Finite Group Databasebeta

← Group #13036615

Character table — Group #13036615

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222244444444444445555555555558888881010101010101010101010101616161616161616162020202020202020202020202020202020202020202020202020203232404040404040
order12224444444445888810101044448888888844202020202244888888882020202020404040402244444444444888888888888882020448888
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
χ911111111-1-11-1-111111111111111111111-1-111111111111111111-1-1-1-11111-1-11-1-1111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1
χ1011111111-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-111111111-111-111-1-1-1-11111
χ1111111111-1-11-1-111111111-1-1-1-1iiii−i−i−i−i-1-11111-1-1-1-1ii−i−iii−i−i1-1-1-1-1111111-111iiii−i−i−i−i-1-1-1-1−i−iiii−i−i−iii-1-111−i−iii
χ1211111111-1-11-1-111111111-1-1-1-1−i−i−i−iiiii-1-11111-1-1-1-1−i−iii−i−iii1-1-1-1-1111111-111−i−i−i−iiiii-1-1-1-1ii−i−i−iiii−i−i-1-111ii−i−i
χ1311111111-1-11-1-11-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111
χ1411111111-1-11-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1-1-11111-111-1111111-1-1-1-1
χ1511111111-1-11-1-11-1-1-1-1111-1-1-1-1iiii−i−i−i−i111111-1-1-1-1ii−i−iii−i−i1-1-1-1-1-1-1-1-111-111−i−i−i−iiiii1111−i−iiii−i−i−iii11-1-1ii−i−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−iii1-1-1-1-1-1-1-1-111-111iiii−i−i−i−i1111ii−i−i−iiii−i−i11-1-1−i−iii
χ1711111-1-1111-1-1-1111-1-11111111111111111-11-1-1111-1-11111-1-1-1-1-111-1-111-1-111-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-11-11-11-11-1
χ1811111-1-1111-1-1-1111-1-11111111-1-1-1-1-1-1-1-11-11-1-1111-1-1-1-1-1-11111-111-1-111-1-111-1-1-1-1-111-1-11111-1-1-1-1-1-11111111-11-1-11-11
χ1911111-1-1111-1-1-1111-1-1111-1-1-1-1iiii−i−i−i−i1-11-1-11-1-111ii−i−i−i−iii-111-1-111-1-1-1-1111ii−i−i−i−iii-1-111ii−i−i−i−i−iiii1-1-11i−i−ii
χ2011111-1-1111-1-1-1111-1-1111-1-1-1-1−i−i−i−iiiii1-11-1-11-1-111−i−iiiii−i−i-111-1-111-1-1-1-1111−i−iiiii−i−i-1-111−i−iiiiii−i−i−i1-1-11−iii−i
χ2111111-1-1111-1-1-11-1-111111111111111111-111-1-1111-1-11111-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-11-11-11-11
χ2211111-1-1111-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-11111-111-1-1-1-11111-1-1-111-1-111-1-1-1-111-1-1-1-1111111-11-111-11-1
χ2311111-1-1111-1-1-11-1-111111-1-1-1-1iiii−i−i−i−i-111-1-11-1-111ii−i−i−i−iii-111-1-1-1-111-1-1111−i−iiiii−i−i11-1-1ii−i−i−i−i−iiii-111-1−iii−i
χ2411111-1-1111-1-1-11-1-111111-1-1-1-1−i−i−i−iiiii-111-1-11-1-111−i−iiiii−i−i-111-1-1-1-111-1-1111ii−i−i−i−iii11-1-1−i−iiiiii−i−i−i-111-1i−i−ii
χ2511111-1-11-1-1-111111-1-1111111111111111-111-1-1111-1-11111-1-1-1-1-1-1-11111-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-111-111-11-11-11-11
χ2611111-1-11-1-1-111111-1-11111111-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-11111-1-1-11111-1-1-1-1-111-1-111-1-11111-1-111111-1-11-1-1-11-111-11-1
χ2711111-1-11-1-1-111111-1-1111-1-1-1-1iiii−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
χ2811111-1-11-1-1-111111-1-1111-1-1-1-1−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
χ2911111-1-11-1-1-1111-1-1111111111111111111-11-1-1111-1-11111-1-1-1-1-1-1-111-1-111-1-1-111-1-111-1-111-1-111-1-1-1-1-111-1111-11-11-11-1
χ3011111-1-11-1-1-1111-1-1111111111-1-1-1-1-1-1-1-11-11-1-1111-1-1-1-1-1-11111-1-1-111-1-111-1-1-11111-1-111-1-1-1-11111111-1-11-1-11-11-1-11-11
χ3111111-1-11-1-1-1111-1-111111-1-1-1-1iiii−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
