Finite Group Databasebeta

← Group #13036614

Character table — Group #13036614

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222244444444444445555555555558888881010101010101010101010101616161616161616162020202020202020202020202020202020202020202020202020203232404040404040
order12224444224445888810101044448888888844202020202244888888881010202020404040404444444444444888888888888882020448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111-1-1-1-1iiii−i−i−i−i111111-1-1-1-1ii−i−iii−i−i111111111-1-1-1-1-1iiii−i−i−i−i-1-1-1-1ii−i−iiii−i−i−i11-1-1ii−i−i
χ4111111111111111111111-1-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−iii−i−iii111111111-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−iii−i−i−iiii11-1-1−i−iii
χ511111111111111-1-1-1-1111111111111111-1-1111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ611111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111-1-1-1-1111-1-1-1-1iiii−i−i−i−i-1-11111-1-1-1-1ii−i−iii−i−i11111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111ii−i−iiii−i−i−i-1-111−i−iii
χ811111111111111-1-1-1-1111-1-1-1-1−i−i−i−iiiii-1-11111-1-1-1-1−i−iii−i−iii11111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111−i−iii−i−i−iiii-1-111ii−i−i
χ911111111-1-1-1-1111111111111111111111-1-11111111111111111-1-11-1-111111-1-1-1-1111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1
χ1011111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-1-1-11111
χ1111111111-1-1-1-1111111111-1-1-1-1iiii−i−i−i−i-1-11111-1-1-1-1ii−i−iii−i−i-1-11-1-11111-11111iiii−i−i−i−i-1-1-1-1−i−iiii−i−i−iii-1-111−i−iii
χ1211111111-1-1-1-1111111111-1-1-1-1−i−i−i−iiiii-1-11111-1-1-1-1−i−iii−i−iii-1-11-1-11111-11111−i−i−i−iiiii-1-1-1-1ii−i−i−iiii−i−i-1-111ii−i−i
χ1311111111-1-1-1-111-1-1-1-1111111111111111111111111111111111-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111
χ1411111111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-111111111-1-1-1-11111-111-1111111-1-1-1-1
χ1511111111-1-1-1-111-1-1-1-1111-1-1-1-1iiii−i−i−i−i111111-1-1-1-1ii−i−iii−i−i-1-11-1-1-1-1-1-1-11111−i−i−i−iiiii1111−i−iiii−i−i−iii11-1-1ii−i−i
χ1611111111-1-1-1-111-1-1-1-1111-1-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−iii−i−iii-1-11-1-1-1-1-1-1-11111iiii−i−i−i−i1111ii−i−i−iiii−i−i11-1-1−i−iii
χ171111-1-11111-1-1-1111-1-11111111111111111-11-1-1111-1-11111-1-1-1-111-1-1-111-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-1-1-11-11-11-11-1
χ181111-1-11111-1-1-1111-1-11111111-1-1-1-1-1-1-1-11-11-1-1111-1-1-1-1-1-1111111-1-1-111-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111111-11-1-11-11
χ191111-1-11111-1-1-1111-1-1111-1-1-1-1iiii−i−i−i−i1-11-1-11-1-111ii−i−i−i−iii11-1-1-111-1-11-1-111ii−i−i−i−iii-1-111ii−i−i−i−i−iiii1-1-11i−i−ii
χ201111-1-11111-1-1-1111-1-1111-1-1-1-1−i−i−i−iiiii1-11-1-11-1-111−i−iiiii−i−i11-1-1-111-1-11-1-111−i−iiiii−i−i-1-111−i−iiiiii−i−i−i1-1-11−iii−i
χ211111-1-11111-1-1-11-1-111111111111111111-111-1-1111-1-11111-1-1-1-111-1-1-1-1-111-111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-11-11-11-11
χ221111-1-11111-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-1111111-1-1-1-1-111-111-1-111-1-111-1-1-1-111-1-1-1-1111111-11-111-11-1
χ231111-1-11111-1-1-11-1-111111-1-1-1-1iiii−i−i−i−i-111-1-11-1-111ii−i−i−i−iii11-1-1-1-1-1111-1-111−i−iiiii−i−i11-1-1ii−i−i−i−i−iiii-111-1−iii−i
