Finite Group Databasebeta

← Group #13020161

Character table — Group #13020161

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11114444444888888101016161616161616161616162020203232404040404040404040404040404080808080
order12222445101010441010202044482020202020404040404442020248888888888884888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ31111111111111111111-1-11-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111-1-11-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111-1-111111111111-1-1-111-1-1i−iiii−i−i−iii−i−i-1-1i−i
χ611111111111111111-1-111111111111-1-1-111-1-1−ii−i−i−iiii−i−iii-1-1−ii
χ711111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-111-1-1i−iiii−i−i−i−i−iii11−ii
χ811111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-111-1-1−ii−i−i−iiiiii−i−i11i−i
χ911111111111-1-11111111-111111-1-1-1-1111-1-1-1-1111-1-11-1-1-1-1-1-11-111
χ1011111111111-1-11111111-111111-1-1-1-1111-1-1-1-1-1-1-111-11111111-1-1-1
χ1111111111111-1-1111111-111-1-1-1-11111111-1-1-1-1111-1-11-1-11111-11-1-1
χ1211111111111-1-1111111-111-1-1-1-11111111-1-1-1-1-1-1-111-111-1-1-1-1-1111
χ1311111111111-1-11111-1-11-111111-1-1-1-1-1-1-1-1-111i−ii−i−i−iii−i−iii-11i−i
χ1411111111111-1-11111-1-11-111111-1-1-1-1-1-1-1-1-111−ii−iiii−i−iii−i−i-11−ii
χ1511111111111-1-11111-1-1-111-1-1-1-11111-1-1-1-1-111i−ii−i−i−iiiii−i−i1-1−ii
χ1611111111111-1-11111-1-1-111-1-1-1-11111-1-1-1-1-111−ii−iiii−i−i−i−iii1-1i−i
χ1722222-2-222220022-2-22200-200000000-2-2200000002-202-200000000
χ1822222-2-222220022-2-22200-200000000-2-220000000-220-2200000000
χ1922222-2-222220022-2-2-2-200-20000000022-200000002i−2i0−2i2i00000000
χ2022222-2-222220022-2-2-2-200-20000000022-20000000−2i2i02i−2i00000000
χ212222-22-2222200-2-2-2-22200200000000-22-2000022-200-20000000000
χ222222-22-2222200-2-2-2-22200200000000-22-20000-2-220020000000000
χ232222-22-2222200-2-2-2-2-2-2002000000002-2200002i−2i−2i002i0000000000
χ242222-22-2222200-2-2-2-2-2-2002000000002-220000−2i2i2i00−2i0000000000
χ252222-2-2222222-2-2-2222200-2000000002-2-22-2-220000000000000000
χ262222-2-2222222-2-2-222-2-200-200000000-2222-22-20000000000000000
χ272222-2-222222-22-2-2222200-2000000002-2-2-222-20000000000000000
χ282222-2-222222-22-2-222-2-200-200000000-222-22-220000000000000000
χ294444444-1-1-1-144-1-1-1-10044-1-1-1-1-1-1-1-1-1000-1-1000000000000000000
χ304444444-1-1-1-144-1-1-1-100-4-4-111111111000-1-1000000000000000000
χ314444444-1-1-1-1-4-4-1-1-1-1004-4-1-1-1-1-1111100011000000000000000000
χ324444444-1-1-1-1-4-4-1-1-1-100-44-11111-1-1-1-100011000000000000000000
χ334444-4-44-1-1-1-14-411-1-10000155−5−555−5−5000-11000000000000000000
χ344444-4-44-1-1-1-14-411-1-100001−5−555−5−555000-11000000000000000000
χ354444-4-44-1-1-1-1-4411-1-10000155−5−5−5−5550001-1000000000000000000
χ364444-4-44-1-1-1-1-4411-1-100001−5−55555−5−50001-1000000000000000000
χ374-4-440004-4-440000004-4000000000000000000000000002i−2i2i−2i0000
χ384-4-440004-4-440000004-400000000000000000000000000−2i2i−2i2i0000
χ394-4-440004-4-44000000-44000000000000000000000000002-2-220000
χ404-4-440004-4-44000000-4400000000000000000000000000-222-20000
χ4188888-8-8-2-2-2-200-2-222000020000000000000000000000000000000
χ428888-88-8-2-2-2-20022220000-20000000000000000000000000000000
χ4388-8-80008-88-8000000000000000000000000000000000000000000
χ4488-8-8000-22-22000025−25000002ζ6−2ζ14−2ζ6+2ζ14−2ζ22+2ζ382ζ22−2ζ38000000000000000000000000000
χ4588-8-8000-22-22000025−2500000−2ζ6+2ζ142ζ6−2ζ142ζ22−2ζ38−2ζ22+2ζ38000000000000000000000000000
χ4688-8-8000-22-220000−252500000−2ζ22+2ζ382ζ22−2ζ38−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000000
χ4788-8-8000-22-220000−2525000002ζ22−2ζ38−2ζ22+2ζ382ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000000
χ488-88-800088-8-8000000000000000000000000000000000000000000
χ498-88-8000-2-2220025−2500000000000−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ3900000000000000000000000
χ508-88-8000-2-2220025−2500000000000ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ3900000000000000000000000
χ518-88-8000-2-22200−252500000000000ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ3900000000000000000000000
χ528-88-8000-2-22200−252500000000000−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ3900000000000000000000000
χ5316-16-1616000-444-4000000000000000000000000000000000000000000

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