χ3211111-1-11-1-1-1111-1-111111-1-1-1-1−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
χ332222-222-200-2002000022222222222222200-222-2-2-222-2-2-2-22222-20000000000-2000000000000000000-200-20000000000
χ342222-222-200-200200002222222-2-2-2-2-2-2-2-200-222-2-2-2222222-2-2-2-2-20000000000-200000000000000000020020000000000
χ352222-222-200-20020000222-2-2-2-22i2i2i2i−2i−2i−2i−2i00-222-222-2-2−2i−2i2i2i2i2i−2i−2i-200000000002000000000000000000−2i002i0000000000
χ362222-222-200-20020000222-2-2-2-2−2i−2i−2i−2i2i2i2i2i00-222-222-2-22i2i−2i−2i−2i−2i2i2i-2000000000020000000000000000002i00−2i0000000000
χ372222-2-2-2-2002002000022222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-220000000000200000000000000000020020000000000
χ382222-2-2-2-200200200002222222-2-2-2-2-2-2-2-200-2-2-2-2-2-2-2-222222222200000000002000000000000000000-200-20000000000
χ392222-2-2-2-20020020000222-2-2-2-22i2i2i2i−2i−2i−2i−2i00-2-2-2-22222−2i−2i2i2i−2i−2i2i2i20000000000-20000000000000000002i00−2i0000000000
χ402222-2-2-2-20020020000222-2-2-2-2−2i−2i−2i−2i2i2i2i2i00-2-2-2-222222i2i−2i−2i2i2i−2i−2i20000000000-2000000000000000000−2i002i0000000000
χ4122-2-2200-22-2000200002-2-222-2-222-2-222-2-200200-22-2002-22-2000002-20000002-20000000000000002-22-200000000000000
χ4222-2-2200-22-2000200002-2-222-2-2-2-222-2-22200200-22-200-22-22000002-20000002-2000000000000000-22-2200000000000000
χ4322-2-2200-22-2000200002-2-2-2-2222i2i−2i−2i−2i−2i2i2i00200-2-22002i−2i−2i2i000002-2000000-220000000000000002i−2i−2i2i00000000000000
χ4422-2-2200-22-2000200002-2-2-2-222−2i−2i2i2i2i2i−2i−2i00200-2-2200−2i2i2i−2i000002-2000000-22000000000000000−2i2i2i−2i00000000000000
χ4522-2-2200-2-22000200002-2-222-2-222-2-222-2-200200-22-2002-22-200000-22000000-22000000000000000-22-2200000000000000
χ4622-2-2200-2-22000200002-2-222-2-2-2-222-2-22200200-22-200-22-2200000-22000000-220000000000000002-22-200000000000000
χ4722-2-2200-2-22000200002-2-2-2-2222i2i−2i−2i−2i−2i2i2i00200-2-22002i−2i−2i2i00000-220000002-2000000000000000−2i2i2i−2i00000000000000
χ4822-2-2200-2-22000200002-2-2-2-222−2i−2i2i2i2i2i−2i−2i00200-2-2200−2i2i2i−2i00000-220000002-20000000000000002i−2i−2i2i00000000000000
χ4922-2-2-20020002i−2i200002-2-222-2-222-2-222-2-200-2002-2200-22-2200000002i−2i00000002i−2i000000000000000002i−2i02i−2i00000000
χ5022-2-2-20020002i−2i200002-2-222-2-2-2-222-2-22200-2002-22002-22-200000002i−2i00000002i−2i00000000000000000−2i2i0−2i2i00000000
χ5122-2-2-20020002i−2i200002-2-2-2-2222i2i−2i−2i−2i−2i2i2i00-20022-200−2i2i2i−2i00000002i−2i0000000−2i2i00000000000000000-2202-200000000
χ5222-2-2-20020002i−2i200002-2-2-2-222−2i−2i2i2i2i2i−2i−2i00-20022-2002i−2i−2i2i00000002i−2i0000000−2i2i000000000000000002-20-2200000000
χ5322-2-2-2002000−2i2i200002-2-222-2-222-2-222-2-200-2002-2200-22-220000000−2i2i0000000−2i2i00000000000000000−2i2i0−2i2i00000000
χ5422-2-2-2002000−2i2i200002-2-222-2-2-2-222-2-22200-2002-22002-22-20000000−2i2i0000000−2i2i000000000000000002i−2i02i−2i00000000
χ5522-2-2-2002000−2i2i200002-2-2-2-2222i2i−2i−2i−2i−2i2i2i00-20022-200−2i2i2i−2i0000000−2i2i00000002i−2i000000000000000002-20-2200000000
χ5622-2-2-2002000−2i2i200002-2-2-2-222−2i−2i2i2i2i2i−2i−2i00-20022-2002i−2i−2i2i0000000−2i2i00000002i−2i00000000000000000-2202-200000000
χ572-22-202-20000002i2−i2i2−i2-2-222i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30002-20002i−2i00002ζ−2ζ2ζ3−2ζ300000i2−i2i2−i2000001−i−1+i1−i−1+i1+i−1−i1+i−1−i2−22−2000000000000000000
