Finite Group Databasebeta

← Group #13031895

Character table — Group #13031895

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222244444444444445555555555558888881010101010101010101010101616161616161616162020202020202020202020202020202020202020202020202020203232404040404040
order12224444444445888810101044448888888824202020204444888888882020202020404040402224488888888888888888888881020448888
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−i111111111-1-1-1-1-1-1-1-1-1iiiii−i−i−i−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−i−i−iiiiii−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−i11111-1-1-1-1-1-1-1-1-11111iiiii−i−i−i−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−i−i−iiiiiiiiii−i−i−i−i-1-111ii−i−i
χ911111111-1-11-1-111111111111111111111-1-111111111111111111-1-1-1-111111-1-1-1-111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1
χ1011111111-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-11111-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ1111111111-1-11-1-111111111-1-1-1-1iiii−i−i−i−i-1-11111-1-1-1-1iiii−i−i−i−i1-1-1-1-11111-11111-1-1-1-1i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iii
χ1211111111-1-11-1-111111111-1-1-1-1−i−i−i−iiiii-1-11111-1-1-1-1−i−i−i−iiiii1-1-1-1-11111-11111-1-1-1-1−iiiiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i
χ1311111111-1-11-1-11-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111
χ1411111111-1-11-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-11111-11111111111111111-1-1-1-1
χ1511111111-1-11-1-11-1-1-1-1111-1-1-1-1iiii−i−i−i−i111111-1-1-1-1iiii−i−i−i−i1-1-1-1-1-1-1-1-1-111111111i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−i
χ1611111111-1-11-1-11-1-1-1-1111-1-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−iiiii1-1-1-1-1-1-1-1-1-111111111−iiiiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii
χ171111-1-11111-1-1-1111-1-11111111111111111-1-1-111-1-11111-1-111-1-1-1-1-11111-1-1-1-1-11111-1-1-111-1-1-111-1-111-1-111-1-11-11-11-11-1
χ181111-1-11111-1-1-1111-1-11111111-1-1-1-1-1-1-1-11-1-1-111-1-111-1-111-1-111-1-1-11111-1-1-1-1-11111-1-11-1-1111-1-111-1-111-1-1111-11-1-11-11
χ191111-1-11111-1-1-1111-1-1111-1-1-1-1iiii−i−i−i−i1-1-1-11111-1-1ii−i−i−i−iii-1-1-11111-1-1111-1-1-1-111−iii−i−ii−i−iiiii−i−i−i−iii1-1-11i−i−ii
χ201111-1-11111-1-1-1111-1-1111-1-1-1-1−i−i−i−iiiii1-1-1-11111-1-1−i−iiiii−i−i-1-1-11111-1-1111-1-1-1-111i−i−iii−iii−i−i−i−iiiii−i−i1-1-11−iii−i
χ211111-1-11111-1-1-11-1-111111111111111111-11-1-111-1-11111-1-111-1-1-1-1-111-1-111-1-1-111-1-111-111-1-1-111-1-1-1-111-1-111-11-11-11-11
χ221111-1-11111-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-11-1-111-1-111-1-111-1-111-1-1-111-1-111-1-1-111-1-1111-1-1111-1-11111-1-111-1-1-11-111-11-1
χ231111-1-11111-1-1-11-1-111111-1-1-1-1iiii−i−i−i−i-11-1-11111-1-1ii−i−i−i−iii-1-1-111-1-111111-1-111-1-1−iii−i−ii−i−iii−i−iiiii−i−i-111-1−iii−i
χ241111-1-11111-1-1-11-1-111111-1-1-1-1−i−i−i−iiiii-11-1-11111-1-1−i−iiiii−i−i-1-1-111-1-111111-1-111-1-1i−i−iii−iii−i−iii−i−i−i−iii-111-1i−i−ii
χ251111-1-111-1-1-111111-1-1111111111111111-11-1-111-1-11111-1-111-1-1-111-1-111-1-1-111-1-111-1-1-1-1-111-1-1-11111-1-111-1-1-11-11-11-11
