Finite Group Databasebeta

← Group #12013521

Character table — Group #12013521

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size111122222222222222224444444444444444444888888888888888888888888881616161616161616161620202020202020203232323232404040408080160
order1222444455888810101010101048820202020202020204040404040404040248810101010202020202020404040404040404040404040884040404040404040161616161616161621010101016161616882
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ5111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-111-1
χ6111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11
χ7111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-11
χ8111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1
χ92222222222-2-2-2-22222222-2-222222222-2-2-2-2-2-2-2-222-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000
χ102222222222-2-2-2-22222222-2-222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000000000
χ1122222222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522222−1+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+52−1−52−1−52−1−52−1−5222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52000000002−1+52−1+52−1−52−1−520000000
χ1222222222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522222−1+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+52−1−52−1−52−1−52−1−52-2-21−521−521−521−521+521+521+521+5200000000-21−521−521+521+520000000
χ1322222222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2-2-21−521−521+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+5222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200000000-21−521−521+521+520000000
χ1422222222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2-2-21−521−521+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+52-2-21−521−521−521−521+521+521+521+52000000002−1+52−1+52−1−52−1−520000000
χ1522222222−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−522-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+5222-2-2−1+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+5200ζ24−ζ56ζ24−ζ56−ζ24+ζ56−ζ24+ζ56−ζ8+ζ72−ζ8+ζ72ζ8−ζ72ζ8−ζ72000000000ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ720000000
χ1622222222−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−522-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+5222-2-2−1+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+5200−ζ24+ζ56−ζ24+ζ56ζ24−ζ56ζ24−ζ56ζ8−ζ72ζ8−ζ72−ζ8+ζ72−ζ8+ζ72000000000−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ720000000
χ1722222222−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−522-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-2-2221−521−521+521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200ζ24−ζ56ζ24−ζ56−ζ24+ζ56−ζ24+ζ56−ζ8+ζ72−ζ8+ζ72ζ8−ζ72ζ8−ζ72000000000−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ720000000
χ1822222222−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−522-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-2-2221−521−521+521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200−ζ24+ζ56−ζ24+ζ56ζ24−ζ56ζ24−ζ56ζ8−ζ72ζ8−ζ72−ζ8+ζ72−ζ8+ζ72000000000ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ720000000
χ1922222222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52222−1−52−1+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+522222−1−52−1−52−1+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+5222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52000000002−1−52−1−52−1+52−1+520000000
χ2022222222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52222−1−52−1+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+522222−1−52−1−52−1+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+52-2-21+521+521+521+521−521−521−521−5200000000-21+521+521−521−520000000
