Finite Group Databasebeta

← Group #13017201

Character table — Group #13017201

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222244444444444445555555555558888881010101010101010101010101616161616161616162020202020202020202020202020202020202020202020202020203232404040404040
order12224444458888888810101044448888888844202020202244888888882040404040404040404444444448888888888888888882020448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111-1-1-1-1iiii−i−i−i−i111111-1-1-1-1ii−i−iii−i−i111111111-1iiii−i−i−i−i-1-1-1-1-1-1-1-1i−iiiii−i−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−i−i−i−iiiii-1-1-1-1-1-1-1-1−ii−i−i−i−iiiii11-1-1−i−iii
χ511111111111111-1-1-1-1111111111111111-1-1111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1
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−i−i−i−iiiii-1-1-1-11111i−iiiii−i−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−iii11111-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111−ii−i−i−i−iiiii-1-111ii−i−i
χ91111111111-1-1-1-11111111111111111111-1-111111111111111111-1-1-1-11111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ101111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111
χ111111111111-1-1-1-11111111-1-1-1-1iiii−i−i−i−i-1-11111-1-1-1-1ii−i−iii−i−i1-1-1-1-11111-1iiii−i−i−i−i1111-1-1-1-1i−i−i−i−i−iiiii-1-111−i−iii
χ121111111111-1-1-1-11111111-1-1-1-1−i−i−i−iiiii-1-11111-1-1-1-1−i−iii−i−iii1-1-1-1-11111-1−i−i−i−iiiii1111-1-1-1-1−iiiiii−i−i−i−i-1-111ii−i−i
χ131111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ141111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ151111111111-1-1-1-1-1-1-1-1111-1-1-1-1iiii−i−i−i−i111111-1-1-1-1ii−i−iii−i−i1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11111111i−i−i−i−i−iiiii11-1-1ii−i−i
χ161111111111-1-1-1-1-1-1-1-1111-1-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−iii−i−iii1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11111111−iiiiii−i−i−i−i11-1-1−i−iii
χ171111-1-1-1-111ii−i−iii−i−i1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11ii−i−iii−i−i1ii−i−iii−i−iii−i−iii−i−i11ii−i−iii−i−i1-11-11-11-1
χ181111-1-1-1-111ii−i−iii−i−i1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111111ii−i−iii−i−i1−i−iii−i−iiiii−i−iii−i−i-1-1−i−iii−i−iii1-11-1-11-11
χ191111-1-1-1-111ii−i−iii−i−i111-1-1-1-1iiii−i−i−i−i1-1-1-1-1-11111−i−iii−i−iii1ii−i−iii−i−i-1-1-11111-1-1−i−iii−i−iiii−i-1-11111-1-11-1-11i−i−ii
χ201111-1-1-1-111ii−i−iii−i−i111-1-1-1-1−i−i−i−iiiii1-1-1-1-1-11111ii−i−iii−i−i1ii−i−iii−i−i-111-1-1-1-111−i−iii−i−iii−ii11-1-1-1-1111-1-11−iii−i
χ211111-1-1-1-111ii−i−i−i−iii111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11ii−i−i−i−iii1−i−iii−i−iiiii−i−i−i−iii11ii−i−iii−i−i-11-11-11-11
χ221111-1-1-1-111ii−i−i−i−iii1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111ii−i−i−i−iii1ii−i−iii−i−iii−i−i−i−iii-1-1−i−iii−i−iii-11-111-11-1
χ231111-1-1-1-111ii−i−i−i−iii111-1-1-1-1iiii−i−i−i−i-11-1-1-1-11111−i−iii−i−iii1ii−i−i−i−iii-111-1-1-1-111−i−iiiii−i−ii−i-1-11111-1-1-111-1−iii−i
χ241111-1-1-1-111ii−i−i−i−iii111-1-1-1-1−i−i−i−iiiii-11-1-1-1-11111ii−i−iii−i−i1ii−i−i−i−iii-1-1-11111-1-1−i−iiiii−i−i−ii11-1-1-1-111-111-1i−i−ii
