Finite Group Databasebeta

← Group #12254556

Character table — Group #12254556

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11222222244444444448888888888888101016161616161616161616161616161616161616161616202020202032323232404040404080808080
order12244551010248810102020202088888101020204040404088241616404040404040404040408080808080808080448881010202022444441616
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1
χ311111111111111111111111111111111-1-11111111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1111-1-1
χ611111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11-1-111
χ711111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111
χ811111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-111-1-1
χ9111111111-1-111111111-111-1-1-1-1-1-11111111-11-1-1-11111-1-1-1-11111-1-1-1-1-1-11-1-111-1-11-11-111-11-1
χ10111111111-1-111111111-111-1-1-1-1-1-1111111-11-11-1-11111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1111-11-11-11-11
χ11111111111-1-111111111-111-1-1-1-1-1-11111-1-11-11-1-1-11111-1-1-1-11111-1-1-1-111-11111-1-1-11-11-1-11-11
χ12111111111-1-111111111-111-1-1-1-1-1-11111-1-1-11-11-1-11111-1-1-1-1-1-1-1-1111111-111-1-111-11-11-11-11-1
χ13111111111-1-111111111-1-1-111-1-1-1-11111111-1-11-1-1-1-1-1-11111-1-1-1-11111-1-11-1-111-1-1-11-1111-1-11
χ14111111111-1-111111111-1-1-111-1-1-1-1111111-111-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1-1-111-11-111-111-1
χ15111111111-1-111111111-1-1-111-1-1-1-11111-1-11-1-11-1-1-1-1-1-11111-1-1-1-1111111-11111-1-11-11-1-1-111-1
χ16111111111-1-111111111-1-1-111-1-1-1-11111-1-1-111-1-1-1-1-1-1-111111111-1-1-1-111-111-1-1111-11-1-11-1-11
χ1722222222222-2-2222222-200002222-2-2-2-2220000-2-20000000000000000-2-222200000000-20000
χ1822222222222-2-2222222-200002222-2-2-2-2-2-20000-2-2000000000000000022-2-2-20000000020000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2220000220000000000000000222-2-200000000-20000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-20000220000000000000000-2-2-2220000000020000
χ2122222−1+52−1−52−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−5222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52002222−1+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+52−1−52−1−5200000−1+52−1−52−1+52−1−52000000000
χ2222222−1+52−1−52−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−5222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5200-2-2-2-2−1+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+52000001−521+521−521+52000000000
χ2322222−1+52−1−52−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−522-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−520022-2-2−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+5200000−1+52−1−52−1+52−1−52000000000
χ2422222−1+52−1−52−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−522-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5200-2-222−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000001−521+521−521+52000000000
χ2522222−1+52−1−52−1+52−1−52-2-222−1+52−1−52−1+52−1−52−1+52−1−52-222-2-21−521+521−521+52−1+52−1+52−1−52−1−52002-22-21−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+5200000−1+52−1−521−521+52000000000
χ2622222−1+52−1−52−1+52−1−52-2-222−1+52−1−52−1+52−1−52−1+52−1−52-222-2-21−521+521−521+52−1+52−1+52−1−52−1−5200-22-221−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52000001−521+52−1+52−1−52000000000
χ2722222−1+52−1−52−1+52−1−52-2-222−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2221−521+521−521+52−1+52−1+52−1−52−1−52002-2-221−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200000−1+52−1−521−521+52000000000
χ2822222−1+52−1−52−1+52−1−52-2-222−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2221−521+521−521+52−1+52−1+52−1−52−1−5200-222-21−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52000001−521+52−1+52−1−52000000000
χ2922222−1−52−1+52−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+5222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52002222−1−52−1+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+5200000−1−52−1+52−1−52−1+52000000000
χ3022222−1−52−1+52−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+5222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5200-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000001+521−521+521−52000000000
χ3122222−1−52−1+52−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+522-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+520022-2-2−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−5200000−1−52−1+52−1−52−1+52000000000
χ3222222−1−52−1+52−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+522-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5200-2-222−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000001+521−521+521−52000000000
χ3322222−1−52−1+52−1−52−1+52-2-222−1−52−1+52−1−52−1+52−1−52−1+52-222-2-21+521−521+521−52−1−52−1−52−1+52−1+52002-22-21+521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−5200000−1−52−1+521+521−52000000000
χ3422222−1−52−1+52−1−52−1+52-2-222−1−52−1+52−1−52−1+52−1−52−1+52-222-2-21+521−521+521−52−1−52−1−52−1+52−1+5200-22-221+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+52000001+521−52−1−52−1+52000000000
χ3522222−1−52−1+52−1−52−1+52-2-222−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2221+521−521+521−52−1−52−1−52−1+52−1+52002-2-221+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+5200000−1−52−1+521+521−52000000000