χ2122222222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52222−1−52−1+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+52-2-2-2-21+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−5222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200000000-21+521+521−521−520000000
χ2222222222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52222−1−52−1+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+52-2-2-2-21+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52-2-21+521+521+521+521−521−521−521−52000000002−1−52−1−52−1+52−1+520000000
χ2322222222−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+522-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−5222-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−5200−ζ8+ζ72−ζ8+ζ72ζ8−ζ72ζ8−ζ72−ζ24+ζ56−ζ24+ζ56ζ24−ζ56ζ24−ζ56000000000−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ560000000
χ2422222222−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+522-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−5222-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−5200ζ8−ζ72ζ8−ζ72−ζ8+ζ72−ζ8+ζ72ζ24−ζ56ζ24−ζ56−ζ24+ζ56−ζ24+ζ56000000000ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ560000000
χ2522222222−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+522-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-2-2221+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+5200−ζ8+ζ72−ζ8+ζ72ζ8−ζ72ζ8−ζ72−ζ24+ζ56−ζ24+ζ56ζ24−ζ56ζ24−ζ56000000000ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ560000000
χ2622222222−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+522-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-2-2221+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+5200ζ8−ζ72ζ8−ζ72−ζ8+ζ72−ζ8+ζ72ζ24−ζ56ζ24−ζ56−ζ24+ζ56−ζ24+ζ56000000000−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ560000000
χ27222222-2-2222222222222-2-2-2-2-22222-2-22222222200000000-2-20000-2-2-2-20000000000000000002222-2-2-2-2000000000000
χ28222222-2-2222222222222-2-2-2-2-22222-2-22222222200000000-2-20000-2-2-2-2000000000000000000-2-2-2-22222000000000000
χ29222222-2-222-2-2-2-2222222-222-2-22222-2-2-2-2-2-2-2-2-2-200000000-2-20000222200000000000000000000000000000002i2i−2i−2i000
χ30222222-2-222-2-2-2-2222222-222-2-22222-2-2-2-2-2-2-2-2-2-200000000-2-2000022220000000000000000000000000000000−2i−2i2i2i000
χ312222-2-222220000222222-20022-2-2-2-222000000002-2002222-2-2-2-2-2-2000000000000000000000022−2−222−2−2000002−22−2000
χ322222-2-222220000222222-20022-2-2-2-222000000002-2002222-2-2-2-2-2-20000000000000000000000−2−222−2−22200000−22−22000
χ332222-2-222220000222222-20022-2-2-2-22200000000-2200-2-2-2-2-2-22222000000000000000000000022−2−222−2−200000−22−22000
χ342222-2-222220000222222-20022-2-2-2-22200000000-2200-2-2-2-2-2-222220000000000000000000000−2−222−2−222000002−22−2000
χ352222-2-2-2-2220000222222200-2-2-2-2-2-2-2-200000000002i−2i000022000000002i2i−2i−2i2i2i−2i−2i000000000022−2−2−2−22200000i2−i2−i2i2000
χ362222-2-2-2-2220000222222200-2-2-2-2-2-2-2-200000000002i−2i000022000000002i2i−2i−2i2i2i−2i−2i0000000000−2−22222−2−200000−i2i2i2−i2000
χ372222-2-2-2-2220000222222200-2-2-2-2-2-2-2-20000000000−2i2i00002200000000−2i−2i2i2i−2i−2i2i2i000000000022−2−2−2−22200000−i2i2i2−i2000
χ382222-2-2-2-2220000222222200-2-2-2-2-2-2-2-20000000000−2i2i00002200000000−2i−2i2i2i−2i−2i2i2i0000000000−2−22222−2−200000i2−i2−i2i2000
χ392-2-22-220022-2-222-2-2-2-22200000-2-2220022-2-222-2-2000000000000000000000000002−22−22−22−22−200002-22-20000000002−20
χ402-2-22-220022-2-222-2-2-2-22200000-2-2220022-2-222-2-2000000000000000000000000002−22−22−22−22−20000-22-22000000000−220
χ412-2-22-220022-2-222-2-2-2-22200000-2-2220022-2-222-2-200000000000000000000000000−22−22−22−22−2200002-22-2000000000−220
χ422-2-22-220022-2-222-2-2-2-22200000-2-2220022-2-222-2-200000000000000000000000000−22−22−22−22−220000-22-220000000002−20
