Finite Group Databasebeta

← Group #12012473

Character table — Group #12012473

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111222222222244444488888888881616161616161616161616161616161616161616161616161616161616161616404080808080808080
order1222225510101010101044101010104420202020202020204444882020202020202020202020202020202020204040404040404040442248888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1
χ411111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1
χ6111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-1-1
χ922222222222222222222-2-22222-2-2-2-2000000-2-200000000000000000000000022-2000000
χ1022222222222222222222-2-22222-2-2-2-2000000-2-2000000000000000000000000-2-22000000
χ1122222222222222-2-222222-2-2-2-2-22222002-200-2-2000000002222-2-2-2-200000000000000000
χ1222222222222222-2-222222-2-2-2-2-2222200-2200-2-200000000-2-2-2-2222200000000000000000
χ1322222222222222-2-22222-22-2-2-2-2-2-2-2-2000000220000000000000000000000000002-20000
χ1422222222222222-2-22222-22-2-2-2-2-2-2-2-200000022000000000000000000000000000-220000
χ15222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52222222−1+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+52−1−52−1−52−1−52−1−52000000000
χ16222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2-2-2-2−1+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+52000000000
χ17222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-222-2-2−1+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+52000000000
χ18222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-222−1+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+52−1−52−1−52−1−52−1−52000000000
χ19222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−52−1+52−1−522-21−521−521+521+52−1+52−1+52−1−52−1−52002-2001−521+52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−1+52−1+52−1−52−1−521−521−521+521+52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36000000000
χ20222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−52−1+52−1−522-21−521−521+521+52−1+52−1+52−1−52−1−52002-2001−521+52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36−1+52−1+52−1−52−1−521−521−521+521+52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36000000000
χ21222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−52−1+52−1−522-21−521−521+521+52−1+52−1+52−1−52−1−5200-22001−521+52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ361−521−521+521+52−1+52−1+52−1−52−1−52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36000000000
χ22222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−52−1+52−1−522-21−521−521+521+52−1+52−1+52−1−52−1−5200-22001−521+52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ361−521−521+521+52−1+52−1+52−1−52−1−52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36000000000
χ23222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52222222−1−52−1+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+52000000000
χ24222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2-2-2-2−1−52−1+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+521−521−521−521−52000000000
χ25222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-222-2-2−1−52−1+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+521−521−521−521−52000000000
χ26222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-222−1−52−1+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+52000000000
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+522-21+521+521−521−52−1−52−1−52−1+52−1+52002-2001+521−52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28−1−52−1−52−1+52−1+521+521+521−521−52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28000000000
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+522-21+521+521−521−52−1−52−1−52−1+52−1+52002-2001+521−52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−1−52−1−52−1+52−1+521+521+521−521−52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28000000000
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+522-21+521+521−521−52−1−52−1−52−1+52−1+5200-22001+521−52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ281+521+521−521−52−1−52−1−52−1+52−1+52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28000000000
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+522-21+521+521−521−52−1−52−1−52−1+52−1+5200-22001+521−52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ281+521+521−521−52−1−52−1−52−1+52−1+52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28000000000
χ3122-2-22-22222-2-2-2-2-2222-2-2002-22-2000000002−20000000000000000002−22−22−22−22i−2i00000i2−i2
χ3222-2-22-22222-2-2-2-2-2222-2-2002-22-2000000002−20000000000000000002−22−22−22−2−2i2i00000−i2i2
χ3322-2-22-22222-2-2-2-2-2222-2-2002-22-200000000−22000000000000000000−22−22−22−222i−2i00000−i2i2
χ3422-2-22-22222-2-2-2-2-2222-2-2002-22-200000000−22000000000000000000−22−22−22−22−2i2i00000i2−i2
χ35444444−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−544−1+5−1−5−1+5−1−5-4-4−1+5−1+5−1−5−1−51−51−51+51+50000001−51+5000000000000000000000000000000000
χ36444444−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-4-4−1+5−1−5−1+5−1−5-441−51−51+51+51−51−51+51+5000000−1+5−1−5000000000000000000000000000000000
χ37444444−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+544−1−5−1+5−1−5−1+5-4-4−1−5−1−5−1+5−1+51+51+51−51−50000001+51−5000000000000000000000000000000000