χ261111-1-111-1-1-111111-1-11111111-1-1-1-1-1-1-1-1-11-1-111-1-111-1-111-1-111-111-1-111-1-1-111-1-111-1-1111-1-1111-1-1-1-111-1-111-11-111-11-1
χ271111-1-111-1-1-111111-1-1111-1-1-1-1iiii−i−i−i−i-11-1-11111-1-1ii−i−i−i−iii-111-1-111-1-11-1-111-1-111−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-11-1-11111-1-1−i−iiiii−i−i-111-1-111-1-11-1-111-1-111iii−i−i−i−i−iii−i−iiiii−i−i-111-1i−i−ii
χ291111-1-111-1-1-1111-1-1111111111111111111-1-1-111-1-11111-1-111-1-1-111-1-1-1-111-111-1-1-1-111-1-1-111-1-1-111-1-111-1-1111-11-11-11-1
χ301111-1-111-1-1-1111-1-1111111111-1-1-1-1-1-1-1-11-1-1-111-1-111-1-111-1-111-111-1-1-1-111-111-1-1-1-111111-1-1111-1-111-1-111-1-11-11-1-11-11
χ311111-1-111-1-1-1111-1-111111-1-1-1-1iiii−i−i−i−i1-1-1-11111-1-1ii−i−i−i−iii-111-1-1-1-1111-1-11111-1-1−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−iiiii1-1-1-11111-1-1−i−iiiii−i−i-111-1-1-1-1111-1-11111-1-1iii−i−i−i−i−iiiii−i−i−i−iii1-1-11−iii−i
χ33222222-2-200-200200002222222222222220022-2-222-2-2-2-222-2-222-200000000-200000000-20000-200000000000000000000
χ34222222-2-200-200200002222222-2-2-2-2-2-2-2-20022-2-222-2-222-2-222-2-2-200000000-20000000020000200000000000000000000
χ35222222-2-200-20020000222-2-2-2-22i2i2i2i−2i−2i−2i−2i0022-2-2-2-222−2i−2i2i2i2i2i−2i−2i-200000000200000000−2i00002i00000000000000000000
χ36222222-2-200-20020000222-2-2-2-2−2i−2i−2i−2i2i2i2i2i0022-2-2-2-2222i2i−2i−2i−2i−2i2i2i-2000000002000000002i0000−2i00000000000000000000
χ372222-2-2-2-2002002000022222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-220000000020000000020000200000000000000000000
χ382222-2-2-2-200200200002222222-2-2-2-2-2-2-2-200-2-2-2-2-2-2-2-222222222200000000200000000-20000-200000000000000000000
χ392222-2-2-2-20020020000222-2-2-2-22i2i2i2i−2i−2i−2i−2i00-2-2-2-22222−2i−2i−2i−2i2i2i2i2i200000000-2000000002i0000−2i00000000000000000000
χ402222-2-2-2-20020020000222-2-2-2-2−2i−2i−2i−2i2i2i2i2i00-2-2-2-222222i2i2i2i−2i−2i−2i−2i200000000-200000000−2i00002i00000000000000000000
χ4122-2-2002-22-200020000-2-222i2i−2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000-22002i−2i2ζ−2ζ002ζ3−2ζ3000002-200000002i−2i000002ζ−2ζ0002ζ3−2ζ3000000000000000000
χ4222-2-2002-22-200020000-2-222i2i−2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000-22002i−2i−2ζ2ζ00−2ζ32ζ3000002-200000002i−2i00000−2ζ2ζ000−2ζ32ζ3000000000000000000
χ4322-2-2002-22-200020000-2-22−2i−2i2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000-2200−2i2i2ζ3−2ζ3002ζ−2ζ000002-20000000−2i2i000002ζ3−2ζ30002ζ−2ζ000000000000000000
χ4422-2-2002-22-200020000-2-22−2i−2i2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000-2200−2i2i−2ζ32ζ300−2ζ2ζ000002-20000000−2i2i00000−2ζ32ζ3000−2ζ2ζ000000000000000000
χ4522-2-2002-2-2200020000-2-222i2i−2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000-22002i−2i2ζ−2ζ002ζ3−2ζ300000-220000000−2i2i00000−2ζ2ζ000−2ζ32ζ3000000000000000000
χ4622-2-2002-2-2200020000-2-222i2i−2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000-22002i−2i−2ζ2ζ00−2ζ32ζ300000-220000000−2i2i000002ζ−2ζ0002ζ3−2ζ3000000000000000000
χ4722-2-2002-2-2200020000-2-22−2i−2i2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000-2200−2i2i2ζ3−2ζ3002ζ−2ζ00000-2200000002i−2i00000−2ζ32ζ3000−2ζ2ζ000000000000000000
