Finite Group Databasebeta

← Group #13031925

Character table — Group #13031925

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222244444444444445555555555558888881010101010101010101010101616161616161616162020202020202020202020202020202020202020202020202020203232404040404040
order12224444224445888810101044448888888824202020202244888888881010202020404040402244488888888888888888888881020448888
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−i111111111-1-1-1-1-1-1-1-1-1i−iiiii−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−ii−i−i−i−iiiii−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−i11111-1-1-1-1-1-1-1-1-11111i−iiiii−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−ii−i−i−i−iiiiiiiii−i−i−i−i-1-111i−ii−i
χ911111111-1-11-1-111111111111111111111-1-11111111111111111-1-11-1-11111-1-11-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ1011111111-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-11111-1-11-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ1111111111-1-11-1-111111111-1-1-1-1iiii−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
χ1211111111-1-11-1-111111111-1-1-1-1−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
χ1311111111-1-11-1-11-1-1-1-1111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ1411111111-1-11-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ1511111111-1-11-1-11-1-1-1-1111-1-1-1-1iiii−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
χ1611111111-1-11-1-11-1-1-1-1111-1-1-1-1−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
χ171111-1-11111-1-1-1111-1-11111111111111111-11-1-11-1-1111111-1-1-1-111-1-1-111-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-11-1-11-1-111
χ181111-1-11111-1-1-1111-1-11111111-1-1-1-1-1-1-1-11-11-1-11-1-111-1-1-1-1111111-1-1-111-1-1-1-1-11111-1-111-1-111-1-111-1-111-1-1111-1-1111-1-1
χ191111-1-11111-1-1-1111-1-1111-1-1-1-1iiii−i−i−i−i1-11-1-1111-1-1ii−i−i−i−iii11-1-1-111-1-1111-1-1-1-111−iiii−i−i−i−iiiii−i−i−i−iii1-11-1−iii−i
χ201111-1-11111-1-1-1111-1-1111-1-1-1-1−i−i−i−iiiii1-11-1-1111-1-1−i−iiiii−i−i11-1-1-111-1-1111-1-1-1-111i−i−i−iiiii−i−i−i−iiiii−i−i1-11-1i−i−ii
χ211111-1-11111-1-1-11-1-111111111111111111-111-1-11-1-1111111-1-1-1-111-1-1-1-1-111-1-1-111-1-111-1-111-1-111-1-1-1-111-1-111-111-111-1-1
χ221111-1-11111-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-111-1-11-1-111-1-1-1-1111111-1-1-1-1-111-1-1-111-1-11111-1-111-1-11111-1-111-1-1-111-1-1-111
χ231111-1-11111-1-1-11-1-111111-1-1-1-1iiii−i−i−i−i-111-1-1111-1-1ii−i−i−i−iii11-1-1-1-1-111111-1-111-1-1−iiii−i−i−i−iii−i−iiiii−i−i-11-11i−i−ii
χ241111-1-11111-1-1-11-1-111111-1-1-1-1−i−i−i−iiiii-111-1-1111-1-1−i−iiiii−i−i11-1-1-1-1-111111-1-111-1-1i−i−i−iiiii−i−iii−i−i−i−iii-11-11−iii−i
χ251111-1-111-1-1-111111-1-1111111111111111-111-1-11-1-1111111-1-1-1-1-1-1-11111-1-111-1-1-111-1-1-1-1-1-111-1-11111-1-111-1-1-111-111-1-1
χ261111-1-111-1-1-111111-1-11111111-1-1-1-1-1-1-1-1-111-1-11-1-111-1-1-1-11111-1-1-11111-1-111-1-1-111-1-11111-1-111-1-1-1-111-1-111-111-1-1-111
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-1-1-11111-1-1-1-1111-1-111−ii−i−iiiii−i−iii−i−i−i−iii-11-11i−i−ii
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-1-1-11111-1-1-1-1111-1-111i−iii−i−i−i−iii−i−iiiii−i−i-11-11−iii−i
χ291111-1-111-1-1-1111-1-1111111111111111111-11-1-11-1-1111111-1-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1111-1-11-1-111
χ301111-1-111-1-1-1111-1-1111111111-1-1-1-1-1-1-1-11-11-1-11-1-111-1-1-1-11111-1-1-111-1-11111-1-1-1-1-1111111-1-111-1-111-1-111-1-11-1-1111-1-1
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-1-1-111-1-111-1-111111-1-1−ii−i−iiiii−i−i−i−iiiii−i−i1-11-1−iii−i
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-1-1-111-1-111-1-111111-1-1i−iii−i−i−i−iiiii−i−i−i−iii1-11-1i−i−ii
χ33222222-2-200-2002000022222222222222200-222-222-2-2-2-2-2-2222200-200000000-2000000-2-2000000000000000000000000
χ34222222-2-200-200200002222222-2-2-2-2-2-2-2-200-222-222-2-22222-2-2-2-200-200000000-200000022000000000000000000000000
χ35222222-2-200-20020000222-2-2-2-22i2i2i2i−2i−2i−2i−2i00-222-2-2-222−2i−2i2i2i2i2i−2i−2i00-2000000002000000−2i2i000000000000000000000000
