Finite Group Databasebeta

← Group #13031947

Character table — Group #13031947

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222244444444444445555555555558888881010101010101010101010101616161616161616162020202020202020202020202020202020202020202020202020203232404040404040
order12224444444445888810101044448888888844202020204444888888882020202020404040402224488888888888888888888882020448888
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−i111111-1-1-1-1iiii−i−i−i−i111111111-1-1-1-1-1-1-1-1-1iii−i−i−iii−i−iiiii−i−i−i−i11-1-1ii−i−i
χ4111111111111111111111-1-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−iiiii111111111-1-1-1-1-1-1-1-1-1−i−i−iiii−i−iii−i−i−i−iiiii11-1-1−i−iii
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-1-11111-1-1-1-1iiii−i−i−i−i11111-1-1-1-1-1-1-1-1-11111iii−i−i−iii−i−i−i−i−i−iiiii-1-111−i−iii
χ811111111111111-1-1-1-1111-1-1-1-1−i−i−i−iiiii-1-11111-1-1-1-1−i−i−i−iiiii11111-1-1-1-1-1-1-1-1-11111−i−i−iiii−i−iiiiiii−i−i−i−i-1-111ii−i−i
χ9111111111-1-1-1-111111111111111111111-1-111111111111111111-1-1-1-111111-1-1-1-111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ10111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-111-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ11111111111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i-1-11111-1-1-1-1iiii−i−i−i−i1-1-1-1-11111-11111-1-1-1-1i−i−i−iii−i−iiiiiii−i−i−i−i-1-111−i−iii
χ12111111111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii-1-11111-1-1-1-1−i−i−i−iiiii1-1-1-1-11111-11111-1-1-1-1−iiii−i−iii−i−i−i−i−i−iiiii-1-111ii−i−i
χ13111111111-1-1-1-11-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ14111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-111-1111111111111111111-1-1-1-1
χ15111111111-1-1-1-11-1-1-1-1111-1-1-1-1iiii−i−i−i−i111111-1-1-1-1iiii−i−i−i−i1-1-1-1-1-1-1-1-1-111111111i−i−i−iii−i−iii−i−i−i−iiiii11-1-1ii−i−i
χ16111111111-1-1-1-11-1-1-1-1111-1-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−iiiii1-1-1-1-1-1-1-1-1-111111111−iiii−i−iii−i−iiiii−i−i−i−i11-1-1−i−iii
χ171111-1-111-111-1-1111-1-11111111111111111-11-1-11-1-11111-1-111-1-1-111-1-111-1-1-111-1-111-1-1-111-111-1-1-1-111-1-111-1-11-11-11-11-1
χ181111-1-111-111-1-1111-1-11111111-1-1-1-1-1-1-1-11-11-1-11-1-111-1-111-1-111-111-1-111-1-1-111-1-111-1-11-1-11-1-11111-1-111-1-1111-11-1-11-11
χ191111-1-111-111-1-1111-1-1111-1-1-1-1iiii−i−i−i−i1-11-1-1111-1-1ii−i−i−i−iii-111-1-111-1-11-1-111-1-111−iiii−i−i−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−iiiii1-11-1-1111-1-1−i−iiiii−i−i-111-1-111-1-11-1-111-1-111i−i−i−iiiii−i−i−i−iiiii−i−i1-1-11−iii−i
χ211111-1-111-111-1-11-1-111111111111111111-111-1-11-1-11111-1-111-1-1-111-1-1-1-111-111-1-1-1-111-111-111-1-1-1-1-1-111-1-111-11-11-11-11
χ221111-1-111-111-1-11-1-1111111111-1-1-1-1-1-1-1-1-111-1-11-1-111-1-111-1-111-111-1-1-1-111-111-1-1-1-1111-1-11-1-1111111-1-111-1-1-11-111-11-1
χ231111-1-111-111-1-11-1-111111-1-1-1-1iiii−i−i−i−i-111-1-1111-1-1ii−i−i−i−iii-111-1-1-1-1111-1-11111-1-1−iiii−i−i−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-111-1-1111-1-1−i−iiiii−i−i-111-1-1-1-1111-1-11111-1-1i−i−i−iiiii−i−iii−i−i−i−iii-111-1i−i−ii
χ251111-1-111-1-1-111111-1-1111111111111111-111-1-11-1-11111-1-111-1-1-1-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-11-11-11-11
