Finite Group Databasebeta

← Group #12012960

Character table — Group #12012960

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111122222222224444444444444488888888888816161616161616161616161616161616161616323232323240404040404040404040808080
order122244551010101010104488882020202020202020242020404040404040404088810102020404040404040404040404040420202020441616161616161616244
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-1111
χ411111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111111111-1-1-1
χ51111111111111111111111111111-1-11111111111-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1
χ61111111111111111111111111111-1-11111111111-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ71111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-1
χ81111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-111
χ92222222222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-200222200000000-2-2-2-2000000000000000000
χ102222222222222222-2-2-2-222222222-2-222-2-2-2-2-2-2-2-2200-2-2-2-2000000002222000000000000000000
χ1122222222222222-2-22-2-2222-2-2-2-22200-2-2-2-2-2-222220000000000000000000000002200000000-200
χ1222222222222222-2-22-2-2222-2-2-2-22200-2-2-2-2-2-22222000000000000000000000000-2-200000000200
χ1322222222222222-2-2-222-222-2-2-2-22200-2-22222-2-2-2-2000000000000000000000000000000000002-2
χ1422222222222222-2-2-222-222-2-2-2-22200-2-22222-2-2-2-200000000000000000000000000000000000-22
χ15222222−1+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+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52−1+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+52−1−52−1−522−1+52−1+52−1−52−1−520000000000000
χ16222222−1+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+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522-2-2−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52-21−521−521+521+520000000000000
χ17222222−1+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+52−1−52-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2221−521+521−521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521+521+52-21−521−521+521+520000000000000
χ18222222−1+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+52−1−52-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-21−521+521−521+521−521−521−521−521+521+521+521+521−521−521+521+522−1+52−1+52−1−52−1−520000000000000
χ19222222−1+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+52−1−5222−1+52−1−521−521−521+521+521−521−521+521+52-200−1+52−1−52−1+52−1−52ζ24−ζ56ζ24−ζ56−ζ24+ζ56−ζ24+ζ56−ζ8+ζ72−ζ8+ζ72ζ8−ζ72ζ8−ζ721−521−521+521+520ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ720000000000000
χ20222222−1+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+52−1−5222−1+52−1−521−521−521+521+521−521−521+521+52-200−1+52−1−52−1+52−1−52−ζ24+ζ56−ζ24+ζ56ζ24−ζ56ζ24−ζ56ζ8−ζ72ζ8−ζ72−ζ8+ζ72−ζ8+ζ721−521−521+521+520−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ720000000000000
χ21222222−1+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+52−1−52-2-2−1+52−1−521−521−521+521+521−521−521+521+522001−521+521−521+52ζ24−ζ56ζ24−ζ56−ζ24+ζ56−ζ24+ζ56−ζ8+ζ72−ζ8+ζ72ζ8−ζ72ζ8−ζ72−1+52−1+52−1−52−1−520−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ720000000000000
