−2ζ2ζ3−2ζ3000000000i2−i22−200000−22−i2i20000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000
χ452-22-22i−2i00000002−i2i2−22-2-222i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30002i−2i02-2002ζ3−2ζ32ζ−2ζ000000000−i2i2−2200000−22−i2i20000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ462-22-22i−2i00000002−i2i2−22-2-222i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30002i−2i02-200−2ζ32ζ3−2ζ2ζ000000000−i2i2−2200000−22−i2i200000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ472-22-22i−2i00000002−i2i2−22-2-22−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0002i−2i0-2200−2ζ2ζ−2ζ32ζ3000000000−i2i2−22000002−2i2−i20000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000
χ482-22-22i−2i00000002−i2i2−22-2-22−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0002i−2i0-22002ζ−2ζ2ζ3−2ζ3000000000−i2i2−22000002−2i2−i200000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000
χ492-22-2−2i2i00000002i2−i2−22-2-222i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000−2i2i0-2200−2ζ32ζ3−2ζ2ζ000000000i2−i2−22000002−2−i2i200000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000
χ502-22-2−2i2i00000002i2−i2−22-2-222i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000−2i2i0-22002ζ3−2ζ32ζ−2ζ000000000i2−i2−22000002−2−i2i20000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000
χ512-22-2−2i2i00000002i2−i2−22-2-22−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000−2i2i02-2002ζ−2ζ2ζ3−2ζ3000000000i2−i2−2200000−22i2−i200000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ522-22-2−2i2i00000002i2−i2−22-2-22−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000−2i2i02-200−2ζ2ζ−2ζ32ζ3000000000i2−i2−2200000−22i2−i20000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ532-22-2−2i2i00000002−i2i22−2-2-222i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000−2i2i0-2200−2ζ32ζ3−2ζ2ζ000000000−i2i22−200000−22i2−i20000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000
χ542-22-2−2i2i00000002−i2i22−2-2-222i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000−2i2i0-22002ζ3−2ζ32ζ−2ζ000000000−i2i22−200000−22i2−i200000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000
χ552-22-2−2i2i00000002−i2i22−2-2-22−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000−2i2i02-2002ζ−2ζ2ζ3−2ζ3000000000−i2i22−2000002−2−i2i20000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ562-22-2−2i2i00000002−i2i22−2-2-22−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000−2i2i02-200−2ζ2ζ−2ζ32ζ3000000000−i2i22−2000002−2−i2i200000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ572-2-22002-202i−2i00200002-2-22i−2i−2i2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300-2002002i−2i00002ζ−2ζ2ζ3−2ζ30002i−2i00000002-2000002ζ3−2ζ30002ζ−2ζ000000000000000000
χ582-2-22002-202i−2i00200002-2-22i−2i−2i2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300-2002002i−2i0000−2ζ2ζ−2ζ32ζ30002i−2i00000002-200000−2ζ32ζ3000−2ζ2ζ000000000000000000
χ592-2-22002-202i−2i00200002-2-2−2i2i2i−2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00-200200−2i2i00002ζ3−2ζ32ζ−2ζ0002i−2i0000000-2200000−2ζ2ζ000−2ζ32ζ3000000000000000000
χ602-2-22002-202i−2i00200002-2-2−2i2i2i−2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00-200200−2i2i0000−2ζ32ζ3−2ζ2ζ0002i−2i0000000-22000002ζ−2ζ0002ζ3−2ζ3000000000000000000
χ612-2-22002-20−2i2i00200002-2-22i−2i−2i2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300-2002002i−2i00002ζ−2ζ2ζ3−2ζ3000−2i2i0000000-2200000−2ζ32ζ3000−2ζ2ζ000000000000000000
χ622-2-22002-20−2i2i00200002-2-22i−2i−2i2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300-2002002i−2i0000−2ζ2ζ−2ζ32ζ3000−2i2i0000000-22000002ζ3−2ζ30002ζ−2ζ000000000000000000
