Finite Group Databasebeta

← Group #13020760

Character table — Group #13020760

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size1111222244444444455558888881010101010101010101010101616161616161616161620202020202020202020202020202020203232404040404040808080
order12224444458888101010444488202020204444888888882204040404040404040288888888888888881010888888488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1
χ3111111111111111111111-1-11111111111111111-111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ511111111111111111-1-1-1-1111111-1-1-1-1iiii−i−i−i−i1111111111-1-1-1-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−i-1i−i
χ611111111111111111-1-1-1-1111111-1-1-1-1−i−i−i−iiiii1111111111-1-1-1-1-1−i−iii−i−iii−i−iii11-1-1−i−iii-1−ii
χ711111111111111111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-111111-1-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−i-1-111−i−iii1−ii
χ811111111111111111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-111111-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii-1-111ii−i−i1i−i
χ91111111111-1-1-1-11111111111111111111111111-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1
χ101111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-111
χ111111111111-1-1-1-11111111-1-1111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111
χ121111111111-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-111-1-111111-1-1
χ131111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1iiii−i−i−i−i-11-1-1-1-11111-11111−i−iii−i−iiiii−i−i-1-1-1-1ii−i−i1−ii
χ141111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1−i−i−i−iiiii-11-1-1-1-11111-11111ii−i−iii−i−i−i−iii-1-1-1-1−i−iii1i−i
χ151111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−i1111−i−iii-1i−i
χ161111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii1111ii−i−i-1−ii
χ1722222-22-2-2200002222222002-22-222-2-2222222220-200000000-2000000000000-2-2-2-200000000000
χ1822222-22-2-2200002222222002-22-222-2-2-2-2-2-2-2-2-2-20-200000000-2000000000000222200000000000
χ1922222-22-2-220000222-2-2-2-2002-22-2-2-2222i2i2i2i−2i−2i−2i−2i0-2000000002000000000000−2i−2i2i2i00000000000
χ2022222-22-2-220000222-2-2-2-2002-22-2-2-222−2i−2i−2i−2i2i2i2i2i0-20000000020000000000002i2i−2i−2i00000000000
χ212222-22-22-220000222222200-22-22-2-222000000000-200000000-200002222-2-2-2-2000000000000000
χ222222-22-22-220000222222200-22-22-2-222000000000-200000000-20000-2-2-2-22222000000000000000
χ232222-22-22-220000222-2-2-2-200-22-2222-2-2000000000-200000000200002i2i−2i−2i−2i−2i2i2i000000000000000
χ242222-22-22-220000222-2-2-2-200-22-2222-2-2000000000-20000000020000−2i−2i2i2i2i2i−2i−2i000000000000000
χ252222-2-2-2-2222i2i−2i−2i222222200-2-2-2-2-2-2-2-200000000022i2i−2i−2i000022i2i−2i−2i00000000000000000000000
χ262222-2-2-2-2222i2i−2i−2i222-2-2-2-200-2-2-2-2222200000000022i2i−2i−2i0000-2−2i−2i2i2i00000000000000000000000
χ272222-2-2-2-222−2i−2i2i2i222222200-2-2-2-2-2-2-2-20000000002−2i−2i2i2i00002−2i−2i2i2i00000000000000000000000
χ282222-2-2-2-222−2i−2i2i2i222-2-2-2-200-2-2-2-222220000000002−2i−2i2i2i0000-22i2i−2i−2i00000000000000000000000
χ2922-2-2020-2022−22−22-2-22i−2i2i−2i000-202002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i002−22−200000i2−i2i2−i20000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ391+i−1−i1−i−1+i00000000000
χ3022-2-2020-2022−22−22-2-22i−2i2i−2i000-202002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i002−22−200000i2−i2i2−i200002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−1−i1+i−1+i1−i00000000000
χ3122-2-2020-2022−22−22-2-2−2i2i−2i2i000-20200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i002−22−200000−i2i2−i2i200002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ371−i−1+i1+i−1−i00000000000
χ3222-2-2020-2022−22−22-2-2−2i2i−2i2i000-20200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i002−22−200000−i2i2−i2i20000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−1+i1−i−1−i1+i00000000000
χ3322-2-2020-202−22−222-2-22i−2i2i−2i000-202002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00−22−2200000−i2i2−i2i200002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ391+i−1−i1−i−1+i00000000000
χ3422-2-2020-202−22−222-2-22i−2i2i−2i000-202002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−22−2200000−i2i2−i2i20000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−1−i1+i−1+i1−i00000000000
χ3522-2-2020-202−22−222-2-2−2i2i−2i2i000-20200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00−22−2200000i2−i2i2−i20000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ371−i−1+i1+i−1−i00000000000
χ3622-2-2020-202−22−222-2-2−2i2i−2i2i000-20200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00−22−2200000i2−i2i2−i200002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−1+i1−i−1−i1+i00000000000
χ3722-2-20-20202i2−i2−i2i22-2-22i−2i2i−2i00020-200−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00i2−i2−i2i200000−222−2−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000−1−i1+i−1+i1−i00000000000