χ36222222-2-200-20020000222-2-2-2-2−2i−2i−2i−2i2i2i2i2i00-222-2-2-2222i2i−2i−2i−2i−2i2i2i00-20000000020000002i−2i000000000000000000000000
χ372222-2-2-2-2002002000022222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200200000000200000022000000000000000000000000
χ382222-2-2-2-200200200002222222-2-2-2-2-2-2-2-200-2-2-2-2-2-2-2-222222222002000000002000000-2-2000000000000000000000000
χ392222-2-2-2-20020020000222-2-2-2-22i2i2i2i−2i−2i−2i−2i00-2-2-2-22222−2i−2i2i2i−2i−2i2i2i00200000000-20000002i−2i000000000000000000000000
χ402222-2-2-2-20020020000222-2-2-2-2−2i−2i−2i−2i2i2i2i2i00-2-2-2-222222i2i−2i−2i2i2i−2i−2i00200000000-2000000−2i2i000000000000000000000000
χ4122-2-2002-22-200020000-22-22i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300-2002002i−2i2ζ−2ζ2ζ3−2ζ300002-200000000002i−2i0000002ζ−2ζ002ζ3−2ζ3000000000000000000
χ4222-2-2002-22-200020000-22-22i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300-2002002i−2i−2ζ2ζ−2ζ32ζ300002-200000000002i−2i000000−2ζ2ζ00−2ζ32ζ3000000000000000000
χ4322-2-2002-22-200020000-22-2−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00-200200−2i2i2ζ3−2ζ32ζ−2ζ00002-20000000000−2i2i0000002ζ3−2ζ3002ζ−2ζ000000000000000000
χ4422-2-2002-22-200020000-22-2−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00-200200−2i2i−2ζ32ζ3−2ζ2ζ00002-20000000000−2i2i000000−2ζ32ζ300−2ζ2ζ000000000000000000
χ4522-2-2002-2-2200020000-22-22i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300-2002002i−2i2ζ−2ζ2ζ3−2ζ30000-220000000000−2i2i000000−2ζ2ζ00−2ζ32ζ3000000000000000000
χ4622-2-2002-2-2200020000-22-22i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300-2002002i−2i−2ζ2ζ−2ζ32ζ30000-220000000000−2i2i0000002ζ−2ζ002ζ3−2ζ3000000000000000000
χ4722-2-2002-2-2200020000-22-2−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00-200200−2i2i2ζ3−2ζ32ζ−2ζ0000-2200000000002i−2i000000−2ζ32ζ300−2ζ2ζ000000000000000000
χ4822-2-2002-2-2200020000-22-2−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00-200200−2i2i−2ζ32ζ3−2ζ2ζ0000-2200000000002i−2i0000002ζ3−2ζ3002ζ−2ζ000000000000000000
χ4922-2-200-220002i−2i20000-22-22i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300200-200−2i2i−2ζ2ζ−2ζ32ζ300000002i−2i00002-2000000000002ζ3−2ζ3002ζ−2ζ0000000000000000
χ5022-2-200-220002i−2i20000-22-22i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300200-200−2i2i2ζ−2ζ2ζ3−2ζ300000002i−2i00002-200000000000−2ζ32ζ300−2ζ2ζ0000000000000000
χ5122-2-200-220002i−2i20000-22-2−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00200-2002i−2i−2ζ32ζ3−2ζ2ζ00000002i−2i0000-2200000000000−2ζ2ζ00−2ζ32ζ30000000000000000
χ5222-2-200-220002i−2i20000-22-2−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00200-2002i−2i2ζ3−2ζ32ζ−2ζ00000002i−2i0000-22000000000002ζ−2ζ002ζ3−2ζ30000000000000000
χ5322-2-200-22000−2i2i20000-22-22i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300200-200−2i2i−2ζ2ζ−2ζ32ζ30000000−2i2i0000-2200000000000−2ζ32ζ300−2ζ2ζ0000000000000000
χ5422-2-200-22000−2i2i20000-22-22i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300200-200−2i2i2ζ−2ζ2ζ3−2ζ30000000−2i2i0000-22000000000002ζ3−2ζ3002ζ−2ζ0000000000000000
χ5522-2-200-22000−2i2i20000-22-2−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00200-2002i−2i−2ζ32ζ3−2ζ2ζ0000000−2i2i00002-2000000000002ζ−2ζ002ζ3−2ζ30000000000000000
χ5622-2-200-22000−2i2i20000-22-2−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00200-2002i−2i2ζ3−2ζ32ζ−2ζ0000000−2i2i00002-200000000000−2ζ2ζ00−2ζ32ζ30000000000000000
χ572-22-22i−2i000000022−2i2−i22-2-22i−2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0002i−2i02-20000002ζ−2ζ2ζ3−2ζ3000002−2i2−i200000i2−i22−200000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ582-22-22i−2i000000022−2i2−i22-2-22i−2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0002i−2i02-2000000−2ζ2ζ−2ζ32ζ3000002−2i2−i200000i2−i22−20000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ592-22-22i−2i000000022−2i2−i22-2-2−2i2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30002i−2i0-22000000−2ζ32ζ3−2ζ2ζ000002−2i2−i200000−i2i2−220000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000
χ602-22-22i−2i000000022−2i2−i22-2-2−2i2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30002i−2i0-220000002ζ3−2ζ32ζ−2ζ000002−2i2−i200000−i2i2−2200000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000