χ632-2-22002-20−2i2i00200002-2-2−2i2i2i−2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00-200200−2i2i00002ζ3−2ζ32ζ−2ζ000−2i2i00000002-2000002ζ−2ζ0002ζ3−2ζ3000000000000000000
χ642-2-22002-20−2i2i00200002-2-2−2i2i2i−2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00-200200−2i2i0000−2ζ32ζ3−2ζ2ζ000−2i2i00000002-200000−2ζ2ζ000−2ζ32ζ3000000000000000000
χ652-2-2200-220002-2200002-2-22i−2i−2i2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300200-200−2i2i0000−2ζ2ζ−2ζ32ζ32-200000002i−2i00000000002ζ−2ζ0002ζ3−2ζ30000000000000000
χ662-2-2200-220002-2200002-2-22i−2i−2i2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300200-200−2i2i00002ζ−2ζ2ζ3−2ζ32-200000002i−2i0000000000−2ζ2ζ000−2ζ32ζ30000000000000000
χ672-2-2200-220002-2200002-2-2−2i2i2i−2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00200-2002i−2i0000−2ζ32ζ3−2ζ2ζ2-20000000−2i2i00000000002ζ3−2ζ30002ζ−2ζ0000000000000000
χ682-2-2200-220002-2200002-2-2−2i2i2i−2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00200-2002i−2i00002ζ3−2ζ32ζ−2ζ2-20000000−2i2i0000000000−2ζ32ζ3000−2ζ2ζ0000000000000000
χ692-2-2200-22000-22200002-2-22i−2i−2i2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300200-200−2i2i0000−2ζ2ζ−2ζ32ζ3-220000000−2i2i0000000000−2ζ2ζ000−2ζ32ζ30000000000000000
χ702-2-2200-22000-22200002-2-22i−2i−2i2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300200-200−2i2i00002ζ−2ζ2ζ3−2ζ3-220000000−2i2i00000000002ζ−2ζ0002ζ3−2ζ30000000000000000
χ712-2-2200-22000-22200002-2-2−2i2i2i−2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00200-2002i−2i0000−2ζ32ζ3−2ζ2ζ-2200000002i−2i0000000000−2ζ32ζ3000−2ζ2ζ0000000000000000
χ722-2-2200-22000-22200002-2-2−2i2i2i−2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00200-2002i−2i00002ζ3−2ζ32ζ−2ζ-2200000002i−2i00000000002ζ3−2ζ30002ζ−2ζ0000000000000000
χ734444444444444-14444-1-1-100000000000044-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1000000000000000000000000000-1-1000000
χ744444444444444-1-4-4-4-4-1-1-1000000000000-4-4-1-1-1-1000000000000-1-1-1-1-1111100000000000000000000000000011000000
χ75444444444-4-4-4-4-14444-1-1-1000000000000-4-4-1-1-1-100000000000011-111-1-1-1-100000000000000000000000000011000000
χ76444444444-4-4-4-4-1-4-4-4-4-1-1-100000000000044-1-1-1-100000000000011-1111111000000000000000000000000000-1-1000000
χ774444-4-444-444-4-4-144-4-4-1-1-10000000000004-4-111-1000000000000111-1-1-1-111000000000000000000000000000-11000000
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χ85888888-8-8-80000-20000-2-2-2000000000000002-2-2200000000000000200000000000000000000000000000000000000000
χ868888-8-8-8-880000-20000-2-2-200000000000000222200000000000000-200000000000000000000000000000000000000000
χ878-88-88i−8i0000000-24i2−4i242−4222-2000000000000000−2i2i000000000000000000−i2i2−2200000000000000000000000000000000000
χ888-88-88i−8i0000000-2−4i24i2−424222-2000000000000000−2i2i000000000000000000i2−i22−200000000000000000000000000000000000
χ898-88-8−8i8i0000000-24i2−4i2−424222-20000000000000002i−2i000000000000000000−i2i22−200000000000000000000000000000000000
χ908-88-8−8i8i0000000-2−4i24i242−4222-20000000000000002i−2i000000000000000000i2−i2−2200000000000000000000000000000000000
χ918-8-88008-808i−8i00-20000-22200000000000000200-2000000000000000−2i2i000000000000000000000000000000000000000
χ928-8-88008-80−8i8i00-20000-22200000000000000200-20000000000000002i−2i000000000000000000000000000000000000000
χ938-8-8800-880008-8-20000-22200000000000000-2002000000000000-22000000000000000000000000000000000000000000
χ948-8-8800-88000-88-20000-22200000000000000-20020000000000002-2000000000000000000000000000000000000000000
χ951616-16-16000000000-400004-4400000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.