χ261111-1-111-1-1-111111-1-11111111-1-1-1-1-1-1-1-1-111-1-11-1-111-1-111-1-111-1-1-11111-1-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-111-11-111-11-1
χ271111-1-111-1-1-111111-1-1111-1-1-1-1iiii−i−i−i−i-111-1-1111-1-1ii−i−i−i−iii-1-1-11111-1-1111-1-1-1-111−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-111-1-1111-1-1−i−iiiii−i−i-1-1-11111-1-1111-1-1-1-111iii−i−i−i−i−iii−i−iiiii−i−i-111-1i−i−ii
χ291111-1-111-1-1-1111-1-1111111111111111111-11-1-11-1-11111-1-111-1-1-1-1-111-1-111-1-1-111-1-111-1-1-1-1-1-11111-1-111-1-1111-11-11-11-1
χ301111-1-111-1-1-1111-1-1111111111-1-1-1-1-1-1-1-11-11-1-11-1-111-1-111-1-111-1-1-111-1-111-1-1-111-1-111111111-1-1-1-111-1-111-1-11-11-1-11-11
χ311111-1-111-1-1-1111-1-111111-1-1-1-1iiii−i−i−i−i1-11-1-1111-1-1ii−i−i−i−iii-1-1-111-1-111111-1-111-1-1−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−iiiii1-11-1-1111-1-1−i−iiiii−i−i-1-1-111-1-111111-1-111-1-1iii−i−i−i−i−iiiii−i−i−i−iii1-1-11−iii−i
χ33222222-2-2-200002000022222222222222200-222-222-2-2-2-222-2-222-200000000-200000000-200-20000000000000000000000
χ34222222-2-2-20000200002222222-2-2-2-2-2-2-2-200-222-222-2-222-2-222-2-2-200000000-20000000020020000000000000000000000
χ35222222-2-2-2000020000222-2-2-2-22i2i2i2i−2i−2i−2i−2i00-222-2-2-222−2i−2i2i2i2i2i−2i−2i-200000000200000000−2i002i0000000000000000000000
χ36222222-2-2-2000020000222-2-2-2-2−2i−2i−2i−2i2i2i2i2i00-222-2-2-2222i2i−2i−2i−2i−2i2i2i-2000000002000000002i00−2i0000000000000000000000
χ372222-2-2-2-2200002000022222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-220000000020000000020020000000000000000000000
χ382222-2-2-2-220000200002222222-2-2-2-2-2-2-2-200-2-2-2-2-2-2-2-222222222200000000200000000-200-20000000000000000000000
χ392222-2-2-2-22000020000222-2-2-2-22i2i2i2i−2i−2i−2i−2i00-2-2-2-22222−2i−2i−2i−2i2i2i2i2i200000000-2000000002i00−2i0000000000000000000000
χ402222-2-2-2-22000020000222-2-2-2-2−2i−2i−2i−2i2i2i2i2i00-2-2-2-222222i2i2i2i−2i−2i−2i−2i200000000-200000000−2i002i0000000000000000000000
χ412-22-22-200000002i2−i2i2−i2-2-222i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30002-202i−2i00002ζ−2ζ002ζ3−2ζ300000i2−i2i2−i2000002−22−200000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ422-22-22-200000002i2−i2i2−i2-2-222i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30002-202i−2i0000−2ζ2ζ00−2ζ32ζ300000i2−i2i2−i2000002−22−20000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ432-22-22-200000002i2−i2i2−i2-2-22−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0002-20−2i2i00002ζ3−2ζ3002ζ−2ζ00000i2−i2i2−i200000−22−2200000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ442-22-22-200000002i2−i2i2−i2-2-22−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0002-20−2i2i0000−2ζ32ζ300−2ζ2ζ00000i2−i2i2−i200000−22−220000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ452-22-22-200000002−i2i2−i2i2-2-222i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30002-202i−2i00002ζ−2ζ002ζ3−2ζ300000−i2i2−i2i200000−22−220000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ462-22-22-200000002−i2i2−i2i2-2-222i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30002-202i−2i0000−2ζ2ζ00−2ζ32ζ300000−i2i2−i2i200000−22−2200000