Finite Group Databasebeta

← Group #13019082

Character table — Group #13019082

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111222244444555588888888881010101016161616161616161620202020202020202020202020202020203232404040404040404040408080
order12224444451010104444228888202020204444204040404040404040244444444888888881010448888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ511111111111111111-1-111-1-11111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ611111111111111111-1-111-1-11111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111
χ711111111111111111-1-1-1-111111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1
χ811111111111111111-1-1-1-111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111
χ91111111111111-1-1-1-11111111111-1-1-1-1111111111-1iiii−i−i−i−iii−i−iii−i−i11-1-1-1-1-1-1i−ii−ii−i
χ101111111111111-1-1-1-11111111111-1-1-1-1111111111-1−i−i−i−iiiii−i−iii−i−iii11-1-1-1-1-1-1−ii−ii−ii
χ111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−iii−i−iii11-1-11111−ii−iii−i
χ121111111111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiii−i−iii−i−i11-1-11111i−ii−i−ii
χ131111111111111-1-1-1-1-1-111-1-11111-1-1-1-111111-1-1-1-1-1iiii−i−i−i−iii−i−i−i−iii-1-111-1-111i−i−ii−ii
χ141111111111111-1-1-1-1-1-111-1-11111-1-1-1-111111-1-1-1-1-1−i−i−i−iiiii−i−iiiii−i−i-1-111-1-111−iii−ii−i
χ151111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-11111-1iiii−i−i−i−i−i−iiiii−i−i-1-11111-1-1−iii−i−ii
χ161111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-11111-1−i−i−i−iiiiiii−i−i−i−iii-1-11111-1-1i−i−iii−i
χ1722222-22-2-2222222220000002-22-222-2-2-200000000-200000000000022220000000000-2-200
χ1822222-22-2-2222222220000002-22-222-2-2-200000000-2000000000000-2-2-2-200000000002200
χ1922222-22-2-22222-2-2-2-20000002-22-2-2-222-20000000020000000000002i2i−2i−2i0000000000−2i2i00
χ2022222-22-2-22222-2-2-2-20000002-22-2-2-222-2000000002000000000000−2i−2i2i2i00000000002i−2i00
χ212222-22-22-222222222000000-22-22-2-222-200000000-2000000002222000000000000-2-20000
χ222222-22-22-222222222000000-22-22-2-222-200000000-200000000-2-2-2-2000000000000220000
χ232222-22-22-22222-2-2-2-2000000-22-2222-2-2-2000000002000000002i2i−2i−2i000000000000−2i2i0000
χ242222-22-22-22222-2-2-2-2000000-22-2222-2-2-200000000200000000−2i−2i2i2i0000000000002i−2i0000
χ252222-2-2-2-22222222222-20000-2-2-2-2-2-2-2-2200000000200000000000000002-22-20000000000
χ262222-2-2-2-2222222222-220000-2-2-2-2-2-2-2-220000000020000000000000000-22-220000000000
χ272222-2-2-2-222222-2-2-2-22-20000-2-2-2-22222200000000-200000000000000002-2-220000000000
χ282222-2-2-2-222222-2-2-2-2-220000-2-2-2-22222200000000-20000000000000000-222-20000000000
χ2922-2-2020-2022-2-22i−2i2i−2i002−2000-202002i−2i022−2−2000001+i1+i−1−i−1−i1−i1−i−1+i−1+i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000i2−i200000000
χ3022-2-2020-2022-2-22i−2i2i−2i002−2000-202002i−2i022−2−200000−1−i−1−i1+i1+i−1+i−1+i1−i1−i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000i2−i200000000
χ3122-2-2020-2022-2-22i−2i2i−2i00−22000-202002i−2i0−2−222000001+i1+i−1−i−1−i1−i1−i−1+i−1+i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000−i2i200000000
χ3222-2-2020-2022-2-22i−2i2i−2i00−22000-202002i−2i0−2−22200000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000−i2i200000000
χ3322-2-2020-2022-2-2−2i2i−2i2i002−2000-20200−2i2i022−2−2000001−i1−i−1+i−1+i1+i1+i−1−i−1−i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000−i2i200000000
χ3422-2-2020-2022-2-2−2i2i−2i2i002−2000-20200−2i2i022−2−200000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000−i2i200000000
χ3522-2-2020-2022-2-2−2i2i−2i2i00−22000-20200−2i2i0−2−222000001−i1−i−1+i−1+i1+i1+i−1−i−1−i−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000i2−i200000000
