Finite Group Databasebeta

← Group #12073402

Character table — Group #12073402

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222222244444444888888888888888881010101016161616161616161616161616161616161616161616161616161616202020204040404040404040408080
order1222225510101010101044441010101044444888820202020202020204444442020202020202020202020202020202020204040404040404040444422444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11-1-11111-1-1
χ611111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-111-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1
χ911111111111111-1-1111111-111-1-111-1-1-1-1-1-1111111111-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-1-11-111-1-11-1
χ1011111111111111-1-1111111-111-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-111-11-1-111-11
χ1111111111111111-1-1111111-111-1-1-1-111-1-1-1-111111111-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-1-11-1-1-111-11
χ1211111111111111-1-1111111-111-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-1111-1-11-1
χ1311111111111111-1-1111111-1-1-11111-1-1-1-1-1-111111111-11-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-11-1-1111-1-1-11
χ1411111111111111-1-1111111-1-1-11111-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-11-111-1-1-1111-1
χ1511111111111111-1-1111111-1-1-111-1-111-1-1-1-1111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-11-1-11-1-1111-1
χ1611111111111111-1-1111111-1-1-111-1-111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11-111-111-1-1-11
χ172222222222222222-2-22222-2000000002222-2-2-2-2222200-2-200000000000000000000000022-2-200-200000000
χ182222222222222222-2-22222-2000000002222-2-2-2-2-2-2-2-200-2-2000000000000000000000000-2-22200200000000
χ1922222222222222-2-2-2-22222200000000-2-2-2-2-2-2-2-222220022000000000000000000000000-2-2-2-200200000000
χ2022222222222222-2-2-2-22222200000000-2-2-2-2-2-2-2-2-2-2-2-20022000000000000000000000000222200-200000000
χ21222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222−1+52−1−52−1+52−1−52222222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000022−1+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+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000
χ22222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222−1+52−1−52−1+52−1−5222222-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52000000000000000
χ23222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222−1+52−1−52−1+52−1−522-2-2-2-22222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000-2-2−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000
χ24222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222−1+52−1−52−1+52−1−522-2-2-2-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000022−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52000000000000000
χ25222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-222−1+52−1−52−1+52−1−52-222-2-222-2-21−521−521+521+52−1+52−1+52−1−52−1−5200002-21−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000000000000
χ26222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-222−1+52−1−52−1+52−1−52-222-2-2-2-2221−521−521+521+52−1+52−1+52−1−52−1−520000-221−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000
χ27222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-222−1+52−1−52−1+52−1−52-2-2-22222-2-21−521−521+521+52−1+52−1+52−1−52−1−520000-221−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52000000000000000
χ28222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-222−1+52−1−52−1+52−1−52-2-2-222-2-2221−521−521+521+52−1+52−1+52−1−52−1−5200002-21−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000
χ29222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522222−1−52−1+52−1−52−1+52222222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000022−1−52−1+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+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000
χ30222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522222−1−52−1+52−1−52−1+5222222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52000000000000000
χ31222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522222−1−52−1+52−1−52−1+522-2-2-2-22222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000-2-2−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000