χ251111-1-1-1-111−i−iiiii−i−i111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i−iiiii−i−i1ii−i−iii−i−i−i−iiiii−i−i11−i−iii−i−iii-11-11-11-11
χ261111-1-1-1-111−i−iiiii−i−i1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111−i−iiiii−i−i1−i−iii−i−iii−i−iiiii−i−i-1-1ii−i−iii−i−i-11-111-11-1
χ271111-1-1-1-111−i−iiiii−i−i111-1-1-1-1iiii−i−i−i−i-11-1-1-1-11111−i−iii−i−iii1−i−iiiii−i−i-1-1-11111-1-1ii−i−i−i−iiii−i11-1-1-1-111-111-1−iii−i
χ281111-1-1-1-111−i−iiiii−i−i111-1-1-1-1−i−i−i−iiiii-11-1-1-1-11111ii−i−iii−i−i1−i−iiiii−i−i-111-1-1-1-111ii−i−i−i−iii−ii-1-11111-1-1-111-1i−i−ii
χ291111-1-1-1-111−i−iii−i−iii1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i−iii−i−iii1−i−iii−i−iii−i−iii−i−iii11−i−iii−i−iii1-11-11-11-1
χ301111-1-1-1-111−i−iii−i−iii1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111111−i−iii−i−iii1ii−i−iii−i−i−i−iii−i−iii-1-1ii−i−iii−i−i1-11-1-11-11
χ311111-1-1-1-111−i−iii−i−iii111-1-1-1-1iiii−i−i−i−i1-1-1-1-1-11111−i−iii−i−iii1−i−iii−i−iii-111-1-1-1-111ii−i−iii−i−ii−i11-1-1-1-1111-1-11i−i−ii
χ321111-1-1-1-111−i−iii−i−iii111-1-1-1-1−i−i−i−iiiii1-1-1-1-1-11111ii−i−iii−i−i1−i−iii−i−iii-1-1-11111-1-1ii−i−iii−i−i−ii-1-11111-1-11-1-11−iii−i
χ3322222-2-22-2200000000222222222222222002-22-222-2-22222-2-2-2-2-200000000-20000000000000000-2-20000000000000000
χ3422222-2-22-22000000002222222-2-2-2-2-2-2-2-2002-22-222-2-2-2-2-2-22222-200000000-20000000000000000220000000000000000
χ3522222-2-22-2200000000222-2-2-2-22i2i2i2i−2i−2i−2i−2i002-22-2-2-2222i2i−2i−2i−2i−2i2i2i-20000000020000000000000000−2i2i0000000000000000
χ3622222-2-22-2200000000222-2-2-2-2−2i−2i−2i−2i2i2i2i2i002-22-2-2-222−2i−2i2i2i2i2i−2i−2i-200000000200000000000000002i−2i0000000000000000
χ372222-222-2-220000000022222222222222200-22-22-2-222-2-2-2-22222-200000000-20000000000000000-2-20000000000000000
χ382222-222-2-22000000002222222-2-2-2-2-2-2-2-200-22-22-2-2222222-2-2-2-2-200000000-20000000000000000220000000000000000
χ392222-222-2-2200000000222-2-2-2-22i2i2i2i−2i−2i−2i−2i00-22-2222-2-2−2i−2i2i2i2i2i−2i−2i-20000000020000000000000000−2i2i0000000000000000
χ402222-222-2-2200000000222-2-2-2-2−2i−2i−2i−2i2i2i2i2i00-22-2222-2-22i2i−2i−2i−2i−2i2i2i-200000000200000000000000002i−2i0000000000000000
χ4122-2-2200-2022−22−200002-2-222-2-222-2-222-2-20020-202-2002-22-2000002−22−200000000000002−22−20000002−22−22−22−200000000
χ4222-2-2200-2022−22−200002-2-222-2-2-2-222-2-2220020-202-200-22-22000002−22−200000000000002−22−2000000−22−22−22−2200000000
χ4322-2-2200-2022−22−200002-2-2-2-2222i2i−2i−2i−2i−2i2i2i0020-20-22002i−2i−2i2i000002−22−20000000000000−22−22000000i2−i2i2−i2−i2i2−i2i200000000
χ4422-2-2200-2022−22−200002-2-2-2-222−2i−2i2i2i2i2i−2i−2i0020-20-2200−2i2i2i−2i000002−22−20000000000000−22−22000000−i2i2−i2i2i2−i2i2−i200000000
χ4522-2-2200-202−22−2200002-2-222-2-222-2-222-2-20020-202-2002-22-200000−22−220000000000000−22−22000000−22−22−22−2200000000
χ4622-2-2200-202−22−2200002-2-222-2-2-2-222-2-2220020-202-200-22-2200000−22−220000000000000−22−220000002−22−22−22−200000000
χ4722-2-2200-202−22−2200002-2-2-2-2222i2i−2i−2i−2i−2i2i2i0020-20-22002i−2i−2i2i00000−22−2200000000000002−22−2000000−i2i2−i2i2i2−i2i2−i200000000