χ612-22-22i−2i00000002−22−i2i22-2-22i−2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0002i−2i02-20000002ζ−2ζ2ζ3−2ζ300000−22−i2i200000−i2i2−220000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ622-22-22i−2i00000002−22−i2i22-2-22i−2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0002i−2i02-2000000−2ζ2ζ−2ζ32ζ300000−22−i2i200000−i2i2−2200000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ632-22-22i−2i00000002−22−i2i22-2-2−2i2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30002i−2i0-22000000−2ζ32ζ3−2ζ2ζ00000−22−i2i200000i2−i22−200000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000
χ642-22-22i−2i00000002−22−i2i22-2-2−2i2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30002i−2i0-220000002ζ3−2ζ32ζ−2ζ00000−22−i2i200000i2−i22−20000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000
χ652-22-2−2i2i000000022−2−i2i22-2-22i−2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000−2i2i0-22000000−2ζ2ζ−2ζ32ζ3000002−2−i2i200000i2−i2−2200000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000
χ662-22-2−2i2i000000022−2−i2i22-2-22i−2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000−2i2i0-220000002ζ−2ζ2ζ3−2ζ3000002−2−i2i200000i2−i2−220000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000
χ672-22-2−2i2i000000022−2−i2i22-2-2−2i2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000−2i2i02-20000002ζ3−2ζ32ζ−2ζ000002−2−i2i200000−i2i22−20000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ682-22-2−2i2i000000022−2−i2i22-2-2−2i2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000−2i2i02-2000000−2ζ32ζ3−2ζ2ζ000002−2−i2i200000−i2i22−200000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ692-22-2−2i2i00000002−22i2−i22-2-22i−2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000−2i2i0-22000000−2ζ2ζ−2ζ32ζ300000−22i2−i200000−i2i22−20000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000
χ702-22-2−2i2i00000002−22i2−i22-2-22i−2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000−2i2i0-220000002ζ−2ζ2ζ3−2ζ300000−22i2−i200000−i2i22−200000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000
χ712-22-2−2i2i00000002−22i2−i22-2-2−2i2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000−2i2i02-20000002ζ3−2ζ32ζ−2ζ00000−22i2−i200000i2−i2−2200000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ722-22-2−2i2i00000002−22i2−i22-2-2−2i2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000−2i2i02-2000000−2ζ32ζ3−2ζ2ζ00000−22i2−i200000i2−i2−220000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
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
χ7544444444-4-44-4-4-14444-1-1-1000000000000-4-4-1-1-1-100000000000011-111-1-1-1-100000000000000000000000000011000000
χ7644444444-4-44-4-4-1-4-4-4-4-1-1-100000000000044-1-1-1-100000000000011-1111111000000000000000000000000000-1-1000000
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χ85888888-8-800-800-20000-2-2-2000000000000002-2-2200000000000000200000000000000000000000000000000000000000
χ868888-8-8-8-800800-20000-2-2-200000000000000222200000000000000-200000000000000000000000000000000000000000
χ8788-8-8008-88-8000-200002-2200000000000000200-2000000000000-22000000000000000000000000000000000000000000
χ8888-8-8008-8-88000-200002-2200000000000000200-20000000000002-2000000000000000000000000000000000000000000
χ8988-8-800-880008i−8i-200002-2200000000000000-2002000000000000000−2i2i000000000000000000000000000000000000000
χ9088-8-800-88000−8i8i-200002-2200000000000000-20020000000000000002i−2i000000000000000000000000000000000000000
χ918-88-88i−8i0000000-242−424i2−4i2-222000000000000000−2i2i000000000000000000−22−i2i200000000000000000000000000000000000
χ928-88-88i−8i0000000-2−4242−4i24i2-222000000000000000−2i2i0000000000000000002−2i2−i200000000000000000000000000000000000
χ938-88-8−8i8i0000000-242−42−4i24i2-2220000000000000002i−2i000000000000000000−22i2−i200000000000000000000000000000000000
χ948-88-8−8i8i0000000-2−42424i2−4i2-2220000000000000002i−2i0000000000000000002−2−i2i200000000000000000000000000000000000
χ9516-16-1616000000000-4000044-400000000000000000000000000000000000000000000000000000000000000000000000000

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