χ43444444-4-4−1+5−1−54444−1+5−1+5−1−5−1−5−1+5−1−5-4-4-41−51+5−1+5−1−5−1+5−1−51−51+5−1+5−1+5−1+5−1+5−1−5−1−5−1−5−1−5000000001−51+500001−51−51+51+500000000000000000000000000000000000000
χ44444444-4-4−1+5−1−5-4-4-4-4−1+5−1+5−1−5−1−5−1+5−1−5-4441−51+5−1+5−1−5−1+5−1−51−51+51−51−51−51−51+51+51+51+5000000001−51+50000−1+5−1+5−1−5−1−500000000000000000000000000000000000000
χ45444444-4-4−1−5−1+54444−1−5−1−5−1+5−1+5−1−5−1+5-4-4-41+51−5−1−5−1+5−1−5−1+51+51−5−1−5−1−5−1−5−1−5−1+5−1+5−1+5−1+5000000001+51−500001+51+51−51−500000000000000000000000000000000000000
χ46444444-4-4−1−5−1+5-4-4-4-4−1−5−1−5−1+5−1+5−1−5−1+5-4441+51−5−1−5−1+5−1−5−1+51+51−51+51+51+51+51−51−51−51−5000000001+51−50000−1−5−1−5−1+5−1+500000000000000000000000000000000000000
χ474444-4-444−1+5−1−50000−1+5−1+5−1−5−1−5−1+5−1−5-400−1+5−1−51−51+51−51+5−1+5−1−5000000004-400−1+5−1+5−1−5−1−51−51+51−51−51+51+5000000000000000000000000000000000000000000
χ484444-4-444−1+5−1−50000−1+5−1+5−1−5−1−5−1+5−1−5-400−1+5−1−51−51+51−51+5−1+5−1−500000000-44001−51−51+51+51−51+5−1+5−1+5−1−5−1−5000000000000000000000000000000000000000000
χ494444-4-444−1−5−1+50000−1−5−1−5−1+5−1+5−1−5−1+5-400−1−5−1+51+51−51+51−5−1−5−1+5000000004-400−1−5−1−5−1+5−1+51+51−51+51+51−51−5000000000000000000000000000000000000000000
χ504444-4-444−1−5−1+50000−1−5−1−5−1+5−1+5−1−5−1+5-400−1−5−1+51+51−51+51−5−1−5−1+500000000-44001+51+51−51−51+51−5−1−5−1−5−1+5−1+5000000000000000000000000000000000000000000
χ514444-4-4-4-4−1+5−1−50000−1+5−1+5−1−5−1−5−1+5−1−54001−51+51−51+51−51+51−51+500000000004i−4i0000−1+5−1−500000000−2ζ44−2ζ76−2ζ44−2ζ762ζ44+2ζ762ζ44+2ζ76−2ζ12−2ζ28−2ζ12−2ζ282ζ12+2ζ282ζ12+2ζ28000000000000000000000000000000
χ524444-4-4-4-4−1+5−1−50000−1+5−1+5−1−5−1−5−1+5−1−54001−51+51−51+51−51+51−51+50000000000−4i4i0000−1+5−1−5000000002ζ44+2ζ762ζ44+2ζ76−2ζ44−2ζ76−2ζ44−2ζ762ζ12+2ζ282ζ12+2ζ28−2ζ12−2ζ28−2ζ12−2ζ28000000000000000000000000000000
χ534444-4-4-4-4−1−5−1+50000−1−5−1−5−1+5−1+5−1−5−1+54001+51−51+51−51+51−51+51−500000000004i−4i0000−1−5−1+500000000−2ζ12−2ζ28−2ζ12−2ζ282ζ12+2ζ282ζ12+2ζ28−2ζ44−2ζ76−2ζ44−2ζ762ζ44+2ζ762ζ44+2ζ76000000000000000000000000000000
χ544444-4-4-4-4−1−5−1+50000−1−5−1−5−1+5−1+5−1−5−1+54001+51−51+51−51+51−51+51−50000000000−4i4i0000−1−5−1+5000000002ζ12+2ζ282ζ12+2ζ28−2ζ12−2ζ28−2ζ12−2ζ282ζ44+2ζ762ζ44+2ζ76−2ζ44−2ζ76−2ζ44−2ζ76000000000000000000000000000000
χ5544-4-400004422−2222−224-44-4-4-40000000000022−2222−2222−2222−220000000000000000000000000000000000002ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ79−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ79−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ772ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ770000000000000000
χ5644-4-400004422−2222−224-44-4-4-40000000000022−2222−2222−2222−22000000000000000000000000000000000000−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ792ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ792ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ77−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ770000000000000000
χ5744-4-4000044−2222−22224-44-4-4-400000000000−2222−2222−2222−2222000000000000000000000000000000000000−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ772ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ77−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ792ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ790000000000000000
χ5844-4-4000044−2222−22224-44-4-4-400000000000−2222−2222−2222−22220000000000000000000000000000000000002ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ77−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ772ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ79−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ790000000000000000
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Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.