Finite Group Databasebeta

← Group #13019068

Character table — Group #13019068

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111222244444555588888888881010101016161616161616161620202020202020202020202020202020203232404040404040404040408080
order12224444451010104444228888202020202244204040404040404040488888888888888881010448888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ41111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ511111111111111111-1-111-1-11111111111111-1-1-1-111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1
χ611111111111111111-1-111-1-11111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ711111111111111111-1-1-1-111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ811111111111111111-1-1-1-111111111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-1-1-111-1-111-1-1
χ91111111111111-1-1-1-11111111111-1-1-1-1111111111-1ii−i−iii−i−iiiii−i−i−i−i11-1-1-1-1-1-1i−ii−ii−i
χ101111111111111-1-1-1-11111111111-1-1-1-1111111111-1−i−iii−i−iii−i−i−i−iiiii11-1-1-1-1-1-1−ii−ii−ii
χ111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1ii−i−iii−i−i−i−i−i−iiiii11-1-11111i−ii−i−ii
χ121111111111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1−i−iii−i−iiiiiii−i−i−i−i11-1-11111−ii−iii−i
χ131111111111111-1-1-1-1-1-111-1-11111-1-1-1-111111-1-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i-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−iiiii−i−i−i−i−i−iiiii-1-111-1-111−iii−ii−i
χ151111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-11111-1ii−i−i−i−iii−i−i−i−iiiii-1-11111-1-1i−i−iii−i
χ161111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-11111-1−i−iiiii−i−iiiii−i−i−i−i-1-11111-1-1−iii−i−ii
χ1722222-2-22-2222222220000002-22-222-2-2-200000000-2222200000000000000000000-2-20000
χ1822222-2-22-2222222220000002-22-222-2-2-200000000-2-2-2-2-200000000000000000000220000
χ1922222-2-22-22222-2-2-2-20000002-22-2-2-222-20000000022i2i−2i−2i00000000000000000000−2i2i0000
χ2022222-2-22-22222-2-2-2-20000002-22-2-2-222-2000000002−2i−2i2i2i000000000000000000002i−2i0000
χ212222-222-2-222222222000000-22-22-2-222-200000000-200002222000000000000000000-2-200
χ222222-222-2-222222222000000-22-22-2-222-200000000-20000-2-2-2-20000000000000000002200
χ232222-222-2-22222-2-2-2-2000000-22-2222-2-2-200000000200002i2i−2i−2i000000000000000000−2i2i00
χ242222-222-2-22222-2-2-2-2000000-22-2222-2-2-20000000020000−2i−2i2i2i0000000000000000002i−2i00
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
χ2922-2-20-220022-2-22i−2i2i−2i0000i2−i2020-2002i−2i00000i2i2−i2−i200000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ391−i1−i−1+i−1+i1+i1+i−1−i−1−i0000002−2000000
χ3022-2-20-220022-2-22i−2i2i−2i0000i2−i2020-2002i−2i00000i2i2−i2−i2000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000002−2000000
χ3122-2-20-220022-2-22i−2i2i−2i0000−i2i2020-2002i−2i00000−i2−i2i2i200000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000−22000000
χ3222-2-20-220022-2-22i−2i2i−2i0000−i2i2020-2002i−2i00000−i2−i2i2i2000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ391−i1−i−1+i−1+i1+i1+i−1−i−1−i000000−22000000
χ3322-2-20-220022-2-2−2i2i−2i2i0000i2−i2020-200−2i2i00000i2i2−i2−i200000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ371+i1+i−1−i−1−i1−i1−i−1+i−1+i000000−22000000
χ3422-2-20-220022-2-2−2i2i−2i2i0000i2−i2020-200−2i2i00000i2i2−i2−i2000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000−22000000
χ3522-2-20-220022-2-2−2i2i−2i2i0000−i2i2020-200−2i2i00000−i2−i2i2i200000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000002−2000000
χ3622-2-20-220022-2-2−2i2i−2i2i0000−i2i2020-200−2i2i00000−i2−i2i2i2000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ371+i1+i−1−i−1−i1−i1−i−1+i−1+i0000002−2000000
χ372-2-22-200202-22-222-2-2002−200-20202-200022−2−2000002i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i200002−200000000
χ382-2-22-200202-22-222-2-2002−200-20202-200022−2−200000−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i200002−200000000
χ392-2-22-200202-22-222-2-200−2200-20202-2000−2−222000002i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i20000−2200000000
χ402-2-22-200202-22-222-2-200−2200-20202-2000−2−22200000−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i20000−2200000000
χ412-2-22-200202-22-2-2-222002−200-2020-2200022−2−2000002-2-2200002−22−2−22−220000−2200000000
χ422-2-22-200202-22-2-2-222002−200-2020-2200022−2−200000-222-20000−22−222−22−20000−2200000000
χ432-2-22-200202-22-2-2-22200−2200-2020-22000−2−222000002-2-220000−22−222−22−200002−200000000
χ442-2-22-200202-22-2-2-22200−2200-2020-22000−2−22200000-222-200002−22−2−22−2200002−200000000
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
χ5344-4-404-40044-4-44i−4i4i−4i0000000-40400−4i4i0000000000000000000000000000000000000000
χ5444-4-404-40044-4-4−4i4i−4i4i0000000-404004i−4i0000000000000000000000000000000000000000
χ554-44-4000004-4-444i−4i−4i4i00000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000
χ564-44-4000004-4-444i−4i−4i4i000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000
χ574-44-4000004-4-44−4i4i4i−4i00000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000
χ584-44-4000004-4-44−4i4i4i−4i000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000
χ594-4-44400-404-44-444-4-400000040-40-44000000000000000000000000000000000000000000
χ604-4-44400-404-44-4-4-44400000040-404-4000000000000000000000000000000000000000000
χ6188888-8-88-8-2-2-2-20000000000-22-2200002000000000000000000000000000000000000000
χ628888-888-8-8-2-2-2-200000000002-22-200002000000000000000000000000000000000000000
χ6388-8-808-800-2-2220000000000020-200000000010−10−10100000000000000000000000000000000
χ6488-8-808-800-2-2220000000000020-2000000000−101010−100000000000000000000000000000000
χ6588-8-80-8800-2-222000000004i2−4i20-202000000000−i2−i2i2i20000000000000000000000000000000
χ6688-8-80-8800-2-22200000000−4i24i20-202000000000i2i2−i2−i20000000000000000000000000000000
χ678-8-88800-80-22-220000000000-202000000i10−i10−i10i1000000000000000000000000000000000000
χ688-8-88800-80-22-220000000000-202000000−i10i10i10−i1000000000000000000000000000000000000
χ698-8-88-80080-22-2200000042−420020-2000000−2−22200000000000000000000000000000000000
χ708-8-88-80080-22-22000000−42420020-200000022−2−200000000000000000000000000000000000
χ7116-1616-1600000-444-40000000000000000000000000000000000000000000000000000000000

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