χ241111-1-11111-1-1-11-1-111111-1-1-1-1−i−i−i−iiiii-111-1-11-1-111−i−iiiii−i−i11-1-1-1-1-1111-1-111ii−i−i−i−iii11-1-1−i−iiiiii−i−i−i-111-1i−i−ii
χ251111-1-111-1-111-1111-1-1111111111111111-111-1-1111-1-11111-1-1-1-1-1-1-11111-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-111-111-11-11-11-11
χ261111-1-111-1-111-1111-1-11111111-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-11111-1-1-11111-1-1-1-1-111-1-111-1-11111-1-111111-1-11-1-1-11-111-11-1
χ271111-1-111-1-111-1111-1-1111-1-1-1-1iiii−i−i−i−i-111-1-11-1-111ii−i−i−i−iii-1-1-11111-1-1111-1-1ii−i−i−i−iii-1-111−i−iii−iiii−i−i-111-1−iii−i
χ281111-1-111-1-111-1111-1-1111-1-1-1-1−i−i−i−iiiii-111-1-11-1-111−i−iiiii−i−i-1-1-11111-1-1111-1-1−i−iiiii−i−i-1-111ii−i−ii−i−i−iii-111-1i−i−ii
χ291111-1-111-1-111-11-1-1111111111111111111-11-1-1111-1-11111-1-1-1-1-1-1-111-1-111-1-1-111-1-111-1-111-1-111-1-1-1-1-111-1111-11-11-11-1
χ301111-1-111-1-111-11-1-1111111111-1-1-1-1-1-1-1-11-11-1-1111-1-1-1-1-1-11111-1-1-111-1-111-1-1-11111-1-111-1-1-1-11111111-1-11-1-11-11-1-11-11
χ311111-1-111-1-111-11-1-111111-1-1-1-1iiii−i−i−i−i1-11-1-11-1-111ii−i−i−i−iii-1-1-111-1-111111-1-1−i−iiiii−i−i11-1-1−i−iii−iiii−i−i1-1-11i−i−ii
χ321111-1-111-1-111-11-1-111111-1-1-1-1−i−i−i−iiiii1-11-1-11-1-111−i−iiiii−i−i-1-1-111-1-111111-1-1ii−i−i−i−iii11-1-1ii−i−ii−i−i−iii1-1-11−iii−i
χ33222222-2-20000-22000022222222222222200-222-2-2-222-2-2-2-2222200-2000000-200000000000000000000-200-20000000000
χ34222222-2-20000-2200002222222-2-2-2-2-2-2-2-200-222-2-2-2222222-2-2-2-200-2000000-20000000000000000000020020000000000
χ35222222-2-20000-220000222-2-2-2-22i2i2i2i−2i−2i−2i−2i00-222-222-2-2−2i−2i2i2i2i2i−2i−2i00-2000000200000000000000000000−2i002i0000000000
χ36222222-2-20000-220000222-2-2-2-2−2i−2i−2i−2i2i2i2i2i00-222-222-2-22i2i−2i−2i−2i−2i2i2i00-20000002000000000000000000002i00−2i0000000000
χ372222-2-2-2-2000022000022222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200200000020000000000000000000020020000000000
χ382222-2-2-2-200002200002222222-2-2-2-2-2-2-2-200-2-2-2-2-2-2-2-222222222002000000200000000000000000000-200-20000000000
χ392222-2-2-2-20000220000222-2-2-2-22i2i2i2i−2i−2i−2i−2i00-2-2-2-22222−2i−2i2i2i−2i−2i2i2i002000000-2000000000000000000002i00−2i0000000000
χ402222-2-2-2-20000220000222-2-2-2-2−2i−2i−2i−2i2i2i2i2i00-2-2-2-222222i2i−2i−2i2i2i−2i−2i002000000-200000000000000000000−2i002i0000000000
χ4122-2-22-2000000022−22−2-2-222i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30002-20002i−2i00002ζ−2ζ2ζ3−2ζ3000002−22−2000001+i−1−i1+i−1−i1−i−1+i1−i−1+ii2−i2i2−i2000000000000000000
χ4222-2-22-2000000022−22−2-2-222i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30002-20002i−2i0000−2ζ2ζ−2ζ32ζ3000002−22−200000−1−i1+i−1−i1+i−1+i1−i−1+i1−ii2−i2i2−i2000000000000000000
χ4322-2-22-2000000022−22−2-2-22−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0002-2000−2i2i00002ζ3−2ζ32ζ−2ζ000002−22−200000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−i2i2−i2i2000000000000000000
χ4422-2-22-2000000022−22−2-2-22−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0002-2000−2i2i0000−2ζ32ζ3−2ζ2ζ000002−22−2000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−i2i2−i2i2000000000000000000
χ4522-2-22-200000002−22−22-2-222i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30002-20002i−2i00002ζ−2ζ2ζ3−2ζ300000−22−2200000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−i2i2−i2i2000000000000000000