χ4822-2-2002-2-2200020000-2-22−2i−2i2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000-2200−2i2i−2ζ32ζ300−2ζ2ζ00000-2200000002i−2i000002ζ3−2ζ30002ζ−2ζ000000000000000000
χ4922-2-200-220002i−2i20000-2-222i2i−2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300002-200−2i2i−2ζ2ζ00−2ζ32ζ30002i−2i00000002-20000000002ζ3−2ζ30002ζ−2ζ0000000000000000
χ5022-2-200-220002i−2i20000-2-222i2i−2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300002-200−2i2i2ζ−2ζ002ζ3−2ζ30002i−2i00000002-2000000000−2ζ32ζ3000−2ζ2ζ0000000000000000
χ5122-2-200-220002i−2i20000-2-22−2i−2i2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00002-2002i−2i−2ζ32ζ300−2ζ2ζ0002i−2i0000000-22000000000−2ζ2ζ000−2ζ32ζ30000000000000000
χ5222-2-200-220002i−2i20000-2-22−2i−2i2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00002-2002i−2i2ζ3−2ζ3002ζ−2ζ0002i−2i0000000-220000000002ζ−2ζ0002ζ3−2ζ30000000000000000
χ5322-2-200-22000−2i2i20000-2-222i2i−2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300002-200−2i2i−2ζ2ζ00−2ζ32ζ3000−2i2i0000000-22000000000−2ζ32ζ3000−2ζ2ζ0000000000000000
χ5422-2-200-22000−2i2i20000-2-222i2i−2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300002-200−2i2i2ζ−2ζ002ζ3−2ζ3000−2i2i0000000-220000000002ζ3−2ζ30002ζ−2ζ0000000000000000
χ5522-2-200-22000−2i2i20000-2-22−2i−2i2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00002-2002i−2i−2ζ32ζ300−2ζ2ζ000−2i2i00000002-20000000002ζ−2ζ0002ζ3−2ζ30000000000000000
χ5622-2-200-22000−2i2i20000-2-22−2i−2i2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00002-2002i−2i2ζ3−2ζ3002ζ−2ζ000−2i2i00000002-2000000000−2ζ2ζ000−2ζ32ζ30000000000000000
χ572-22-22i−2i00000002i2−i22−2-22-22-22-22-22-22-22-2002i−2i002i−2i00002i−2i002i−2i00000i2−i22−200000i2−i22−20000000000i2−i22−2i2−i22−200000000
χ582-22-22i−2i00000002i2−i22−2-22-22-22-2-22-22-22-22002i−2i002i−2i0000−2i2i00−2i2i00000i2−i22−200000i2−i22−20000000000−i2i2−22−i2i2−2200000000
χ592-22-22i−2i00000002i2−i22−2-22-2-22-222i−2i2i−2i−2i2i−2i2i002i−2i00−2i2i0000-22002-200000i2−i22−200000−i2i2−220000000000−22i2−i22−2−i2i200000000
χ602-22-22i−2i00000002i2−i22−2-22-2-22-22−2i2i−2i2i2i−2i2i−2i002i−2i00−2i2i00002-200-2200000i2−i22−200000−i2i2−2200000000002−2−i2i2−22i2−i200000000
χ612-22-22i−2i00000002−i2i2−22-22-22-22-22-22-22-22-2002i−2i002i−2i00002i−2i002i−2i00000−i2i2−2200000−i2i2−220000000000−i2i2−22−i2i2−2200000000
χ622-22-22i−2i00000002−i2i2−22-22-22-22-2-22-22-22-22002i−2i002i−2i0000−2i2i00−2i2i00000−i2i2−2200000−i2i2−220000000000i2−i22−2i2−i22−200000000
χ632-22-22i−2i00000002−i2i2−22-22-2-22-222i−2i2i−2i−2i2i−2i2i002i−2i00−2i2i0000-22002-200000−i2i2−2200000i2−i22−200000000002−2−i2i2−22i2−i200000000
χ642-22-22i−2i00000002−i2i2−22-22-2-22-22−2i2i−2i2i2i−2i2i−2i002i−2i00−2i2i00002-200-2200000−i2i2−2200000i2−i22−20000000000−22i2−i22−2−i2i200000000
χ652-22-2−2i2i00000002i2−i2−22-22-22-22-22-22-22-22-200−2i2i00−2i2i0000−2i2i00−2i2i00000i2−i2−2200000i2−i2−220000000000i2−i2−22i2−i2−2200000000
χ662-22-2−2i2i00000002i2−i2−22-22-22-22-2-22-22-22-2200−2i2i00−2i2i00002i−2i002i−2i00000i2−i2−2200000i2−i2−220000000000−i2i22−2−i2i22−200000000
χ672-22-2−2i2i00000002i2−i2−22-22-2-22-222i−2i2i−2i−2i2i−2i2i00−2i2i002i−2i00002-200-2200000i2−i2−2200000−i2i22−20000000000−22−i2i22−2i2−i200000000
