Finite Group Databasebeta

← Group #12011819

Character table — Group #12011819

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1122222224444444488888888881616161616161616161616161616161616161616161616163232323240404040808080808080
order12244551010241010202020208810102020404040402444101010101616202020204040808080808080808020202020448824441616
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ411111111111111111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ6111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ7111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1
χ922222222222222222-2-22222-2-2-2-200000000000000-2-200000000000022-2-2000000
χ1022222222222222222-2-22222-2-2-2-200000000000000-2-2000000000000-2-222000000
χ11222222222-2-22222222-2-2-2-2-22222002-20000000000-2-20000000022-2-20000000000
χ12222222222-2-22222222-2-2-2-2-2222200-220000000000-2-200000000-2-2220000000000
χ13222222222-2-2222222-22-2-2-2-2-2-2-2-2000000000000002200000000000000002-20000
χ14222222222-2-2222222-22-2-2-2-2-2-2-2-200000000000000220000000000000000-220000
χ1522222−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222−1+52−1+52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1−52−1+52−1−520000000000
χ1622222−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222-2-2−1+52−1+52−1−52−1−52-2-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+521−521+521−521+520000000000
χ1722222−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2221−521−521+521+52-2-21−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1−52−1+52−1−520000000000
χ1822222−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2-2-21−521−521+521+52221−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521+521−521+520000000000
χ1922222−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−522-21−521+521−521+52−1+52−1+52−1−52−1−52002-2ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ3600ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ361−521+52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−1+52−1−521−521+520000000000
χ2022222−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−522-21−521+521−521+52−1+52−1+52−1−52−1−52002-2−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ3600−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ361−521+52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36−1+52−1−521−521+520000000000
χ2122222−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−522-21−521+521−521+52−1+52−1+52−1−52−1−5200-22ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ3600ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ361−521+52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ361−521+52−1+52−1−520000000000
χ2222222−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−522-21−521+521−521+52−1+52−1+52−1−52−1−5200-22−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ3600−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ361−521+52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ361−521+52−1+52−1−520000000000
χ2322222−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522222−1−52−1−52−1+52−1+5222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52−1−52−1+520000000000
χ2422222−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222-2-2−1−52−1−52−1+52−1+52-2-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−521+521−521+521−520000000000
χ2522222−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2221+521+521−521−52-2-21+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1+52−1−52−1+520000000000
χ2622222−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2-2-21+521+521−521−52221+521+521−521−52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521−521+521−520000000000
χ2722222−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+522-21+521−521+521−52−1−52−1−52−1+52−1+52002-2−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ2800−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ281+521−52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28−1−52−1+521+521−520000000000
χ2822222−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+522-21+521−521+521−52−1−52−1−52−1+52−1+52002-2ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ2800ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ281+521−52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−1−52−1+521+521−520000000000
χ2922222−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+522-21+521−521+521−52−1−52−1−52−1+52−1+5200-22−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ2800−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ281+521−52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ281+521−52−1−52−1+520000000000
