Finite Group Databasebeta

← Group #13020239

Character table — Group #13020239

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111444444488881010101016161616161616162020202020203232323240404040404040404040404080808080
order12224445101010442020444448202040404040248888202020202488888888884448
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-11
χ31111111111111111111-1-111-1-1-1-111111111-1-111-1-1-1-1111111-1-1-1-1
χ41111111111111111111-1-111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-111-1
χ5111111111111111-1-1-1-111111111-1-1ii−i−i1111-1-1ii−i−iiii−i−i−i-1i−i-1
χ6111111111111111-1-1-1-111111111-1-1−i−iii1111-1-1−i−iii−i−i−iiii-1−ii-1
χ7111111111111111-1-1-1-1-1-111-1-1-1-1-1-1ii−i−i11-1-1-1-1−i−iiiiii−i−i−i1−ii1
χ8111111111111111-1-1-1-1-1-111-1-1-1-1-1-1−i−iii11-1-1-1-1ii−i−i−i−i−iiii1i−i1
χ911111111111-1-11111111-111-1-1-1-1111111-1-111-1-111111-1-11-1-11-1-1-1
χ1011111111111-1-11111111-111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-111-111111-1
χ1111111111111-1-1111111-11111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1111
χ1211111111111-1-1111111-1111111111-1-1-1-1-1-1-1-1-1-11111-111-111-1-1-11
χ1311111111111-1-111-1-1-1-11-111-1-1-1-1-1-1ii−i−i-1-11111ii−i−ii−i−i−iii-1−ii1
χ1411111111111-1-111-1-1-1-11-111-1-1-1-1-1-1−i−iii-1-11111−i−iii−iiii−i−i-1i−i1
χ1511111111111-1-111-1-1-1-1-11111111-1-1ii−i−i-1-1-1-111−i−iiii−i−i−iii1i−i-1
χ1611111111111-1-111-1-1-1-1-11111111-1-1−i−iii-1-1-1-111ii−i−i−iiii−i−i1−ii-1
χ1722222-2-2222200-2-2222200-220000-2-222220000000000-200-2000000
χ1822222-2-2222200-2-2222200-220000-2-2-2-2-2-200000000002002000000
χ1922222-2-2222200-2-2-2-2-2-200-220000222i2i−2i−2i0000000000−2i002i000000
χ2022222-2-2222200-2-2-2-2-2-200-22000022−2i−2i2i2i00000000002i00−2i000000
χ212222-22-2222200-2-222-2-2002-20000-220000000000000002i−2i02i−2i0000
χ222222-22-2222200-2-222-2-2002-20000-22000000000000000−2i2i0−2i2i0000
χ232222-22-2222200-2-2-2-222002-200002-20000000000000002-20-220000
χ242222-22-2222200-2-2-2-222002-200002-2000000000000000-2202-20000
χ252222-2-2222222-22222-2-200-2-200002-20000-22002-200000000000000
χ262222-2-2222222-222-2-22200-2-20000-220000-2200-2200000000000000
χ272222-2-222222-222222-2-200-2-200002-200002-200-2200000000000000
χ282222-2-222222-2222-2-22200-2-20000-2200002-2002-200000000000000
χ294444444-1-1-1-144-1-1000044-1-1-1-1-1-1000000-1-1-1-10000000000000000
χ304444444-1-1-1-144-1-10000-4-4-1-11111000000-1-1110000000000000000
χ314444444-1-1-1-1-4-4-1-100004-4-1-1111100000011-1-10000000000000000
χ324444444-1-1-1-1-4-4-1-10000-44-1-1-1-1-1-100000011110000000000000000
χ334444-4-44-1-1-1-14-4-1-10000001155−5−50000001-15−50000000000000000
χ344444-4-44-1-1-1-14-4-1-100000011−5−5550000001-1−550000000000000000
χ354444-4-44-1-1-1-1-44-1-10000001155−5−5000000-11−550000000000000000
χ364444-4-44-1-1-1-1-44-1-100000011−5−555000000-115−50000000000000000
χ3744-4-40004-4-440000004i−4i00000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ3844-4-40004-4-440000004i−4i000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ3944-4-40004-4-44000000−4i4i00000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ4044-4-40004-4-44000000−4i4i000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ414-4-440004-44-400004i−4i0000000000002+2i−2−2i2−2i−2+2i00000000000000000000
χ424-4-440004-44-400004i−4i000000000000−2−2i2+2i−2+2i2−2i00000000000000000000
χ434-4-440004-44-40000−4i4i0000000000002−2i−2+2i2+2i−2−2i00000000000000000000
χ444-4-440004-44-40000−4i4i000000000000−2+2i2−2i−2−2i2+2i00000000000000000000
χ4588888-8-8-2-2-2-200220000002-2000000000000000000000000000000
χ468888-88-8-2-2-2-20022000000-22000000000000000000000000000000
χ478-88-800088-8-8000000000000000000000000000000000000000000
χ488-88-8000-2-2220025−25000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000000
χ498-88-8000-2-2220025−2500000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000000
χ508-88-8000-2-22200−252500000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000000
χ518-88-8000-2-22200−2525000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000000
χ521616-16-16000-444-4000000000000000000000000000000000000000000
χ5316-16-1616000-44-44000000000000000000000000000000000000000000

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