χ3822-2-20-20202i2−i2−i2i22-2-22i−2i2i−2i00020-200−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00i2−i2−i2i200000−222−22ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700001+i−1−i1−i−1+i00000000000
χ3922-2-20-20202i2−i2−i2i22-2-2−2i2i−2i2i00020-2002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00i2−i2−i2i2000002−2−22−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000−1+i1−i−1−i1+i00000000000
χ4022-2-20-20202i2−i2−i2i22-2-2−2i2i−2i2i00020-2002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00i2−i2−i2i2000002−2−222ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900001−i−1+i1+i−1−i00000000000
χ4122-2-20-20202−i2i2i2−i22-2-22i−2i2i−2i00020-200−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00−i2i2i2−i2000002−2−222ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000−1−i1+i−1+i1−i00000000000
χ4222-2-20-20202−i2i2i2−i22-2-22i−2i2i−2i00020-200−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−i2i2i2−i2000002−2−22−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700001+i−1−i1−i−1+i00000000000
χ4322-2-20-20202−i2i2i2−i22-2-2−2i2i−2i2i00020-2002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00−i2i2i2−i200000−222−22ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000−1+i1−i−1−i1+i00000000000
χ4422-2-20-20202−i2i2i2−i22-2-2−2i2i−2i2i00020-2002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00−i2i2i2−i200000−222−2−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900001−i−1+i1+i−1−i00000000000
χ452-22-220-20020000-22-22i−2i−2i2i2−2-20202i−2i00−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000022−2−20000000000000000000i2−i21−i−1+i1+i−1−i000
χ462-22-220-20020000-22-22i−2i−2i2i2−2-20202i−2i002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000022−2−20000000000000000000i2−i2−1+i1−i−1−i1+i000
χ472-22-220-20020000-22-22i−2i−2i2i−22-20202i−2i00−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−2−2220000000000000000000−i2i2−1+i1−i−1−i1+i000
χ482-22-220-20020000-22-22i−2i−2i2i−22-20202i−2i002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000−2−2220000000000000000000−i2i21−i−1+i1+i−1−i000
χ492-22-220-20020000-22-2−2i2i2i−2i2−2-2020−2i2i00−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000022−2−20000000000000000000−i2i2−1−i1+i−1+i1−i000
χ502-22-220-20020000-22-2−2i2i2i−2i2−2-2020−2i2i002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000022−2−20000000000000000000−i2i21+i−1−i1−i−1+i000
χ512-22-220-20020000-22-2−2i2i2i−2i−22-2020−2i2i00−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−2−2220000000000000000000i2−i21+i−1−i1−i−1+i000
χ522-22-220-20020000-22-2−2i2i2i−2i−22-2020−2i2i002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000−2−2220000000000000000000i2−i2−1−i1+i−1+i1−i000
χ53444444444-14444-1-1-1000044-1-1-1-10000000000004-1-1-1-1-1-1-1-1-100000000000000000-1-1000000000
χ54444444444-14444-1-1-10000-4-4-1-1-1-1000000000000-4-1-1-1-1-111110000000000000000011000000000
χ55444444444-1-4-4-4-4-1-1-1000044-1-1-1-1000000000000-4-11111-1-1-1-10000000000000000011000000000
χ56444444444-1-4-4-4-4-1-1-10000-4-4-1-1-1-10000000000004-11111111100000000000000000-1-1000000000
χ574444-4-4-4-44-14i4i−4i−4i-1-1-100000011110000000000000-1−i−iiii5−i5i5−i5000000000000000005−5000000000
χ584444-4-4-4-44-14i4i−4i−4i-1-1-100000011110000000000000-1−i−iii−i5i5−i5i500000000000000000−55000000000
χ594444-4-4-4-44-1−4i−4i4i4i-1-1-100000011110000000000000-1ii−i−ii5−i5i5−i500000000000000000−55000000000
χ604444-4-4-4-44-1−4i−4i4i4i-1-1-100000011110000000000000-1ii−i−i−i5i5−i5i5000000000000000005−5000000000
χ614-44-4-4040040000-44-44i−4i−4i4i0040-40−4i4i000000000000000000000000000000000000000000000000
χ624-44-4-4040040000-44-4−4i4i4i−4i0040-404i−4i000000000000000000000000000000000000000000000000
χ634-4-440000040000-4-4444-4-400000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ644-4-440000040000-4-4444-4-40000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ654-4-440000040000-4-44-4-444000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ664-4-440000040000-4-44-4-4440000000000−222222−2222−22−222200000000000000000000000000000000000000
χ6788888-88-8-8-20000-2-2-2000000-22-2200000000000002000000000000000000000000000000000000
χ688888-88-88-8-20000-2-2-20000002-22-200000000000002000000000000000000000000000000000000
χ6988-8-8080-80-242−4242−42-222000000020-200000000000000−22−2200000000000000000000000000000000
χ7088-8-8080-80-2−4242−4242-222000000020-2000000000000002−22−200000000000000000000000000000000
χ7188-8-80-8080-24i2−4i2−4i24i2-2220000000-20200000000000000−i2i2i2−i200000000000000000000000000000000
χ7288-8-80-8080-2−4i24i24i2−4i2-2220000000-20200000000000000i2−i2−i2i200000000000000000000000000000000
χ738-88-880-800-200002-22000042−4220-20000000000000000000−2−2220000000000000000000000000000
χ748-88-880-800-200002-220000−424220-2000000000000000000022−2−20000000000000000000000000000
χ758-88-8-80800-200002-22000000-2020000000000000000000i10−i10−i10i100000000000000000000000000000
χ768-88-8-80800-200002-22000000-2020000000000000000000−i10i10i10−i100000000000000000000000000000
χ7716-16-161600000-4000044-4000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.