Finite Group Databasebeta

← Group #13020744

Character table — Group #13020744

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size1111222244444444455558888881010101010101010101010101616161616161616161620202020202020202020202020202020203232404040404040808080
order12224444458888101010444488202020202244444444444204040404040404040444448888888888882020888888488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1
χ3111111111111111111111-1-11111111111111111-111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-1111111-1-1-1-1-1-1-1-111-111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ511111111111111111-1-1-1-1111111-1-1iiii−i−i−i−i-1-11111111111-1ii−i−i-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i-1i−i
χ611111111111111111-1-1-1-1111111-1-1−i−i−i−iiiii-1-11111111111-1−i−iii-1-1-1-1−i−i−i−iiiii11-1-1−i−iii-1−ii
χ711111111111111111-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-1-111111-1-1-1-1-1ii−i−i-1-1-1-1iiii−i−i−i−i-1-111−i−iii1−ii
χ811111111111111111-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-1-111111-1-1-1-1-1−i−iii-1-1-1-1−i−i−i−iiiii-1-111ii−i−i1i−i
χ91111111111-1-1-1-11111111111111111111111111-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1
χ101111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-111-11-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-111
χ111111111111-1-1-1-11111111-1-1111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111
χ121111111111-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111111-1-1
χ131111111111-1-1-1-1111-1-1-1-1111111-1-1iiii−i−i−i−i-1-1-11-1-1-1-11111-1ii−i−i1111−i−i−i−iiiii-1-1-1-1ii−i−i1−ii
χ141111111111-1-1-1-1111-1-1-1-1111111-1-1−i−i−i−iiiii-1-1-11-1-1-1-11111-1−i−iii1111iiii−i−i−i−i-1-1-1-1−i−iii1i−i
χ151111111111-1-1-1-1111-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-111-1-1-1-1-1-1-1-1-1ii−i−i1111−i−i−i−iiiii1111−i−iii-1i−i
χ161111111111-1-1-1-1111-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-111-1-1-1-1-1-1-1-1-1−i−iii1111iiii−i−i−i−i1111ii−i−i-1−ii
χ1722222-2-22-2200002222222002-22-22222222222-2-20-200000000-2-2-2-2-200000000000000000000000
χ1822222-2-22-2200002222222002-22-222-2-2-2-2-2-2-2-2-2-20-200000000-2222200000000000000000000000
χ1922222-2-22-220000222-2-2-2-2002-22-2-2-22i2i2i2i−2i−2i−2i−2i220-2000000002−2i−2i2i2i00000000000000000000000
χ2022222-2-22-220000222-2-2-2-2002-22-2-2-2−2i−2i−2i−2i2i2i2i2i220-20000000022i2i−2i−2i00000000000000000000000
χ212222-222-2-220000222222200-22-22-2-200000000220-200000000-20000000022-2-222-2-200000000000
χ222222-222-2-220000222222200-22-22-2-200000000220-200000000-200000000-2-222-2-22200000000000
χ232222-222-2-220000222-2-2-2-200-22-222200000000-2-20-2000000002000000002i2i−2i−2i−2i−2i2i2i00000000000
χ242222-222-2-220000222-2-2-2-200-22-222200000000-2-20-200000000200000000−2i−2i2i2i2i2i−2i−2i00000000000
χ252222-2-2-2-2222i2i−2i−2i222222200-2-2-2-2-2-200000000-2-2022i2i−2i−2i0000200002i2i−2i−2i0000000000000000000
χ262222-2-2-2-2222i2i−2i−2i222-2-2-2-200-2-2-2-2220000000022022i2i−2i−2i0000-20000−2i−2i2i2i0000000000000000000
χ272222-2-2-2-222−2i−2i2i2i222222200-2-2-2-2-2-200000000-2-202−2i−2i2i2i000020000−2i−2i2i2i0000000000000000000
χ282222-2-2-2-222−2i−2i2i2i222-2-2-2-200-2-2-2-222000000002202−2i−2i2i2i0000-200002i2i−2i−2i0000000000000000000
χ2922-2-2-20020200002-2-222-2-2i2−i2-20202-222-2-222-2-200000000i2i2−i2−i20000000000000000000i2−i2i2−i2i2−i2000
χ3022-2-2-20020200002-2-222-2-2i2−i2-20202-2-2-222-2-22200000000i2i2−i2−i20000000000000000000i2−i2−i2i2−i2i2000
χ3122-2-2-20020200002-2-222-2-2−i2i2-20202-222-2-222-2-200000000−i2−i2i2i20000000000000000000−i2i2−i2i2−i2i2000
χ3222-2-2-20020200002-2-222-2-2−i2i2-20202-2-2-222-2-22200000000−i2−i2i2i20000000000000000000−i2i2i2−i2i2−i2000
χ3322-2-2-20020200002-2-2-2-222i2−i2-2020-222i2i−2i−2i−2i−2i2i2i00000000i2i2−i2−i20000000000000000000−i2i2−222−2000
χ3422-2-2-20020200002-2-2-2-222i2−i2-2020-22−2i−2i2i2i2i2i−2i−2i00000000i2i2−i2−i20000000000000000000−i2i22−2−22000
χ3522-2-2-20020200002-2-2-2-222−i2i2-2020-222i2i−2i−2i−2i−2i2i2i00000000−i2−i2i2i20000000000000000000i2−i22−2−22000
χ3622-2-2-20020200002-2-2-2-222−i2i2-2020-22−2i−2i2i2i2i2i−2i−2i00000000−i2−i2i2i20000000000000000000i2−i2−222−2000
χ372-22-202-20022−22−2-2-222i−2i2i−2i000-202001+i−1−i1+i−1−i1−i−1+i1−i−1+i2i−2i002−22−2000001+i−1−i1−i−1+ii2−i2i2−i200−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000
χ382-22-202-20022−22−2-2-222i−2i2i−2i000-20200−1−i1+i−1−i1+i−1+i1−i−1+i1−i2i−2i002−22−200000−1−i1+i−1+i1−ii2−i2i2−i2002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000