χ4622-2-22-200000002−22−22-2-222i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30002-20002i−2i0000−2ζ2ζ−2ζ32ζ300000−22−22000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−i2i2−i2i2000000000000000000
χ4722-2-22-200000002−22−22-2-22−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0002-2000−2i2i00002ζ3−2ζ32ζ−2ζ00000−22−22000001−i−1+i1−i−1+i1+i−1−i1+i−1−ii2−i2i2−i2000000000000000000
χ4822-2-22-200000002−22−22-2-22−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0002-2000−2i2i0000−2ζ32ζ3−2ζ2ζ00000−22−2200000−1+i1−i−1+i1−i−1−i1+i−1−i1+ii2−i2i2−i2000000000000000000
χ4922-2-2-22000000022−2−22-2-222i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000-22000−2i2i0000−2ζ2ζ−2ζ32ζ3000002−2−22000001+i−1−i−1−i1+i1−i−1+i−1+i1−ii2−i2−i2i2000000000000000000
χ5022-2-2-22000000022−2−22-2-222i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000-22000−2i2i00002ζ−2ζ2ζ3−2ζ3000002−2−2200000−1−i1+i1+i−1−i−1+i1−i1−i−1+ii2−i2−i2i2000000000000000000
χ5122-2-2-22000000022−2−22-2-22−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000-220002i−2i0000−2ζ32ζ3−2ζ2ζ000002−2−2200000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−i2i2i2−i2000000000000000000
χ5222-2-2-22000000022−2−22-2-22−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000-220002i−2i00002ζ3−2ζ32ζ−2ζ000002−2−22000001−i−1+i−1+i1−i1+i−1−i−1−i1+i−i2i2i2−i2000000000000000000
χ5322-2-2-2200000002−222−2-2-222i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000-22000−2i2i0000−2ζ2ζ−2ζ32ζ300000−222−200000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−i2i2i2−i2000000000000000000
χ5422-2-2-2200000002−222−2-2-222i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000-22000−2i2i00002ζ−2ζ2ζ3−2ζ300000−222−2000001+i−1−i−1−i1+i1−i−1+i−1+i1−i−i2i2i2−i2000000000000000000
χ5522-2-2-2200000002−222−2-2-22−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000-220002i−2i0000−2ζ32ζ3−2ζ2ζ00000−222−2000001−i−1+i−1+i1−i1+i−1−i−1−i1+ii2−i2−i2i2000000000000000000
χ5622-2-2-2200000002−222−2-2-22−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000-220002i−2i00002ζ3−2ζ32ζ−2ζ00000−222−200000−1+i1−i1−i−1+i−1−i1+i1+i−1−ii2−i2−i2i2000000000000000000
χ572-22-2002-22-2000200002-2-222-2-22-22-22-22-200200-22-2002-22-200002-2000000002-2000000000000002-22-200000000000000
χ582-22-2002-22-2000200002-2-222-2-2-22-22-22-2200200-22-200-22-2200002-2000000002-200000000000000-22-2200000000000000
χ592-22-2002-22-2000200002-2-2-2-2222i−2i2i−2i−2i2i−2i2i00200-2-22002i−2i−2i2i00002-200000000-22000000000000002i−2i−2i2i00000000000000
χ602-22-2002-22-2000200002-2-2-2-222−2i2i−2i2i2i−2i2i−2i00200-2-2200−2i2i2i−2i00002-200000000-2200000000000000−2i2i2i−2i00000000000000
χ612-22-2002-2-22000200002-2-222-2-22-22-22-22-200200-22-2002-22-20000-2200000000-2200000000000000-22-2200000000000000
χ622-22-2002-2-22000200002-2-222-2-2-22-22-22-2200200-22-200-22-220000-2200000000-22000000000000002-22-200000000000000
χ632-22-2002-2-22000200002-2-2-2-2222i−2i2i−2i−2i2i−2i2i00200-2-22002i−2i−2i2i0000-22000000002-200000000000000−2i2i2i−2i00000000000000
χ642-22-2002-2-22000200002-2-2-2-222−2i2i−2i2i2i−2i2i−2i00200-2-2200−2i2i2i−2i0000-22000000002-2000000000000002i−2i−2i2i00000000000000
χ652-22-200-22002i−2i0200002-2-222-2-22-22-22-22-200-2002-2200-22-2200000002i−2i00000002i−2i000000000000000002i−2i02i−2i00000000
χ662-22-200-22002i−2i0200002-2-222-2-2-22-22-22-2200-2002-22002-22-200000002i−2i00000002i−2i00000000000000000−2i2i0−2i2i00000000