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ472-22-22-200000002−i2i2−i2i2-2-22−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0002-20−2i2i00002ζ3−2ζ3002ζ−2ζ00000−i2i2−i2i2000002−22−20000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ482-22-22-200000002−i2i2−i2i2-2-22−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0002-20−2i2i0000−2ζ32ζ300−2ζ2ζ00000−i2i2−i2i2000002−22−200000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ492-22-2-2200000002i2−i2−i2i2-2-222i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000-220−2i2i0000−2ζ2ζ00−2ζ32ζ300000i2−i2−i2i2000002−2−2200000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ502-22-2-2200000002i2−i2−i2i2-2-222i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000-220−2i2i00002ζ−2ζ002ζ3−2ζ300000i2−i2−i2i2000002−2−220000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ512-22-2-2200000002i2−i2−i2i2-2-22−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000-2202i−2i0000−2ζ32ζ300−2ζ2ζ00000i2−i2−i2i200000−222−200000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ522-22-2-2200000002i2−i2−i2i2-2-22−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000-2202i−2i00002ζ3−2ζ3002ζ−2ζ00000i2−i2−i2i200000−222−20000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ532-22-2-2200000002−i2i2i2−i2-2-222i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000-220−2i2i0000−2ζ2ζ00−2ζ32ζ300000−i2i2i2−i200000−222−20000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ542-22-2-2200000002−i2i2i2−i2-2-222i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000-220−2i2i00002ζ−2ζ002ζ3−2ζ300000−i2i2i2−i200000−222−200000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ552-22-2-2200000002−i2i2i2−i2-2-22−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000-2202i−2i0000−2ζ32ζ300−2ζ2ζ00000−i2i2i2−i2000002−2−220000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ562-22-2-2200000002−i2i2i2−i2-2-22−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000-2202i−2i00002ζ3−2ζ3002ζ−2ζ00000−i2i2i2−i2000002−2−2200000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ572-2-22002-202i−2i00200002-2-22i−2i−2i2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300-2002002i−2i2ζ−2ζ002ζ3−2ζ30002i−2i00000002-200000002ζ3−2ζ302ζ−2ζ00000000000000000000
χ582-2-22002-202i−2i00200002-2-22i−2i−2i2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300-2002002i−2i−2ζ2ζ00−2ζ32ζ30002i−2i00000002-20000000−2ζ32ζ30−2ζ2ζ00000000000000000000
χ592-2-22002-202i−2i00200002-2-2−2i2i2i−2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00-200200−2i2i2ζ3−2ζ3002ζ−2ζ0002i−2i0000000-220000000−2ζ2ζ0−2ζ32ζ300000000000000000000
χ602-2-22002-202i−2i00200002-2-2−2i2i2i−2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00-200200−2i2i−2ζ32ζ300−2ζ2ζ0002i−2i0000000-2200000002ζ−2ζ02ζ3−2ζ300000000000000000000
χ612-2-22002-20−2i2i00200002-2-22i−2i−2i2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300-2002002i−2i2ζ−2ζ002ζ3−2ζ3000−2i2i0000000-220000000−2ζ32ζ30−2ζ2ζ00000000000000000000
χ622-2-22002-20−2i2i00200002-2-22i−2i−2i2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300-2002002i−2i−2ζ2ζ00−2ζ32ζ3000−2i2i0000000-2200000002ζ3−2ζ302ζ−2ζ00000000000000000000