χ22222222−1+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+52−1−52-2-2−1+52−1−521−521−521+521+521−521−521+521+522001−521+521−521+52−ζ24+ζ56−ζ24+ζ56ζ24−ζ56ζ24−ζ56ζ8−ζ72ζ8−ζ72−ζ8+ζ72−ζ8+ζ72−1+52−1+52−1−52−1−520ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ720000000000000
χ23222222−1−52−1+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+5222−1−52−1+52−1−52−1−52−1+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+522−1−52−1−52−1+52−1+520000000000000
χ24222222−1−52−1+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+5222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522-2-2−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+52-21+521+521−521−520000000000000
χ25222222−1−52−1+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+52-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2221+521−521+521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521−521−52-21+521+521−521−520000000000000
χ26222222−1−52−1+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+52-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-21+521−521+521−521+521+521+521+521−521−521−521−521+521+521−521−522−1−52−1−52−1+52−1+520000000000000
χ27222222−1−52−1+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+5222−1−52−1+521+521+521−521−521+521+521−521−52-200−1−52−1+52−1−52−1+52−ζ8+ζ72−ζ8+ζ72ζ8−ζ72ζ8−ζ72−ζ24+ζ56−ζ24+ζ56ζ24−ζ56ζ24−ζ561+521+521−521−520−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ560000000000000
χ28222222−1−52−1+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+5222−1−52−1+521+521+521−521−521+521+521−521−52-200−1−52−1+52−1−52−1+52ζ8−ζ72ζ8−ζ72−ζ8+ζ72−ζ8+ζ72ζ24−ζ56ζ24−ζ56−ζ24+ζ56−ζ24+ζ561+521+521−521−520ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ560000000000000
χ29222222−1−52−1+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+52-2-2−1−52−1+521+521+521−521−521+521+521−521−522001+521−521+521−52−ζ8+ζ72−ζ8+ζ72ζ8−ζ72ζ8−ζ72−ζ24+ζ56−ζ24+ζ56ζ24−ζ56ζ24−ζ56−1−52−1−52−1+52−1+520ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ560000000000000
χ30222222−1−52−1+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+52-2-2−1−52−1+521+521+521−521−521+521+521−521−522001+521−521+521−52ζ8−ζ72ζ8−ζ72−ζ8+ζ72−ζ8+ζ72ζ24−ζ56ζ24−ζ56−ζ24+ζ56−ζ24+ζ56−1−52−1−52−1+52−1+520−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ560000000000000
χ312222-2-222222222-220000-2-22222-2-22-2-2-20000000000022-2-2000000000000000000022−2−222−2−2000
χ322222-2-222222222-220000-2-22222-2-22-2-2-20000000000022-2-20000000000000000000−2−222−2−222000
χ332222-2-222222222-220000-2-22222-2-2-22-2-200000000000-2-222000000000000000000022−2−2−2−222000
χ342222-2-222222222-220000-2-22222-2-2-22-2-200000000000-2-2220000000000000000000−2−22222−2−2000
χ3522-2-2-2222-2-2-2-22200200-2-2-2000022000000002-22-202−200002−22−22−22−20000000002i−2ii2−i2i2−i20000000
χ3622-2-2-2222-2-2-2-22200200-2-2-2000022000000002-22-202−200002−22−22−22−2000000000−2i2i−i2i2−i2i20000000
χ3722-2-2-2222-2-2-2-22200200-2-2-2000022000000002-22-20−220000−22−22−22−220000000002i−2i−i2i2−i2i20000000
χ3822-2-2-2222-2-2-2-22200200-2-2-2000022000000002-22-20−220000−22−22−22−22000000000−2i2ii2−i2i2−i20000000
χ39444444−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-4-44-4-44−1+5−1−51−51−51+51+5−1+5−1−5001−51+51−51−51+51+5−1+5−1+5−1−5−1−50000000000000000000000000000000000000