χ3022222−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+522-21+521−521+521−52−1−52−1−52−1+52−1+5200-22ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ2800ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ281+521−52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ281+521−52−1−52−1+520000000000
χ31222-2-222222-222-2-2-2-20022-2-20000000000002−20000002−22−22−22−200002-20000002−2
χ32222-2-222222-222-2-2-2-20022-2-20000000000002−20000002−22−22−22−20000-22000000−22
χ33222-2-222222-222-2-2-2-20022-2-2000000000000−22000000−22−22−22−2200002-2000000−22
χ34222-2-222222-222-2-2-2-20022-2-2000000000000−22000000−22−22−22−220000-220000002−2
χ3544444−1+5−1−5−1+5−1−544−1+5−1−5−1+5−1−5−1+5−1−5-4-4−1+5−1−5−1+5−1−51−51−51+51+5000000000000001−51+50000000000000000000000
χ3644444−1+5−1−5−1+5−1−5-4-4−1+5−1−5−1+5−1−5−1+5−1−5-441−51+51−51+51−51−51+51+500000000000000−1+5−1−50000000000000000000000
χ3744444−1−5−1+5−1−5−1+544−1−5−1+5−1−5−1+5−1−5−1+5-4-4−1−5−1+5−1−5−1+51+51+51−51−5000000000000001+51−50000000000000000000000
χ3844444−1−5−1+5−1−5−1+5-4-4−1−5−1+5−1−5−1+5−1−5−1+5-441+51−51+51−51+51+51−51−500000000000000−1−5−1+50000000000000000000000
χ39444-4-44444-4444-4-4-4-400-4-444000000000000000000000000000000000000000000
χ40444-4-4−1+5−1−5−1+5−1−54-4−1+5−1−51−51+51−51+500−1+5−1−51−51+500000000000022−22000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ3900000000000000
χ41444-4-4−1+5−1−5−1+5−1−54-4−1+5−1−51−51+51−51+500−1+5−1−51−51+5000000000000−2222000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ3900000000000000
χ42444-4-4−1+5−1−5−1+5−1−5-44−1+5−1−51−51+51−51+5001−51+5−1+5−1−500000000000000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ3900000000000000
χ43444-4-4−1+5−1−5−1+5−1−5-44−1+5−1−51−51+51−51+5001−51+5−1+5−1−500000000000000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ3900000000000000
χ44444-4-4−1−5−1+5−1−5−1+54-4−1−5−1+51+51−51+51−500−1−5−1+51+51−500000000000022−22000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ3700000000000000
χ45444-4-4−1−5−1+5−1−5−1+54-4−1−5−1+51+51−51+51−500−1−5−1+51+51−5000000000000−2222000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ3700000000000000
χ46444-4-4−1−5−1+5−1−5−1+5-44−1−5−1+51+51−51+51−5001+51−5−1−5−1+500000000000000000000−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ3700000000000000
χ47444-4-4−1−5−1+5−1−5−1+5-44−1−5−1+51+51−51+51−5001+51−5−1−5−1+500000000000000000000ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ3700000000000000
χ4844-44-4444400-4-444-4-4000000000000000000000000000000000000000000002i−2i00
χ4944-44-4444400-4-444-4-400000000000000000000000000000000000000000000−2i2i00
χ5044-4-44444400-4-4-4-44400000000002-200222200-2-2-2-2000000000000000000000000
χ5144-4-44444400-4-4-4-4440000000000-2200-2-2-2-2002222000000000000000000000000
χ5244-4-44−1+5−1−5−1+5−1−5001−51+51−51+5−1+5−1−50000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ362-200−2ζ28−2ζ12−2ζ4−2ζ36002ζ282ζ122ζ42ζ36000000000000000000000000
χ5344-4-44−1+5−1−5−1+5−1−5001−51+51−51+5−1+5−1−50000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36-22002ζ282ζ122ζ42ζ3600−2ζ28−2ζ12−2ζ4−2ζ36000000000000000000000000
χ5444-4-44−1+5−1−5−1+5−1−5001−51+51−51+5−1+5−1−5000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ362-200−2ζ12−2ζ28−2ζ36−2ζ4002ζ122ζ282ζ362ζ4000000000000000000000000
χ5544-4-44−1+5−1−5−1+5−1−5001−51+51−51+5−1+5−1−5000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36-22002ζ122ζ282ζ362ζ400−2ζ12−2ζ28−2ζ36−2ζ4000000000000000000000000
χ5644-4-44−1−5−1+5−1−5−1+5001+51−51+51−5−1−5−1+5000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ282-200−2ζ4−2ζ36−2ζ12−2ζ28002ζ42ζ362ζ122ζ28000000000000000000000000
χ5744-4-44−1−5−1+5−1−5−1+5001+51−51+51−5−1−5−1+5000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28-22002ζ42ζ362ζ122ζ2800−2ζ4−2ζ36−2ζ12−2ζ28000000000000000000000000
χ5844-4-44−1−5−1+5−1−5−1+5001+51−51+51−5−1−5−1+50000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ282-200−2ζ36−2ζ4−2ζ28−2ζ12002ζ362ζ42ζ282ζ12000000000000000000000000
χ5944-4-44−1−5−1+5−1−5−1+5001+51−51+51−5−1−5−1+50000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28-22002ζ362ζ42ζ282ζ1200−2ζ36−2ζ4−2ζ28−2ζ12000000000000000000000000
χ6088-88-8−2+25−2−25−2+25−2−25002−252+25−2+25−2−252−252+25000000000000000000000000000000000000000000000000
χ6188-88-8−2−25−2+25−2−25−2+25002+252−25−2−25−2+252+252−25000000000000000000000000000000000000000000000000
χ628-800088-8-80000000000000000000000000000000000000000000000002i2−2i2000000
χ638-800088-8-8000000000000000000000000000000000000000000000000−2i22i2000000
χ6416-16000−4+45−4−454−454+4500000000000000000000000000000000000000000000000000000000
χ6516-16000−4−45−4+454+454−4500000000000000000000000000000000000000000000000000000000

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