Finite Group Databasebeta

← Group #12012049

Character table — Group #12012049

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222444444888888888888161616161616161616161616161616161616161616161616161616161616164040404040408080808080
order1222225510101010101044101010102244202020202020202044488101010102020202020202020202020202020404040404040404022224448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1
χ411111111111111111111111111111111-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111-1-1
χ611111111111111111111-1-1111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111
χ711111111111111111111-1-11111111111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-111
χ811111111111111111111-1-11111111111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1111-1-1
χ92222222222222222222200-2-22222-2-2-2-20000000000000-2-200000000000000002200-2-200000
χ102222222222222222222200-2-22222-2-2-2-20000000000000-2-20000000000000000-2-2002200000
χ1122222222222222-2-2222200-22-2-2-2-2-2-2-2-20000000000000220000000000000000002200-20000
χ1222222222222222-2-2222200-22-2-2-2-2-2-2-2-2000000000000022000000000000000000-2-20020000
χ1322222222222222-2-22222222-2-2-2-2-2222200-20022220000-2-20000-2-2-2-20000000000000000000
χ1422222222222222-2-22222-2-22-2-2-2-2-2222200200-2-2-2-20000-2-2000022220000000000000000000
χ15222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+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+52−1−52−1−52−1−52−1−5200000000000
χ16222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-22-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+5200000000000
χ17222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2-2-21−521−521+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+521−521−521−521−521+521+521+521+5200000000000
χ18222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2221−521−521+521+521−521−521+521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200000000000
χ19222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52222-21−521−521+521+52−1+52−1+52−1−52−1−5200-200−1+52−1+52−1−52−1−52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ361−521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ361−521−521+521+52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ3600000000000
χ20222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52222-21−521−521+521+52−1+52−1+52−1−52−1−5200-200−1+52−1+52−1−52−1−52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ361−521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ361−521−521+521+52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ3600000000000
χ21222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52-2-22-21−521−521+521+52−1+52−1+52−1−52−1−52002001−521−521+521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ361−521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−1+52−1+52−1−52−1−52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ3600000000000
χ22222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52-2-22-21−521−521+521+52−1+52−1+52−1−52−1−52002001−521−521+521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ361−521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−1+52−1+52−1−52−1−52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ3600000000000
χ23222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+522222−1−52−1−52−1+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+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+5200000000000
χ24222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-22-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−5200000000000
χ25222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2-2-21+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+521−521−521+521+521+521+521−521−521−521−5200000000000
χ26222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2221+521+521−521−521+521+521−521−52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200000000000
χ27222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52222-21+521+521−521−52−1−52−1−52−1+52−1+5200-200−1−52−1−52−1+52−1+52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ281+521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ281+521+521−521−52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ2800000000000
χ28222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52222-21+521+521−521−52−1−52−1−52−1+52−1+5200-200−1−52−1−52−1+52−1+52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ281+521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ281+521+521−521−52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ2800000000000
χ29222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52-2-22-21+521+521−521−52−1−52−1−52−1+52−1+52002001+521+521−521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ281+521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−1−52−1−52−1+52−1+52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ2800000000000
χ30222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52-2-22-21+521+521−521−52−1−52−1−52−1+52−1+52002001+521+521−521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ281+521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−1−52−1−52−1+52−1+52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ2800000000000
χ3122-2-2-222222-2-2-2-22-2-2-22200002-22-20000000i2−i2000000000000000000i2−i2i2−i2i2−i2i2−i22-20000000i2−i2
χ3222-2-2-222222-2-2-2-22-2-2-22200002-22-20000000i2−i2000000000000000000i2−i2i2−i2i2−i2i2−i2-220000000−i2i2
χ3322-2-2-222222-2-2-2-22-2-2-22200002-22-20000000−i2i2000000000000000000−i2i2−i2i2−i2i2−i2i22-20000000−i2i2
χ3422-2-2-222222-2-2-2-22-2-2-22200002-22-20000000−i2i2000000000000000000−i2i2−i2i2−i2i2−i2i2-220000000i2−i2
χ35444444−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−544−1+5−1−5−1+5−1−500-4-4−1+5−1+5−1−5−1−51−51−51+51+500000000000001−51+5000000000000000000000000000