χ582-22-202-20000002i2−i2i2−i2-2-222i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30002-20002i−2i0000−2ζ2ζ−2ζ32ζ300000i2−i2i2−i200000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2−22−2000000000000000000
χ592-22-202-20000002i2−i2i2−i2-2-22−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0002-2000−2i2i00002ζ3−2ζ32ζ−2ζ00000i2−i2i2−i2000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−22−22000000000000000000
χ602-22-202-20000002i2−i2i2−i2-2-22−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0002-2000−2i2i0000−2ζ32ζ3−2ζ2ζ00000i2−i2i2−i200000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−22−22000000000000000000
χ612-22-202-20000002−i2i2−i2i2-2-222i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30002-20002i−2i00002ζ−2ζ2ζ3−2ζ300000−i2i2−i2i200000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−22−22000000000000000000
χ622-22-202-20000002−i2i2−i2i2-2-222i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30002-20002i−2i0000−2ζ2ζ−2ζ32ζ300000−i2i2−i2i2000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−22−22000000000000000000
χ632-22-202-20000002−i2i2−i2i2-2-22−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0002-2000−2i2i00002ζ3−2ζ32ζ−2ζ00000−i2i2−i2i200000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2−22−2000000000000000000
χ642-22-202-20000002−i2i2−i2i2-2-22−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0002-2000−2i2i0000−2ζ32ζ3−2ζ2ζ00000−i2i2−i2i2000001+i−1−i1+i−1−i1−i−1+i1−i−1+i2−22−2000000000000000000
χ652-22-20-220000002i2−i2−i2i2-2-222i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000-22000−2i2i0000−2ζ2ζ−2ζ32ζ300000i2−i2−i2i2000001−i−1+i−1+i1−i1+i−1−i−1−i1+i2−2−22000000000000000000
χ662-22-20-220000002i2−i2−i2i2-2-222i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000-22000−2i2i00002ζ−2ζ2ζ3−2ζ300000i2−i2−i2i200000−1+i1−i1−i−1+i−1−i1+i1+i−1−i2−2−22000000000000000000
χ672-22-20-220000002i2−i2−i2i2-2-22−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000-220002i−2i0000−2ζ32ζ3−2ζ2ζ00000i2−i2−i2i2000001+i−1−i−1−i1+i1−i−1+i−1+i1−i−222−2000000000000000000
χ682-22-20-220000002i2−i2−i2i2-2-22−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000-220002i−2i00002ζ3−2ζ32ζ−2ζ00000i2−i2−i2i200000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−222−2000000000000000000
χ692-22-20-220000002−i2i2i2−i2-2-222i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000-22000−2i2i0000−2ζ2ζ−2ζ32ζ300000−i2i2i2−i200000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−222−2000000000000000000
χ702-22-20-220000002−i2i2i2−i2-2-222i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000-22000−2i2i00002ζ−2ζ2ζ3−2ζ300000−i2i2i2−i2000001−i−1+i−1+i1−i1+i−1−i−1−i1+i−222−2000000000000000000
χ712-22-20-220000002−i2i2i2−i2-2-22−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000-220002i−2i0000−2ζ32ζ3−2ζ2ζ00000−i2i2i2−i200000−1−i1+i1+i−1−i−1+i1−i1−i−1+i2−2−22000000000000000000
χ722-22-20-220000002−i2i2i2−i2-2-22−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000-220002i−2i00002ζ3−2ζ32ζ−2ζ00000−i2i2i2−i2000001+i−1−i−1−i1+i1−i−1+i−1+i1−i2−2−22000000000000000000
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χ938-88-80-88000000-24i2−4i2−4i24i222-20000000000000002-2000000000000000000−i2i2i2−i200000000000000000000000000000000000
χ948-88-80-88000000-2−4i24i24i2−4i222-20000000000000002-2000000000000000000i2−i2−i2i200000000000000000000000000000000000
χ9516-16-1616000000000-400004-4400000000000000000000000000000000000000000000000000000000000000000000000000

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