χ392-22-202-20022−22−2-2-22−2i2i−2i2i000-202001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2i2i002−22−2000001−i−1+i1+i−1−i−i2i2−i2i2002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000
χ402-22-202-20022−22−2-2-22−2i2i−2i2i000-20200−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2i2i002−22−200000−1+i1−i−1−i1+i−i2i2−i2i200−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000
χ412-22-202-2002−22−22-2-222i−2i2i−2i000-202001+i−1−i1+i−1−i1−i−1+i1−i−1+i2i−2i00−22−22000001+i−1−i1−i−1+i−i2i2−i2i2002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000
χ422-22-202-2002−22−22-2-222i−2i2i−2i000-20200−1−i1+i−1−i1+i−1+i1−i−1+i1−i2i−2i00−22−2200000−1−i1+i−1+i1−i−i2i2−i2i200−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000
χ432-22-202-2002−22−22-2-22−2i2i−2i2i000-202001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2i2i00−22−22000001−i−1+i1+i−1−ii2−i2i2−i200−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000
χ442-22-202-2002−22−22-2-22−2i2i−2i2i000-20200−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2i2i00−22−2200000−1+i1−i−1−i1+ii2−i2i2−i2002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000
χ452-22-20-22002i2−i2−i2i2-2-222i−2i2i−2i00020-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i−2i2i00i2−i2−i2i200000−1−i1+i−1+i1−i−222−2−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000000
χ462-22-20-22002i2−i2−i2i2-2-222i−2i2i−2i00020-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2i2i00i2−i2−i2i2000001+i−1−i1−i−1+i−222−22ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000000
χ472-22-20-22002i2−i2−i2i2-2-22−2i2i−2i2i00020-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i2i−2i00i2−i2−i2i200000−1+i1−i−1−i1+i2−2−22−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000000
χ482-22-20-22002i2−i2−i2i2-2-22−2i2i−2i2i00020-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i2i−2i00i2−i2−i2i2000001−i−1+i1+i−1−i2−2−222ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000000
χ492-22-20-22002−i2i2i2−i2-2-222i−2i2i−2i00020-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i−2i2i00−i2i2i2−i200000−1−i1+i−1+i1−i2−2−222ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000000
χ502-22-20-22002−i2i2i2−i2-2-222i−2i2i−2i00020-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2i2i00−i2i2i2−i2000001+i−1−i1−i−1+i2−2−22−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000000
χ512-22-20-22002−i2i2i2−i2-2-22−2i2i−2i2i00020-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i2i−2i00−i2i2i2−i200000−1+i1−i−1−i1+i−222−22ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000000
χ522-22-20-22002−i2i2i2−i2-2-22−2i2i−2i2i00020-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i2i−2i00−i2i2i2−i2000001−i−1+i1+i−1−i−222−2−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000000
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
χ6144-4-4400-40400004-4-444-4-40040-40-44000000000000000000000000000000000000000000000000
χ6244-4-4400-40400004-4-4-4-4440040-404-4000000000000000000000000000000000000000000000000
χ634-4-440000040000-44-44i−4i−4i4i000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000000
χ644-4-440000040000-44-44i−4i−4i4i00000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000000
χ654-4-440000040000-44-4−4i4i4i−4i000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000000
χ664-4-440000040000-44-4−4i4i4i−4i00000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000000
χ6788888-8-88-8-20000-2-2-2000000-22-2200000000000002000000000000000000000000000000000000
χ688888-888-8-8-20000-2-2-20000002-22-200000000000002000000000000000000000000000000000000
χ6988-8-8800-80-20000-222000000-202000000000000000000010−10−10100000000000000000000000000000
χ7088-8-8800-80-20000-222000000-2020000000000000000000−101010−100000000000000000000000000000
χ7188-8-8-80080-20000-22200004i2−4i220-20000000000000000000−i2−i2i2i20000000000000000000000000000
χ7288-8-8-80080-20000-2220000−4i24i220-20000000000000000000i2i2−i2−i20000000000000000000000000000
χ738-88-808-800-242−4242−4222-2000000020-200000000000000−22−2200000000000000000000000000000000
χ748-88-808-800-2−4242−424222-2000000020-2000000000000002−22−200000000000000000000000000000000
χ758-88-80-8800-24i2−4i2−4i24i222-20000000-20200000000000000−i2i2i2−i200000000000000000000000000000000
χ768-88-80-8800-2−4i24i24i2−4i222-20000000-20200000000000000i2−i2−i2i200000000000000000000000000000000
χ7716-16-161600000-400004-44000000000000000000000000000000000000000000000000000000000000

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