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+5-441+51+51−51−51+51+51−51−5000000−1−5−1+5000000000000000000000000000000000
χ394444-4-44444444400-4-4-4-400000000002-20000002-22-22-22-20000000000000000000000000
χ404444-4-44444444400-4-4-4-40000000000-22000000-22-22-22-220000000000000000000000000
χ414444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5001−51+51−51+50000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ362-2000000−2ζ282ζ28−2ζ122ζ12−2ζ42ζ4−2ζ362ζ360000000000000000000000000
χ424444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5001−51+51−51+50000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36-220000002ζ28−2ζ282ζ12−2ζ122ζ4−2ζ42ζ36−2ζ360000000000000000000000000
χ434444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5001−51+51−51+5000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ362-2000000−2ζ122ζ12−2ζ282ζ28−2ζ362ζ36−2ζ42ζ40000000000000000000000000
χ444444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5001−51+51−51+5000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36-220000002ζ12−2ζ122ζ28−2ζ282ζ36−2ζ362ζ4−2ζ40000000000000000000000000
χ454444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5001+51−51+51−5000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ282-2000000−2ζ42ζ4−2ζ362ζ36−2ζ122ζ12−2ζ282ζ280000000000000000000000000
χ464444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5001+51−51+51−5000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28-220000002ζ4−2ζ42ζ36−2ζ362ζ12−2ζ122ζ28−2ζ280000000000000000000000000
χ474444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5001+51−51+51−50000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ282-2000000−2ζ362ζ36−2ζ42ζ4−2ζ282ζ28−2ζ122ζ120000000000000000000000000
χ484444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5001+51−51+51−50000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28-220000002ζ36−2ζ362ζ4−2ζ42ζ28−2ζ282ζ12−2ζ120000000000000000000000000
χ4944-4-44-44444-4-4-4-44-444-4-400-44-44000000000000000000000000000000000000000000000
χ5044-4-44-4−1+5−1−5−1+5−1−51−51−51+51+54-4−1+5−1−51−51+5001−5−1+51+5−1−50000000000000000000000000000−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+ζ39000000000
χ5144-4-44-4−1+5−1−5−1+5−1−51−51−51+51+54-4−1+5−1−51−51+5001−5−1+51+5−1−50000000000000000000000000000ζ7+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−ζ39000000000
χ5244-4-44-4−1+5−1−5−1+5−1−51−51−51+51+5-44−1+5−1−51−51+500−1+51−5−1−51+50000000022−22000000000000000000−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+ζ39000000000
χ5344-4-44-4−1+5−1−5−1+5−1−51−51−51+51+5-44−1+5−1−51−51+500−1+51−5−1−51+500000000−2222000000000000000000ζ7−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−ζ39000000000
χ5444-4-44-4−1−5−1+5−1−5−1+51+51+51−51−54-4−1−5−1+51+51−5001+5−1−51−5−1+50000000000000000000000000000−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+ζ37000000000
χ5544-4-44-4−1−5−1+5−1−5−1+51+51+51−51−54-4−1−5−1+51+51−5001+5−1−51−5−1+50000000000000000000000000000ζ21−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−ζ37000000000
χ5644-4-44-4−1−5−1+5−1−5−1+51+51+51−51−5-44−1−5−1+51+51−500−1−51+5−1+51−50000000022−22000000000000000000ζ21+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−ζ37000000000
χ5744-4-44-4−1−5−1+5−1−5−1+51+51+51−51−5-44−1−5−1+51+51−500−1−51+5−1+51−500000000−2222000000000000000000−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+ζ37000000000
χ5844-4-4-444444-4-4-4-400-4-444000000000000000000000000000000000000000000000002i−2i00
χ5944-4-4-444444-4-4-4-400-4-44400000000000000000000000000000000000000000000000−2i2i00
χ6088-8-8-88−2+25−2−25−2+25−2−252−252−252+252+25002−252+25−2+25−2−25000000000000000000000000000000000000000000000000000
χ6188-8-8-88−2−25−2+25−2−25−2+252+252+252−252−25002+252−25−2−25−2+25000000000000000000000000000000000000000000000000000
χ628-88-80088-8-88-88-8000000000000000000000000000000000000000000000000000000000
χ638-88-800−2+25−2−252−252+25−2+252−25−2−252+2500000000000000000000000000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ14000000000000000000000
χ648-88-800−2+25−2−252−252+25−2+252−25−2−252+25000000000000000000000000000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ14000000000000000000000
χ658-88-800−2−25−2+252+252−25−2−252+25−2+252−25000000000000000000000000000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ38000000000000000000000
χ668-88-800−2−25−2+252+252−25−2−252+25−2+252−2500000000000000000000000000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ38000000000000000000000
χ678-8-880088-8-8-88-88000000000000000000000000000000000000000000000000000000000
χ688-8-8800−2+25−2−252−252+252−25−2+252+25−2−25000000000000000000000000000000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ1400000000000000000
χ698-8-8800−2+25−2−252−252+252−25−2+252+25−2−250000000000000000000000000000000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ1400000000000000000
χ708-8-8800−2−25−2+252+252−252+25−2−252−25−2+250000000000000000000000000000000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ3800000000000000000
χ718-8-8800−2−25−2+252+252−252+25−2−252−25−2+25000000000000000000000000000000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ3800000000000000000

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