χ3622222−1−52−1+52−1−52−1+52-2-222−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2221+521−521+521−52−1−52−1−52−1+52−1+5200-222-21+521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52000001+521−52−1−52−1+52000000000
χ3722-22-22222002-2-2-222-2-20002i−2i00002-22-20000000000002i−2i2i−2i000000002i−2i02i−2i000020-2000000
χ3822-22-22222002-2-2-222-2-20002i−2i00002-22-20000000000002i−2i2i−2i00000000−2i2i0−2i2i0000-202000000
χ3922-22-22222002-2-2-222-2-2000−2i2i00002-22-2000000000000−2i2i−2i2i000000002i−2i02i−2i0000-202000000
χ4022-22-22222002-2-2-222-2-2000−2i2i00002-22-2000000000000−2i2i−2i2i00000000−2i2i0−2i2i000020-2000000
χ4122-22-2222200-22-2-222-2-202i−2i000000-22-22000000002i−2i2i−2i0000000000002i−2i0−2i2i0000020-200000
χ4222-22-2222200-22-2-222-2-202i−2i000000-22-22000000002i−2i2i−2i000000000000−2i2i02i−2i00000-20200000
χ4322-22-2222200-22-2-222-2-20−2i2i000000-22-2200000000−2i2i−2i2i0000000000002i−2i0−2i2i00000-20200000
χ4422-22-2222200-22-2-222-2-20−2i2i000000-22-2200000000−2i2i−2i2i000000000000−2i2i02i−2i0000020-200000
χ4544444−1+5−1−5−1+5−1−544-4-4−1+5−1−5−1+5−1−5−1+5−1−5-40000−1+5−1−5−1+5−1−51−51−51+51+50000001−51+50000000000000000000000000000000000
χ4644444−1+5−1−5−1+5−1−5-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5400001−51+51−51+51−51−51+51+5000000−1+5−1−50000000000000000000000000000000000
χ4744444−1−5−1+5−1−5−1+544-4-4−1−5−1+5−1−5−1+5−1−5−1+5-40000−1−5−1+5−1−5−1+51+51+51−51−50000001+51−50000000000000000000000000000000000
χ4844444−1−5−1+5−1−5−1+5-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5400001+51−51+51−51+51+51−51−5000000−1−5−1+50000000000000000000000000000000000
χ49444-4-444444-40044-4-4-4-40000044-4-40000000000000000000000000000000000000000000000
χ50444-4-44444-440044-4-4-4-400000-4-4440000000000000000000000000000000000000000000000
χ51444-4-4−1+5−1−5−1+5−1−54-400−1+5−1−51−51+51−51+500000−1+5−1−51−51+500000000000000000000ζ7−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−ζ39000000000000000000
χ52444-4-4−1+5−1−5−1+5−1−54-400−1+5−1−51−51+51−51+500000−1+5−1−51−51+500000000000000000000−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+ζ39000000000000000000
χ53444-4-4−1+5−1−5−1+5−1−5-4400−1+5−1−51−51+51−51+5000001−51+5−1+5−1−500000000000000000000ζ7−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+ζ39000000000000000000
χ54444-4-4−1+5−1−5−1+5−1−5-4400−1+5−1−51−51+51−51+5000001−51+5−1+5−1−500000000000000000000−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−ζ39000000000000000000
χ55444-4-4−1−5−1+5−1−5−1+54-400−1−5−1+51+51−51+51−500000−1−5−1+51+51−500000000000000000000−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37000000000000000000
χ56444-4-4−1−5−1+5−1−5−1+54-400−1−5−1+51+51−51+51−500000−1−5−1+51+51−500000000000000000000ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37000000000000000000
χ57444-4-4−1−5−1+5−1−5−1+5-4400−1−5−1+51+51−51+51−5000001+51−5−1−5−1+500000000000000000000−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37000000000000000000
χ58444-4-4−1−5−1+5−1−5−1+5-4400−1−5−1+51+51−51+51−5000001+51−5−1−5−1+500000000000000000000ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37000000000000000000
χ5944-44-4−1+5−1−5−1+5−1−5004-41−51+5−1+5−1−51−51+50004i−4i0000−1+51−5−1−51+5000000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400000000000000000000000000
χ6044-44-4−1+5−1−5−1+5−1−5004-41−51+5−1+5−1−51−51+5000−4i4i0000−1+51−5−1−51+50000000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400000000000000000000000000
χ6144-44-4−1+5−1−5−1+5−1−500-441−51+5−1+5−1−51−51+504i−4i0000001−5−1+51+5−1−500000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14000000000000000000000000000000
χ6244-44-4−1+5−1−5−1+5−1−500-441−51+5−1+5−1−51−51+50−4i4i0000001−5−1+51+5−1−5000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14000000000000000000000000000000
χ6344-44-4−1−5−1+5−1−5−1+5004-41+51−5−1−5−1+51+51−50004i−4i0000−1−51+5−1+51−5000000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ3800000000000000000000000000
χ6444-44-4−1−5−1+5−1−5−1+5004-41+51−5−1−5−1+51+51−5000−4i4i0000−1−51+5−1+51−50000000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ3800000000000000000000000000
χ6544-44-4−1−5−1+5−1−5−1+500-441+51−5−1−5−1+51+51−504i−4i0000001+5−1−51−5−1+500000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ38000000000000000000000000000000
χ6644-44-4−1−5−1+5−1−5−1+500-441+51−5−1−5−1+51+51−50−4i4i0000001+5−1−51−5−1+5000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ38000000000000000000000000000000
χ6744-4-4444440000-4-4-4-444000000000000044000000000000000000000000-4000000000000000
χ6844-4-4444440000-4-4-4-4440000000000000-4-40000000000000000000000004000000000000000
χ6988-8-88−2+25−2−25−2+25−2−2500002−252+252−252+25−2+25−2−250000000000000000000000000000000000000000000000000000000
χ7088-8-88−2−25−2+25−2−25−2+2500002+252−252+252−25−2−25−2+250000000000000000000000000000000000000000000000000000000
χ718-800088-8-8000000000000000000000004i2−4i20000000000000000000000000000000000000000
χ728-800088-8-800000000000000000000000−4i24i20000000000000000000000000000000000000000
χ7316-16000−4+45−4−454−454+4500000000000000000000000000000000000000000000000000000000000000000
χ7416-16000−4−45−4+454+454−4500000000000000000000000000000000000000000000000000000000000000000

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