Finite Group Databasebeta

← Group #13020776

Character table — Group #13020776

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size1111222244444444455558888881010101010101010101010101616161616161616161620202020202020202020202020202020203232404040404040808080
order12224444458888101010444488202020202244888888882204040404040404040488888888888888881010444488488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1
χ3111111111111111111111-1-11111111111111111-111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111
χ511111111111111111-1-1-1-1111111-1-1-1-1iiii−i−i−i−i1111111111-1-1-1-1-1ii−i−iii−i−iii−i−i11ii−i−i-1-1-1i−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−i−iii-1-1-1−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-1-1−i−iii111−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-1-1ii−i−i111i−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
χ101111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-111
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
χ121111111111-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1111111-1-11-1-1
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-1-1ii−i−i-1-11−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−i−iii-1-11i−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−i11−i−iii11-1i−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−iii11ii−i−i11-1−ii
χ1722222-2-22-2200002222222002-22-222-2-2000000000-200000000-200002222-2-2-2-2000000000000000
χ1822222-2-22-2200002222222002-22-222-2-2000000000-200000000-20000-2-2-2-22222000000000000000
χ1922222-2-22-220000222-2-2-2-2002-22-2-2-222000000000-200000000200002i2i−2i−2i−2i−2i2i2i000000000000000
χ2022222-2-22-220000222-2-2-2-2002-22-2-2-222000000000-20000000020000−2i−2i2i2i2i2i−2i−2i000000000000000
χ212222-222-2-220000222222200-22-22-2-222222222220-200000000-2000000000000-2-2-2-200000000000
χ222222-222-2-220000222222200-22-22-2-222-2-2-2-2-2-2-2-20-200000000-2000000000000222200000000000
χ232222-222-2-220000222-2-2-2-200-22-2222-2-22i2i2i2i−2i−2i−2i−2i0-2000000002000000000000−2i−2i2i2i00000000000
χ242222-222-2-220000222-2-2-2-200-22-2222-2-2−2i−2i−2i−2i2i2i2i2i0-20000000020000000000002i2i−2i−2i00000000000
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
χ2922-2-202-200200002-2-22i−2i2i−2i2−20-202002i−2i−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ3900000022−2−200000000000000000001+i−1−i1−i−1+ii2−i2000
χ3022-2-202-200200002-2-22i−2i2i−2i2−20-202002i−2i2ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000022−2−20000000000000000000−1−i1+i−1+i1−ii2−i2000
χ3122-2-202-200200002-2-22i−2i2i−2i−220-202002i−2i−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−2−2220000000000000000000−1−i1+i−1+i1−i−i2i2000
χ3222-2-202-200200002-2-22i−2i2i−2i−220-202002i−2i2ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000−2−22200000000000000000001+i−1−i1−i−1+i−i2i2000
χ3322-2-202-200200002-2-2−2i2i−2i2i2−20-20200−2i2i−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ3700000022−2−20000000000000000000−1+i1−i−1−i1+i−i2i2000
χ3422-2-202-200200002-2-2−2i2i−2i2i2−20-20200−2i2i2ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000022−2−200000000000000000001−i−1+i1+i−1−i−i2i2000
χ3522-2-202-200200002-2-2−2i2i−2i2i−220-20200−2i2i−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−2−22200000000000000000001−i−1+i1+i−1−ii2−i2000
χ3622-2-202-200200002-2-2−2i2i−2i2i−220-20200−2i2i2ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000−2−2220000000000000000000−1+i1−i−1−i1+ii2−i2000
χ372-2-22200-202i2−i2i2−i2-22-222-2-20020-20-2200i2−i2i2−i2i2−i2i2−i200i2−i2i2−i200000i2−i2i2−i22-22-20000i2−i2i2−i200000000000