χ32222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522222−1−52−1+52−1−52−1+522-2-2-2-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000022−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000000000000000
χ33222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-222−1−52−1+52−1−52−1+52-222-2-222-2-21+521+521−521−52−1−52−1−52−1+52−1+5200002-21+521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000000000000000
χ34222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-222−1−52−1+52−1−52−1+52-222-2-2-2-2221+521+521−521−52−1−52−1−52−1+52−1+520000-221+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52000000000000000
χ35222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-222−1−52−1+52−1−52−1+52-2-2-22222-2-21+521+521−521−52−1−52−1−52−1+52−1+520000-221+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52000000000000000
χ36222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-222−1−52−1+52−1−52−1+52-2-2-222-2-2221+521+521−521−52−1−52−1−52−1+52−1+5200002-21+521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52000000000000000
χ372222-2-222222222002-2-2-2-2-20002-2000000002-22-222-2-2000000002-22-20000000000000000002-20200-2000000
χ382222-2-222222222002-2-2-2-2-20002-2000000002-22-2-2-222000000002-22-2000000000000000000-220-2002000000
χ392222-2-222222222002-2-2-2-2-2000-22000000002-22-222-2-200000000-22-220000000000000000002-20-2002000000
χ402222-2-222222222002-2-2-2-2-2000-22000000002-22-2-2-22200000000-22-22000000000000000000-220200-2000000
χ412222-2-22222222200-22-2-2-2-202-20000000000-22-2222-2-200002-22-20000000000000000000000-22200-20000000
χ422222-2-22222222200-22-2-2-2-202-20000000000-22-22-2-22200002-22-200000000000000000000002-2-20020000000
χ432222-2-22222222200-22-2-2-2-20-220000000000-22-2222-2-20000-22-220000000000000000000000-22-20020000000
χ442222-2-22222222200-22-2-2-2-20-220000000000-22-22-2-2220000-22-2200000000000000000000002-2200-20000000
χ452-2-22-222222-2-2-2-22-20022-2-2000002−22−22-22-200002i−2i2i−2i000000000000000000002−22−22−22−22i−2i0000000i2−i2i2−i200
χ462-2-22-222222-2-2-2-22-20022-2-2000002−22−22-22-20000−2i2i−2i2i000000000000000000002−22−22−22−2−2i2i0000000−i2i2−i2i200
χ472-2-22-222222-2-2-2-22-20022-2-200000−22−222-22-200002i−2i2i−2i00000000000000000000−22−22−22−222i−2i0000000−i2i2−i2i200
χ482-2-22-222222-2-2-2-22-20022-2-200000−22−222-22-20000−2i2i−2i2i00000000000000000000−22−22−22−22−2i2i0000000i2−i2i2−i200
χ492-2-22-222222-2-2-2-2-220022-2-2000002−2−22-22-2200002i−2i2i−2i000000000000000000002−22−2−22−22−2i2i0000000i2−i2−i2i200
χ502-2-22-222222-2-2-2-2-220022-2-2000002−2−22-22-220000−2i2i−2i2i000000000000000000002−22−2−22−222i−2i0000000−i2i2i2−i200
χ512-2-22-222222-2-2-2-2-220022-2-200000−222−2-22-2200002i−2i2i−2i00000000000000000000−22−222−22−2−2i2i0000000−i2i2i2−i200
χ522-2-22-222222-2-2-2-2-220022-2-200000−222−2-22-220000−2i2i−2i2i00000000000000000000−22−222−22−22i−2i0000000i2−i2−i2i200
χ53444444−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−544-4-4−1+5−1−5−1+5−1−5-400000000−1+5−1+5−1−5−1−51−51−51+51+50000001−51+5000000000000000000000000000000000000000
χ54444444−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-4-4-4-4−1+5−1−5−1+5−1−54000000001−51−51+51+51−51−51+51+5000000−1+5−1−5000000000000000000000000000000000000000
χ55444444−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+544-4-4−1−5−1+5−1−5−1+5-400000000−1−5−1−5−1+5−1+51+51+51−51−50000001+51−5000000000000000000000000000000000000000
χ56444444−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-4-4-4-4−1−5−1+5−1−5−1+54000000001+51+51−51−51+51+51−51−5000000−1−5−1+5000000000000000000000000000000000000000
χ574444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5004-41−51+51−51+50004-400000000−1+51−5−1−51+5000000000000−1+51−5−1−51+50000000000000000000000000000000
χ584444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5004-41−51+51−51+5000-4400000000−1+51−5−1−51+50000000000001−5−1+51+5−1−50000000000000000000000000000000
χ594444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−500-441−51+51−51+504-400000000001−5−1+51+5−1−500000000−1+51−5−1−51+500000000000000000000000000000000000