χ3622-2-2020-2022-2-2−2i2i−2i2i00−22000-20200−2i2i0−2−22200000−1+i−1+i1−i1−i−1−i−1−i1+i1+i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000i2−i200000000
χ372-22-220-2002-22-22i−2i−2i2i00002−2-20202i−2i000000022−2−201−i−1+i1−i−1+i1+i−1−i1+i−1−i0000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000i2−i2000000
χ382-22-220-2002-22-22i−2i−2i2i00002−2-20202i−2i000000022−2−20−1+i1−i−1+i1−i−1−i1+i−1−i1+i00002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000i2−i2000000
χ392-22-220-2002-22-22i−2i−2i2i0000−22-20202i−2i0000000−2−22201−i−1+i1−i−1+i1+i−1−i1+i−1−i00002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000−i2i2000000
χ402-22-220-2002-22-22i−2i−2i2i0000−22-20202i−2i0000000−2−2220−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−i2i2000000
χ412-22-220-2002-22-2−2i2i2i−2i00002−2-2020−2i2i000000022−2−201+i−1−i1+i−1−i1−i−1+i1−i−1+i00002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000−i2i2000000
χ422-22-220-2002-22-2−2i2i2i−2i00002−2-2020−2i2i000000022−2−20−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−i2i2000000
χ432-22-220-2002-22-2−2i2i2i−2i0000−22-2020−2i2i0000000−2−22201+i−1−i1+i−1−i1−i−1+i1−i−1+i0000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000i2−i2000000
χ442-22-220-2002-22-2−2i2i2i−2i0000−22-2020−2i2i0000000−2−2220−1−i1+i−1−i1+i−1+i1−i−1+i1−i00002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000i2−i2000000
χ45444444444-1-1-1-10000444444-1-1-1-10000-1-1-1-1-1-1-1-1-100000000000000000-1-1000000000000
χ46444444444-1-1-1-1000044-4-4-4-4-1-1-1-10000-11111111100000000000000000-1-1000000000000
χ47444444444-1-1-1-10000-4-444-4-4-1-1-1-10000-1-1-1-1-111110000000000000000011000000000000
χ48444444444-1-1-1-10000-4-4-4-444-1-1-1-10000-11111-1-1-1-10000000000000000011000000000000
χ494444-4-4-4-44-1-1-1-100004-4000011110000-1i5−i5i5−i5i5−i5i5−i500000000000000000-11000000000000
χ504444-4-4-4-44-1-1-1-100004-4000011110000-1−i5i5−i5i5−i5i5−i5i500000000000000000-11000000000000
χ514444-4-4-4-44-1-1-1-10000-44000011110000-1i5−i5i5−i5−i5i5−i5i5000000000000000001-1000000000000
χ524444-4-4-4-44-1-1-1-10000-44000011110000-1−i5i5−i5i5i5−i5i5−i5000000000000000001-1000000000000
χ5344-4-40-404044-4-44i−4i4i−4i000000040-400−4i4i0000000000000000000000000000000000000000
χ5444-4-40-404044-4-4−4i4i−4i4i000000040-4004i−4i0000000000000000000000000000000000000000
χ554-44-4-404004-44-44i−4i−4i4i00000040-40−4i4i000000000000000000000000000000000000000000
χ564-44-4-404004-44-4−4i4i4i−4i00000040-404i−4i000000000000000000000000000000000000000000
χ574-4-44000004-4-4444-4-40000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ584-4-44000004-4-4444-4-4000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ594-4-44000004-4-44-4-4440000000000000000000000002-2-222-2-220000000000000000000000
χ604-4-44000004-4-44-4-444000000000000000000000000-222-2-222-20000000000000000000000
χ6188888-88-8-8-2-2-2-20000000000-22-2200002000000000000000000000000000000000000000
χ628888-88-88-8-2-2-2-200000000002-22-200002000000000000000000000000000000000000000
χ6388-8-8080-80-2-22200000042−4200020-200000−2−22200000000000000000000000000000000000
χ6488-8-8080-80-2-222000000−424200020-20000022−2−200000000000000000000000000000000000
χ6588-8-80-8080-2-22200000000000-20200000i10−i10−i10i1000000000000000000000000000000000000
χ6688-8-80-8080-2-22200000000000-20200000−i10i10i10−i1000000000000000000000000000000000000
χ678-88-880-800-22-220000000042−4220-20000000000−2−2220000000000000000000000000000000
χ688-88-880-800-22-2200000000−424220-2000000000022−2−20000000000000000000000000000000
χ698-88-8-80800-22-220000000000-2020000000000i10−i10−i10i100000000000000000000000000000000
χ708-88-8-80800-22-220000000000-2020000000000−i10i10i10−i100000000000000000000000000000000
χ7116-16-161600000-444-40000000000000000000000000000000000000000000000000000000000

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