χ382-2-22200-202i2−i2i2−i2-22-222-2-20020-20-2200−i2i2−i2i2−i2i2−i2i200i2−i2i2−i200000i2−i2i2−i2-22-220000−i2i2−i2i200000000000
χ392-2-22200-202i2−i2i2−i2-22-2-2-2220020-202-2002−22−2−22−2200i2−i2i2−i200000−i2i2−i2i2−2i2i2i−2i00002−2−2200000000000
χ402-2-22200-202i2−i2i2−i2-22-2-2-2220020-202-200−22−222−22−200i2−i2i2−i200000−i2i2−i2i22i−2i−2i2i0000−222−200000000000
χ412-2-22200-202−i2i2−i2i2-22-222-2-20020-20-2200i2−i2i2−i2i2−i2i2−i200−i2i2−i2i200000−i2i2−i2i2-22-220000i2−i2i2−i200000000000
χ422-2-22200-202−i2i2−i2i2-22-222-2-20020-20-2200−i2i2−i2i2−i2i2−i2i200−i2i2−i2i200000−i2i2−i2i22-22-20000−i2i2−i2i200000000000
χ432-2-22200-202−i2i2−i2i2-22-2-2-2220020-202-2002−22−2−22−2200−i2i2−i2i200000i2−i2i2−i22i−2i−2i2i00002−2−2200000000000
χ442-2-22200-202−i2i2−i2i2-22-2-2-2220020-202-200−22−222−22−200−i2i2−i2i200000i2−i2i2−i2−2i2i2i−2i0000−222−200000000000
χ452-2-22-2002022−2−22-22-222-2-200-20202-200i2−i2i2−i2i2−i2i2−i2002−2−22000002−2−2200002i−2i2i−2i−i2i2−i2i200000000000
χ462-2-22-2002022−2−22-22-222-2-200-20202-200−i2i2−i2i2−i2i2−i2i2002−2−22000002−2−220000−2i2i−2i2ii2−i2i2−i200000000000
χ472-2-22-2002022−2−22-22-2-2-22200-2020-22002−22−2−22−22002−2−2200000−222−200002-2-22−222−200000000000
χ482-2-22-2002022−2−22-22-2-2-22200-2020-2200−22−222−22−2002−2−2200000−222−20000-222-22−2−2200000000000
χ492-2-22-200202−222−2-22-222-2-200-20202-200i2−i2i2−i2i2−i2i2−i200−222−200000−222−20000−2i2i−2i2i−i2i2−i2i200000000000
χ502-2-22-200202−222−2-22-222-2-200-20202-200−i2i2−i2i2−i2i2−i2i200−222−200000−222−200002i−2i2i−2ii2−i2i2−i200000000000
χ512-2-22-200202−222−2-22-2-2-22200-2020-22002−22−2−22−2200−222−2000002−2−220000-222-2−222−200000000000
χ522-2-22-200202−222−2-22-2-2-22200-2020-2200−22−222−22−200−222−2000002−2−2200002-2-222−2−2200000000000
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
χ6144-4-40-4400400004-4-44i−4i4i−4i00040-400−4i4i0000000000000000000000000000000000000000000000
χ6244-4-40-4400400004-4-4−4i4i−4i4i00040-4004i−4i0000000000000000000000000000000000000000000000
χ634-44-40000040000-4-444i−4i−4i4i00000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000000000000
χ644-44-40000040000-4-444i−4i−4i4i0000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000000000
χ654-44-40000040000-4-44−4i4i4i−4i00000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000000000
χ664-44-40000040000-4-44−4i4i4i−4i0000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000000000
χ6788888-8-88-8-20000-2-2-2000000-22-2200000000000002000000000000000000000000000000000000
χ688888-888-8-8-20000-2-2-20000002-22-200000000000002000000000000000000000000000000000000
χ6988-8-808-800-20000-222000042−42020-2000000000000000000−2−2220000000000000000000000000000
χ7088-8-808-800-20000-2220000−4242020-200000000000000000022−2−20000000000000000000000000000
χ7188-8-80-8800-20000-2220000000-202000000000000000000i10−i10−i10i100000000000000000000000000000
χ7288-8-80-8800-20000-2220000000-202000000000000000000−i10i10i10−i100000000000000000000000000000
χ738-8-88800-80-24i2−4i24i2−4i22-22000000-202000000000000000−i2i2−i2i200000000000000000000000000000000
χ748-8-88800-80-2−4i24i2−4i24i22-22000000-202000000000000000i2−i2i2−i200000000000000000000000000000000
χ758-8-88-80080-242−42−42422-2200000020-2000000000000000−222−200000000000000000000000000000000
χ768-8-88-80080-2−424242−422-2200000020-20000000000000002−2−2200000000000000000000000000000000
χ7716-1616-1600000-4000044-4000000000000000000000000000000000000000000000000000000000000

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