χ4822-2-2200-202−22−2200002-2-2-2-222−2i−2i2i2i2i2i−2i−2i0020-20-2200−2i2i2i−2i00000−22−2200000000000002−22−2000000i2−i2i2−i2−i2i2−i2i200000000
χ4922-2-2-200202i2−i2−i2i200002-2-222-2-222-2-222-2-200-2020-2200-22-2200000i2−i2−i2i20000000000000i2−i2−i2i2000000i2−i2−i2i2i2−i2−i2i200000000
χ5022-2-2-200202i2−i2−i2i200002-2-222-2-2-2-222-2-22200-2020-22002-22-200000i2−i2−i2i20000000000000i2−i2−i2i2000000−i2i2i2−i2−i2i2i2−i200000000
χ5122-2-2-200202i2−i2−i2i200002-2-2-2-2222i2i−2i−2i−2i−2i2i2i00-20202-200−2i2i2i−2i00000i2−i2−i2i20000000000000−i2i2i2−i2000000−222−22−2−2200000000
χ5222-2-2-200202i2−i2−i2i200002-2-2-2-222−2i−2i2i2i2i2i−2i−2i00-20202-2002i−2i−2i2i00000i2−i2−i2i20000000000000−i2i2i2−i20000002−2−22−222−200000000
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χ5422-2-2-200202−i2i2i2−i200002-2-222-2-2-2-222-2-22200-2020-22002-22-200000−i2i2i2−i20000000000000−i2i2i2−i2000000i2−i2−i2i2i2−i2−i2i200000000
χ5522-2-2-200202−i2i2i2−i200002-2-2-2-2222i2i−2i−2i−2i−2i2i2i00-20202-200−2i2i2i−2i00000−i2i2i2−i20000000000000i2−i2−i2i20000002−2−22−222−200000000
χ5622-2-2-200202−i2i2i2−i200002-2-2-2-222−2i−2i2i2i2i2i−2i−2i00-20202-2002i−2i−2i2i00000−i2i2i2−i20000000000000i2−i2−i2i2000000−222−22−2−2200000000
χ572-2-2202-20020000i2−i2i2−i2-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000-202002i−2i00002ζ−2ζ2ζ3−2ζ300000i2−i2i2−i201−i−1+i1−i−1+i1+i−1−i1+i−1−i00002−22−2000000000000000000
χ582-2-2202-20020000i2−i2i2−i2-22-22i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000-202002i−2i0000−2ζ2ζ−2ζ32ζ300000i2−i2i2−i20−1+i1−i−1+i1−i−1−i1+i−1−i1+i00002−22−2000000000000000000
χ592-2-2202-20020000i2−i2i2−i2-22-2−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000-20200−2i2i00002ζ3−2ζ32ζ−2ζ00000i2−i2i2−i201+i−1−i1+i−1−i1−i−1+i1−i−1+i0000−22−22000000000000000000
χ602-2-2202-20020000i2−i2i2−i2-22-2−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000-20200−2i2i0000−2ζ32ζ3−2ζ2ζ00000i2−i2i2−i20−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000−22−22000000000000000000
χ612-2-2202-20020000−i2i2−i2i2-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000-202002i−2i00002ζ−2ζ2ζ3−2ζ300000−i2i2−i2i20−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000−22−22000000000000000000
χ622-2-2202-20020000−i2i2−i2i2-22-22i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000-202002i−2i0000−2ζ2ζ−2ζ32ζ300000−i2i2−i2i201−i−1+i1−i−1+i1+i−1−i1+i−1−i0000−22−22000000000000000000
χ632-2-2202-20020000−i2i2−i2i2-22-2−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000-20200−2i2i00002ζ3−2ζ32ζ−2ζ00000−i2i2−i2i20−1−i1+i−1−i1+i−1+i1−i−1+i1−i00002−22−2000000000000000000
χ642-2-2202-20020000−i2i2−i2i2-22-2−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000-20200−2i2i0000−2ζ32ζ3−2ζ2ζ00000−i2i2−i2i201+i−1−i1+i−1−i1−i−1+i1−i−1+i00002−22−2000000000000000000
χ652-2-220-2200200002−2−22-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300020-200−2i2i0000−2ζ2ζ−2ζ32ζ3000002−2−220−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000−i2i2i2−i2000000000000000000