χ632-2-22002-20−2i2i00200002-2-2−2i2i2i−2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00-200200−2i2i2ζ3−2ζ3002ζ−2ζ000−2i2i00000002-200000002ζ−2ζ02ζ3−2ζ300000000000000000000
χ642-2-22002-20−2i2i00200002-2-2−2i2i2i−2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00-200200−2i2i−2ζ32ζ300−2ζ2ζ000−2i2i00000002-20000000−2ζ2ζ0−2ζ32ζ300000000000000000000
χ652-2-2200-220002-2200002-2-22i−2i−2i2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300200-200−2i2i−2ζ2ζ00−2ζ32ζ3000002-200000002i−2i00000000002ζ−2ζ2ζ3−2ζ30000000000000000
χ662-2-2200-220002-2200002-2-22i−2i−2i2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300200-200−2i2i2ζ−2ζ002ζ3−2ζ3000002-200000002i−2i0000000000−2ζ2ζ−2ζ32ζ30000000000000000
χ672-2-2200-220002-2200002-2-2−2i2i2i−2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00200-2002i−2i−2ζ32ζ300−2ζ2ζ000002-20000000−2i2i00000000002ζ3−2ζ32ζ−2ζ0000000000000000
χ682-2-2200-220002-2200002-2-2−2i2i2i−2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00200-2002i−2i2ζ3−2ζ3002ζ−2ζ000002-20000000−2i2i0000000000−2ζ32ζ3−2ζ2ζ0000000000000000
χ692-2-2200-22000-22200002-2-22i−2i−2i2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300200-200−2i2i−2ζ2ζ00−2ζ32ζ300000-220000000−2i2i0000000000−2ζ2ζ−2ζ32ζ30000000000000000
χ702-2-2200-22000-22200002-2-22i−2i−2i2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300200-200−2i2i2ζ−2ζ002ζ3−2ζ300000-220000000−2i2i00000000002ζ−2ζ2ζ3−2ζ30000000000000000
χ712-2-2200-22000-22200002-2-2−2i2i2i−2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00200-2002i−2i−2ζ32ζ300−2ζ2ζ00000-2200000002i−2i0000000000−2ζ32ζ3−2ζ2ζ0000000000000000
χ722-2-2200-22000-22200002-2-2−2i2i2i−2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00200-2002i−2i2ζ3−2ζ3002ζ−2ζ00000-2200000002i−2i00000000002ζ3−2ζ32ζ−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
χ75444444444-4-4-4-4-14444-1-1-1000000000000-4-4-1-1-1-1000000000000-11111-1-1-1-100000000000000000000000000011000000
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χ85888888-8-8-80000-20000-2-2-2000000000000002-2-2200000000000020000000000000000000000000000000000000000000
χ868888-8-8-8-880000-20000-2-2-2000000000000002222000000000000-20000000000000000000000000000000000000000000
χ878-88-88-80000000-24i2−4i24i2−4i222-2000000000000000-22000000000000000000−i2i2−i2i200000000000000000000000000000000000
χ888-88-88-80000000-2−4i24i2−4i24i222-2000000000000000-22000000000000000000i2−i2i2−i200000000000000000000000000000000000
χ898-88-8-880000000-24i2−4i2−4i24i222-20000000000000002-2000000000000000000−i2i2i2−i200000000000000000000000000000000000
χ908-88-8-880000000-2−4i24i24i2−4i222-20000000000000002-2000000000000000000i2−i2−i2i200000000000000000000000000000000000
χ918-8-88008-808i−8i00-20000-22200000000000000200-20000000000000−2i2i00000000000000000000000000000000000000000
χ928-8-88008-80−8i8i00-20000-22200000000000000200-200000000000002i−2i00000000000000000000000000000000000000000
χ938-8-8800-880008-8-20000-22200000000000000-2002000000000000000-22000000000000000000000000000000000000000
χ948-8-8800-88000-88-20000-22200000000000000-20020000000000000002-2000000000000000000000000000000000000000
χ951616-16-16000000000-400004-4400000000000000000000000000000000000000000000000000000000000000000000000000

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