χ36444444−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4-4−1+5−1−5−1+5−1−500-441−51−51+51+51−51−51+51+50000000000000−1+5−1−5000000000000000000000000000
χ37444444−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+544−1−5−1+5−1−5−1+500-4-4−1−5−1−5−1+5−1+51+51+51−51−500000000000001+51−5000000000000000000000000000
χ38444444−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4-4−1−5−1+5−1−5−1+500-441+51+51−51−51+51+51−51−50000000000000−1−5−1+5000000000000000000000000000
χ394444-4-44444444400-4-4-4-40000000000002-20000000222200-2-2-2-200000000000000000000000
χ404444-4-44444444400-4-4-4-4000000000000-220000000-2-2-2-200222200000000000000000000000
χ414444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5001−51+51−51+5000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ362-20000000−2ζ28−2ζ12−2ζ4−2ζ36002ζ282ζ122ζ42ζ3600000000000000000000000
χ424444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5001−51+51−51+5000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36-2200000002ζ282ζ122ζ42ζ3600−2ζ28−2ζ12−2ζ4−2ζ3600000000000000000000000
χ434444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5001−51+51−51+500000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ362-20000000−2ζ12−2ζ28−2ζ36−2ζ4002ζ122ζ282ζ362ζ400000000000000000000000
χ444444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5001−51+51−51+500000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36-2200000002ζ122ζ282ζ362ζ400−2ζ12−2ζ28−2ζ36−2ζ400000000000000000000000
χ454444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5001+51−51+51−500000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ282-20000000−2ζ4−2ζ36−2ζ12−2ζ28002ζ42ζ362ζ122ζ2800000000000000000000000
χ464444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5001+51−51+51−500000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28-2200000002ζ42ζ362ζ122ζ2800−2ζ4−2ζ36−2ζ12−2ζ2800000000000000000000000
χ474444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5001+51−51+51−5000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ282-20000000−2ζ36−2ζ4−2ζ28−2ζ12002ζ362ζ42ζ282ζ1200000000000000000000000
χ484444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5001+51−51+51−5000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28-2200000002ζ362ζ42ζ282ζ1200−2ζ36−2ζ4−2ζ28−2ζ1200000000000000000000000
χ4944-4-44-44444-4-4-4-40044-4-4000000000000000000000000000000000000000000000000002i−2i00
χ5044-4-44-44444-4-4-4-40044-4-400000000000000000000000000000000000000000000000000−2i2i00
χ5144-4-4-444444-4-4-4-4-44-4-4440000-44-440000000000000000000000000000000000000000000000
χ5244-4-4-44−1+5−1−5−1+5−1−51−51+51−51+54-41−51+5−1+5−1−50000−1+51−5−1−51+500000002i2−2i2000000000000000000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ3900000000000
χ5344-4-4-44−1+5−1−5−1+5−1−51−51+51−51+54-41−51+5−1+5−1−50000−1+51−5−1−51+50000000−2i22i2000000000000000000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ3900000000000
χ5444-4-4-44−1+5−1−5−1+5−1−51−51+51−51+5-441−51+5−1+5−1−500001−5−1+51+5−1−5000000000000000000000000000ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ3900000000000
χ5544-4-4-44−1+5−1−5−1+5−1−51−51+51−51+5-441−51+5−1+5−1−500001−5−1+51+5−1−5000000000000000000000000000−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ3900000000000
χ5644-4-4-44−1−5−1+5−1−5−1+51+51−51+51−54-41+51−5−1−5−1+50000−1−51+5−1+51−500000002i2−2i2000000000000000000ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ3700000000000
χ5744-4-4-44−1−5−1+5−1−5−1+51+51−51+51−54-41+51−5−1−5−1+50000−1−51+5−1+51−50000000−2i22i2000000000000000000−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ3700000000000
χ5844-4-4-44−1−5−1+5−1−5−1+51+51−51+51−5-441+51−5−1−5−1+500001+5−1−51−5−1+5000000000000000000000000000−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ3700000000000
χ5944-4-4-44−1−5−1+5−1−5−1+51+51−51+51−5-441+51−5−1−5−1+500001+5−1−51−5−1+5000000000000000000000000000ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ3700000000000
χ604-4-440044-4-4-4-4440000002-20000000000000002-22-20000000000000000000000002-22-200000
χ614-4-440044-4-4-4-4440000002-20000000000000002-22-2000000000000000000000000-22-2200000
χ624-4-440044-4-4-4-444000000-22000000000000000-22-220000000000000000000000002-2-2200000
χ634-4-440044-4-4-4-444000000-22000000000000000-22-22000000000000000000000000-222-200000
χ6488-8-88-8−2+25−2−25−2+25−2−252−252+252−252+2500−2+25−2−252−252+25000000000000000000000000000000000000000000000000000000
χ6588-8-88-8−2−25−2+25−2−25−2+252+252−252+252−2500−2−25−2+252+252−25000000000000000000000000000000000000000000000000000000
χ668-88-80088-8-888-8-8000000000000000000000000000000000000000000000000000000000000
χ678-88-800−2+25−2−252−252+25−2+25−2−252−252+250000000000000000000000000000000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ140000000000000000000
χ688-88-800−2+25−2−252−252+25−2+25−2−252−252+2500000000000000000000000000000000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ140000000000000000000
χ698-88-800−2−25−2+252+252−25−2−25−2+252+252−2500000000000000000000000000000000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ380000000000000000000
χ708-88-800−2−25−2+252+252−25−2−25−2+252+252−250000000000000000000000000000000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ380000000000000000000
χ718-8-8800−2+25−2−252−252+252−252+25−2+25−2−250000004-4000000000000000−1+51−5−1−51+5000000000000000000000000000000000
χ728-8-8800−2+25−2−252−252+252−252+25−2+25−2−25000000-440000000000000001−5−1+51+5−1−5000000000000000000000000000000000
χ738-8-8800−2−25−2+252+252−252+252−25−2−25−2+250000004-4000000000000000−1−51+5−1+51−5000000000000000000000000000000000
χ748-8-8800−2−25−2+252+252−252+252−25−2−25−2+25000000-440000000000000001+5−1−51−5−1+5000000000000000000000000000000000

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