χ672-22-200-22002i−2i0200002-2-2-2-2222i−2i2i−2i−2i2i−2i2i00-20022-200−2i2i2i−2i00000002i−2i0000000−2i2i00000000000000000-2202-200000000
χ682-22-200-22002i−2i0200002-2-2-2-222−2i2i−2i2i2i−2i2i−2i00-20022-2002i−2i−2i2i00000002i−2i0000000−2i2i000000000000000002-20-2200000000
χ692-22-200-2200−2i2i0200002-2-222-2-22-22-22-22-200-2002-2200-22-220000000−2i2i0000000−2i2i00000000000000000−2i2i0−2i2i00000000
χ702-22-200-2200−2i2i0200002-2-222-2-2-22-22-22-2200-2002-22002-22-20000000−2i2i0000000−2i2i000000000000000002i−2i02i−2i00000000
χ712-22-200-2200−2i2i0200002-2-2-2-2222i−2i2i−2i−2i2i−2i2i00-20022-200−2i2i2i−2i0000000−2i2i00000002i−2i000000000000000002-20-2200000000
χ722-22-200-2200−2i2i0200002-2-2-2-222−2i2i−2i2i2i−2i2i−2i00-20022-2002i−2i−2i2i0000000−2i2i00000002i−2i00000000000000000-2202-200000000
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
χ7544444444-4-4-4-44-14444-1-1-1000000000000-4-4-1-1-1-100000000000011-111-1-1-1-100000000000000000000000000011000000
χ7644444444-4-4-4-44-1-4-4-4-4-1-1-100000000000044-1-1-1-100000000000011-1111111000000000000000000000000000-1-1000000
χ774444-4-44444-4-4-4-144-4-4-1-1-10000000000004-4-111-1000000000000-1-1111-1-111000000000000000000000000000-11000000
χ784444-4-44444-4-4-4-1-4-444-1-1-1000000000000-44-111-1000000000000-1-111111-1-10000000000000000000000000001-1000000
χ794444-4-444-4-444-4-144-4-4-1-1-1000000000000-44-111-1000000000000111-1-1-1-1110000000000000000000000000001-1000000
χ804444-4-444-4-444-4-1-4-444-1-1-10000000000004-4-111-1000000000000111-1-111-1-1000000000000000000000000000-11000000
χ814-4-4400000000040000-44-44i−4i−4i4i4ζ−4ζ−4ζ4ζ4ζ3−4ζ3−4ζ34ζ300000000000000000000000000000000000000000000000000000000000000
χ824-4-4400000000040000-44-44i−4i−4i4i−4ζ4ζ4ζ−4ζ−4ζ34ζ34ζ3−4ζ300000000000000000000000000000000000000000000000000000000000000
χ834-4-4400000000040000-44-4−4i4i4i−4i4ζ3−4ζ3−4ζ34ζ34ζ−4ζ−4ζ4ζ00000000000000000000000000000000000000000000000000000000000000
χ844-4-4400000000040000-44-4−4i4i4i−4i−4ζ34ζ34ζ3−4ζ3−4ζ4ζ4ζ−4ζ00000000000000000000000000000000000000000000000000000000000000
χ85888888-8-80000-8-20000-2-2-2000000000000002-2-2200000000000000200000000000000000000000000000000000000000
χ868888-8-8-8-800008-20000-2-2-200000000000000222200000000000000-200000000000000000000000000000000000000000
χ8788-8-88-80000000-242−4242−4222-2000000000000000-22000000000000000000−22−2200000000000000000000000000000000000
χ8888-8-88-80000000-2−4242−424222-2000000000000000-220000000000000000002−22−200000000000000000000000000000000000
χ8988-8-8-880000000-242−42−424222-20000000000000002-2000000000000000000−222−200000000000000000000000000000000000
χ9088-8-8-880000000-2−424242−4222-20000000000000002-20000000000000000002−2−2200000000000000000000000000000000000
χ918-88-8008-88-8000-20000-22200000000000000-2002000000000000-22000000000000000000000000000000000000000000
χ928-88-8008-8-88000-20000-22200000000000000-20020000000000002-2000000000000000000000000000000000000000000
χ938-88-800-88008i−8i0-20000-22200000000000000200-2000000000000000−2i2i000000000000000000000000000000000000000
χ948-88-800-8800−8i8i0-20000-22200000000000000200-20000000000000002i−2i000000000000000000000000000000000000000
χ9516-16-1616000000000-400004-4400000000000000000000000000000000000000000000000000000000000000000000000000

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