χ682-22-2−2i2i00000002i2−i2−22-22-2-22-22−2i2i−2i2i2i−2i2i−2i00−2i2i002i−2i0000-22002-200000i2−i2−2200000−i2i22−200000000002−2i2−i2−22−i2i200000000
χ692-22-2−2i2i00000002−i2i22−2-22-22-22-22-22-22-22-200−2i2i00−2i2i0000−2i2i00−2i2i00000−i2i22−200000−i2i22−20000000000−i2i22−2−i2i22−200000000
χ702-22-2−2i2i00000002−i2i22−2-22-22-22-2-22-22-22-2200−2i2i00−2i2i00002i−2i002i−2i00000−i2i22−200000−i2i22−20000000000i2−i2−22i2−i2−2200000000
χ712-22-2−2i2i00000002−i2i22−2-22-2-22-222i−2i2i−2i−2i2i−2i2i00−2i2i002i−2i00002-200-2200000−i2i22−200000i2−i2−2200000000002−2i2−i2−22−i2i200000000
χ722-22-2−2i2i00000002−i2i22−2-22-2-22-22−2i2i−2i2i2i−2i2i−2i00−2i2i002i−2i0000-22002-200000−i2i22−200000i2−i2−220000000000−22−i2i22−2i2−i200000000
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
χ7544444444-4-44-4-4-14444-1-1-1000000000000-4-4-1-1-1-1000000000000-11111-1-1-1-100000000000000000000000000011000000
χ7644444444-4-44-4-4-1-4-4-4-4-1-1-100000000000044-1-1-1-1000000000000-111111111000000000000000000000000000-1-1000000
χ774444-4-44444-4-4-4-144-4-4-1-1-10000000000004-411-1-1000000000000111-1-1-1-111000000000000000000000000000-11000000
χ784444-4-44444-4-4-4-1-4-444-1-1-1000000000000-4411-1-1000000000000111-1-111-1-10000000000000000000000000001-1000000
χ794444-4-444-4-4-444-144-4-4-1-1-1000000000000-4411-1-10000000000001-1-111-1-1110000000000000000000000000001-1000000
χ804444-4-444-4-4-444-1-4-444-1-1-10000000000004-411-1-10000000000001-1-11111-1-1000000000000000000000000000-11000000
χ814-4-44000000000400004-4-44i−4i−4i4i4ζ−4ζ−4ζ4ζ4ζ3−4ζ3−4ζ34ζ300000000000000000000000000000000000000000000000000000000000000
χ824-4-44000000000400004-4-44i−4i−4i4i−4ζ4ζ4ζ−4ζ−4ζ34ζ34ζ3−4ζ300000000000000000000000000000000000000000000000000000000000000
χ834-4-44000000000400004-4-4−4i4i4i−4i4ζ3−4ζ3−4ζ34ζ34ζ−4ζ−4ζ4ζ00000000000000000000000000000000000000000000000000000000000000
χ844-4-44000000000400004-4-4−4i4i4i−4i−4ζ34ζ34ζ3−4ζ3−4ζ4ζ4ζ−4ζ00000000000000000000000000000000000000000000000000000000000000
χ85888888-8-800-800-20000-2-2-200000000000000-2-22200000000000020000000000000000000000000000000000000000000
χ868888-8-8-8-800800-20000-2-2-2000000000000002222000000000000-20000000000000000000000000000000000000000000
χ8788-8-8008-88-8000-2000022-200000000000000002-2000000000000000-22000000000000000000000000000000000000000
χ8888-8-8008-8-88000-2000022-200000000000000002-20000000000000002-2000000000000000000000000000000000000000
χ8988-8-800-880008i−8i-2000022-20000000000000000-220000000000000−2i2i00000000000000000000000000000000000000000
χ9088-8-800-88000−8i8i-2000022-20000000000000000-2200000000000002i−2i00000000000000000000000000000000000000000
χ918-88-88i−8i0000000-24i2−4i242−422-2200000000000000−2i2i0000000000000000000−i2i2−2200000000000000000000000000000000000
χ928-88-88i−8i0000000-2−4i24i2−42422-2200000000000000−2i2i0000000000000000000i2−i22−200000000000000000000000000000000000
χ938-88-8−8i8i0000000-24i2−4i2−42422-22000000000000002i−2i0000000000000000000−i2i22−200000000000000000000000000000000000
χ948-88-8−8i8i0000000-2−4i24i242−422-22000000000000002i−2i0000000000000000000i2−i2−2200000000000000000000000000000000000
χ9516-16-1616000000000-40000-44400000000000000000000000000000000000000000000000000000000000000000000000000

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