χ604444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−500-441−51+51−51+50-4400000000001−5−1+51+5−1−5000000001−5−1+51+5−1−500000000000000000000000000000000000
χ614444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5004-41+51−51+51−50004-400000000−1−51+5−1+51−5000000000000−1−51+5−1+51−50000000000000000000000000000000
χ624444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5004-41+51−51+51−5000-4400000000−1−51+5−1+51−50000000000001+5−1−51−5−1+50000000000000000000000000000000
χ634444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+500-441+51−51+51−504-400000000001+5−1−51−5−1+500000000−1−51+5−1+51−500000000000000000000000000000000000
χ644444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+500-441+51−51+51−50-4400000000001+5−1−51−5−1+5000000001+5−1−51−5−1+500000000000000000000000000000000000
χ654-4-444-44444-4-4-4-40000-4-444000000000000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ664-4-444-44444-4-4-4-40000-4-44400000000000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ674-4-44-44−1+5−1−5−1+5−1−51−51−51+51+54-400−1+5−1−51−51+50000022−2222−22−1+51−5−1−51+50000000000000000000000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39000000000000000
χ684-4-44-44−1+5−1−5−1+5−1−51−51−51+51+54-400−1+5−1−51−51+500000−2222−2222−1+51−5−1−51+50000000000000000000000000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39000000000000000
χ694-4-44-44−1+5−1−5−1+5−1−51−51−51+51+5-4400−1+5−1−51−51+50000022−22−22221−5−1+51+5−1−50000000000000000000000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39000000000000000
χ704-4-44-44−1+5−1−5−1+5−1−51−51−51+51+5-4400−1+5−1−51−51+500000−222222−221−5−1+51+5−1−50000000000000000000000000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39000000000000000
χ714-4-44-44−1−5−1+5−1−5−1+51+51+51−51−54-400−1−5−1+51+51−50000022−2222−22−1−51+5−1+51−50000000000000000000000000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37000000000000000
χ724-4-44-44−1−5−1+5−1−5−1+51+51+51−51−54-400−1−5−1+51+51−500000−2222−2222−1−51+5−1+51−50000000000000000000000000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37000000000000000
χ734-4-44-44−1−5−1+5−1−5−1+51+51+51−51−5-4400−1−5−1+51+51−50000022−22−22221+5−1−51−5−1+50000000000000000000000000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37000000000000000
χ744-4-44-44−1−5−1+5−1−5−1+51+51+51−51−5-4400−1−5−1+51+51−500000−222222−221+5−1−51−5−1+50000000000000000000000000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37000000000000000
χ7588-8-80088-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000
χ7688-8-800−2+25−2−252−252+25−2+252−25−2−252+2500000000000000000000000000000000000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000000
χ7788-8-800−2+25−2−252−252+25−2+252−25−2−252+25000000000000000000000000000000000000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000000
χ7888-8-800−2−25−2+252+252−25−2−252+25−2+252−25000000000000000000000000000000000000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ38000000000000000000000000000
χ7988-8-800−2−25−2+252+252−25−2−252+25−2+252−2500000000000000000000000000000000000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ38000000000000000000000000000
χ808-88-80088-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000
χ818-88-800−2+25−2−252−252+252−25−2+252+25−2−25000000000000000000000000000000000000000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000
χ828-88-800−2+25−2−252−252+252−25−2+252+25−2−250000000000000000000000000000000000000000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000
χ838-88-800−2−25−2+252+252−252+25−2−252−25−2+250000000000000000000000000000000000000000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ3800000000000000000000000
χ848-88-800−2−25−2+252+252−252+25−2−252−25−2+25000000000000000000000000000000000000000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ3800000000000000000000000
χ858-8-888-8−2+25−2−25−2+25−2−252−252−252+252+2500002−252+25−2+25−2−250000000000000000000000000000000000000000000000000000000000000000
χ868-8-888-8−2−25−2+25−2−25−2+252+252+252−252−2500002+252−25−2−25−2+250000000000000000000000000000000000000000000000000000000000000000

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