χ662-2-220-2200200002−2−22-22-22i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300020-200−2i2i00002ζ−2ζ2ζ3−2ζ3000002−2−2201+i−1−i−1−i1+i−1+i1−i1−i−1+i0000−i2i2i2−i2000000000000000000
χ672-2-220-2200200002−2−22-22-2−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00020-2002i−2i0000−2ζ32ζ3−2ζ2ζ000002−2−2201−i−1+i−1+i1−i−1−i1+i1+i−1−i0000i2−i2−i2i2000000000000000000
χ682-2-220-2200200002−2−22-22-2−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00020-2002i−2i00002ζ3−2ζ32ζ−2ζ000002−2−220−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000i2−i2−i2i2000000000000000000
χ692-2-220-220020000−222−2-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300020-200−2i2i0000−2ζ2ζ−2ζ32ζ300000−222−201+i−1−i−1−i1+i−1+i1−i1−i−1+i0000i2−i2−i2i2000000000000000000
χ702-2-220-220020000−222−2-22-22i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300020-200−2i2i00002ζ−2ζ2ζ3−2ζ300000−222−20−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000i2−i2−i2i2000000000000000000
χ712-2-220-220020000−222−2-22-2−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00020-2002i−2i0000−2ζ32ζ3−2ζ2ζ00000−222−20−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000−i2i2i2−i2000000000000000000
χ722-2-220-220020000−222−2-22-2−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00020-2002i−2i00002ζ3−2ζ32ζ−2ζ00000−222−201−i−1+i−1+i1−i−1−i1+i1+i−1−i0000−i2i2i2−i2000000000000000000
χ73444444444-144444444-1-1-100000000000044-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1000000000000000000000000000-1-1000000
χ74444444444-14444-4-4-4-4-1-1-1000000000000-4-4-1-1-1-1000000000000-1-1-1-1-1111100000000000000000000000000011000000
χ75444444444-1-4-4-4-44444-1-1-1000000000000-4-4-1-1-1-1000000000000-11111-1-1-1-100000000000000000000000000011000000
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χ8588888-8-88-8-200000000-2-2-200000000000000-22-2200000000000020000000000000000000000000000000000000000000
χ868888-888-8-8-200000000-2-2-2000000000000002-22-200000000000020000000000000000000000000000000000000000000
χ8788-8-8800-80-242−4242−420000-22200000000000000-20200000000000000−22−22000000000000000000000000000000000000000
χ8888-8-8800-80-2−4242−42420000-22200000000000000-202000000000000002−22−2000000000000000000000000000000000000000
χ8988-8-8-80080-24i2−4i2−4i24i20000-2220000000000000020-200000000000000−i2i2i2−i2000000000000000000000000000000000000000
χ9088-8-8-80080-2−4i24i24i2−4i20000-2220000000000000020-200000000000000i2−i2−i2i2000000000000000000000000000000000000000
χ918-8-8808-800-200004i2−4i24i2−4i22-2200000000000000020-200000000000000000−i2i2−i2i200000000000000000000000000000000000
χ928-8-8808-800-20000−4i24i2−4i24i22-2200000000000000020-200000000000000000i2−i2i2−i200000000000000000000000000000000000
χ938-8-880-8800-2000042−42−42422-22000000000000000-20200000000000000000−222−200000000000000000000000000000000000
χ948-8-880-8800-20000−424242−422-22000000000000000-202000000000000000002−2−2200000000000000000000000000000000000
χ9516-1616-1600000-40000000044-400000000000000000000000000000000000000000000000000000000000000000000000000

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