Finite Group Databasebeta

← Group #13020249

Character table — Group #13020249

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111444444488881010101016161616161616162020202020203232323240404040404040404040404080808080
order12224445101010242020444448202040404040248888102020202488888888884888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1
χ31111111111111111111-1-111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-111
χ5111111111111111-1-1-1-111111111-1-1ii−i−i1111-1-1iii−i−i−iii−i−i-1-1i−i
χ6111111111111111-1-1-1-111111111-1-1−i−iii1111-1-1−i−i−iiii−i−iii-1-1−ii
χ7111111111111111-1-1-1-1-1-111-1-1-1-1-1-1ii−i−i11-1-1-1-1iii−i−i−i−i−iii11−ii
χ8111111111111111-1-1-1-1-1-111-1-1-1-1-1-1−i−iii11-1-1-1-1−i−i−iiiiii−i−i11i−i
χ911111111111-1-11111111-111-1-1-1-1111111-1-111-1-11-1-11-1-111111-1-1-1
χ1011111111111-1-11111111-111-1-1-1-111-1-1-1-1-1-111-1-1-111-111-1-1-1-11-111
χ1111111111111-1-1111111-11111111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1111
χ1211111111111-1-1111111-1111111111-1-1-1-1-1-1-1-1-1-1-111-1111111-11-1-1
χ1311111111111-1-111-1-1-1-11-111-1-1-1-1-1-1ii−i−i-1-11111i−i−i−iiiii−i−i-11−ii
χ1411111111111-1-111-1-1-1-11-111-1-1-1-1-1-1−i−iii-1-11111−iiii−i−i−i−iii-11i−i
χ1511111111111-1-111-1-1-1-1-11111111-1-1ii−i−i-1-1-1-111i−i−i−iii−i−iii1-1i−i
χ1611111111111-1-111-1-1-1-1-11111111-1-1−i−iii-1-1-1-111−iiii−i−iii−i−i1-1−ii
χ1722222-2-2222200-2-222-2-2002-200002-2000000000002i−2i02i−2i00000000
χ1822222-2-2222200-2-222-2-2002-200002-200000000000−2i2i0−2i2i00000000
χ1922222-2-2222200-2-2-2-222002-20000-22000000000002-20-2200000000
χ2022222-2-2222200-2-2-2-222002-20000-2200000000000-2202-200000000
χ212222-22-2222200-2-2222200-220000-2-22222000000-200-20000000000
χ222222-22-2222200-2-2222200-220000-2-2-2-2-2-200000020020000000000
χ232222-22-2222200-2-2-2-2-2-200-220000222i2i−2i−2i000000−2i002i0000000000
χ242222-22-2222200-2-2-2-2-2-200-22000022−2i−2i2i2i0000002i00−2i0000000000
χ252222-2-2222222-22222-2-200-2-20000-2200002-2002-200000000000000
χ262222-2-2222222-222-2-22200-2-200002-200002-200-2200000000000000
χ272222-2-222222-222222-2-200-2-20000-220000-2200-2200000000000000
χ282222-2-222222-2222-2-22200-2-200002-20000-22002-200000000000000
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
χ334444-4-44-1-1-1-14-4-1-10000001155−5−5000000-115−50000000000000000
χ344444-4-44-1-1-1-14-4-1-100000011−5−555000000-11−550000000000000000
χ354444-4-44-1-1-1-1-44-1-10000001155−5−50000001-1−550000000000000000
χ364444-4-44-1-1-1-1-44-1-100000011−5−5550000001-15−50000000000000000
χ3744-4-400044-4-400004-400000000000022−2222−2200000000000000000000
χ3844-4-400044-4-400004-4000000000000−2222−222200000000000000000000
χ3944-4-400044-4-40000-440000000000002i2−2i2−2i22i200000000000000000000
χ4044-4-400044-4-40000-44000000000000−2i22i22i2−2i200000000000000000000
χ414-44-40004-4-440000004i−4i00000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000
χ424-44-40004-4-440000004i−4i000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000
χ434-44-40004-4-44000000−4i4i00000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000
χ444-44-40004-4-44000000−4i4i000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000
χ4588888-8-8-2-2-2-20022000000-22000000000000000000000000000000
χ468888-88-8-2-2-2-200220000002-2000000000000000000000000000000
χ478-8-880008-88-8000000000000000000000000000000000000000000
χ488-8-88000-22-220025−25000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ22+2ζ382ζ22−2ζ3800000000000000000000000000
χ498-8-88000-22-220025−2500000000−2ζ6+2ζ142ζ6−2ζ142ζ22−2ζ38−2ζ22+2ζ3800000000000000000000000000
χ508-8-88000-22-2200−252500000000−2ζ22+2ζ382ζ22−2ζ38−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000
χ518-8-88000-22-2200−2525000000002ζ22−2ζ38−2ζ22+2ζ382ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000
χ521616-16-16000-4-444000000000000000000000000000000000000000000
χ5316-1616-16000-444-4000000000000000000000000000000000000000000

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