χ40444444−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-4-4-444-4−1+5−1−51−51−51+51+5−1+5−1−5001−51+5−1+5−1+5−1−5−1−51−51−51+51+50000000000000000000000000000000000000
χ41444444−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-4-44-4-44−1−5−1+51+51+51−51−5−1−5−1+5001+51−51+51+51−51−5−1−5−1−5−1+5−1+50000000000000000000000000000000000000
χ42444444−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-4-4-444-4−1−5−1+51+51+51−51−5−1−5−1+5001+51−5−1−5−1−5−1+5−1+51+51+51−51−50000000000000000000000000000000000000
χ434444-4-4444444444-40000-4-4-4-4-4-4-4-40044000000000000000000000000000000000000000000000
χ444444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−54-400001−51+51−51−51+51+51−51+500−1+5−1−500000000000000000000000−2ζ44+2ζ762ζ44−2ζ762ζ12−2ζ28−2ζ12+2ζ28000000000000000000
χ454444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−54-400001−51+51−51−51+51+51−51+500−1+5−1−5000000000000000000000002ζ44−2ζ76−2ζ44+2ζ76−2ζ12+2ζ282ζ12−2ζ28000000000000000000
χ464444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-4400001−51+5−1+5−1+5−1−5−1−51−51+54-41−51+500000000000−1+5−1−51−51+5000000000000000000000000000000
χ474444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-4400001−51+5−1+5−1+5−1−5−1−51−51+5-441−51+5000000000001−51+5−1+5−1−5000000000000000000000000000000
χ484444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+54-400001+51−51+51+51−51−51+51−500−1−5−1+5000000000000000000000002ζ12−2ζ28−2ζ12+2ζ282ζ44−2ζ76−2ζ44+2ζ76000000000000000000
χ494444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+54-400001+51−51+51+51−51−51+51−500−1−5−1+500000000000000000000000−2ζ12+2ζ282ζ12−2ζ28−2ζ44+2ζ762ζ44−2ζ76000000000000000000
χ504444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-4400001+51−5−1−5−1−5−1+5−1+51+51−54-41+51−500000000000−1−5−1+51+51−5000000000000000000000000000000
χ514444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-4400001+51−5−1−5−1−5−1+5−1+51+51−5-441+51−5000000000001+51−5−1−5−1+5000000000000000000000000000000
χ5244-4-44-444-4-4-4-444000000440000-4-4000000000000000000000000000000000000002i−2i−2i2i0000000
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χ5644-4-4-44−1+5−1−51−51−51+51+5−1+5−1−500400-41−51+50000−1+5−1−500000000−1+51−5−1−51+50−22220000ζ14−ζ26+ζ46−ζ74−ζ14+ζ26−ζ46+ζ74ζ14−ζ26+ζ46−ζ74−ζ14+ζ26−ζ46+ζ74−ζ42−ζ58+ζ62+ζ78ζ42+ζ58−ζ62−ζ78−ζ42−ζ58+ζ62+ζ78ζ42+ζ58−ζ62−ζ780000000000000000000000
χ5744-4-4-44−1+5−1−51−51−51+51+5−1+5−1−500-40041−51+50000−1+5−1−5000000001−5−1+51+5−1−50000000−ζ14−ζ26+ζ46+ζ74ζ14+ζ26−ζ46−ζ74ζ14+ζ26−ζ46−ζ74−ζ14−ζ26+ζ46+ζ74ζ42−ζ58−ζ62+ζ78−ζ42+ζ58+ζ62−ζ78−ζ42+ζ58+ζ62−ζ78ζ42−ζ58−ζ62+ζ780000000000000000000000
χ5844-4-4-44−1+5−1−51−51−51+51+5−1+5−1−500-40041−51+50000−1+5−1−5000000001−5−1+51+5−1−50000000ζ14+ζ26−ζ46−ζ74−ζ14−ζ26+ζ46+ζ74−ζ14−ζ26+ζ46+ζ74ζ14+ζ26−ζ46−ζ74−ζ42+ζ58+ζ62−ζ78ζ42−ζ58−ζ62+ζ78ζ42−ζ58−ζ62+ζ78−ζ42+ζ58+ζ62−ζ780000000000000000000000
χ5944-4-4-44−1−5−1+51+51+51−51−5−1−5−1+500400-41+51−50000−1−5−1+500000000−1−51+5−1+51−5022−220000ζ42+ζ58−ζ62−ζ78−ζ42−ζ58+ζ62+ζ78ζ42+ζ58−ζ62−ζ78−ζ42−ζ58+ζ62+ζ78−ζ14+ζ26−ζ46+ζ74ζ14−ζ26+ζ46−ζ74−ζ14+ζ26−ζ46+ζ74ζ14−ζ26+ζ46−ζ740000000000000000000000
χ6044-4-4-44−1−5−1+51+51+51−51−5−1−5−1+500400-41+51−50000−1−5−1+500000000−1−51+5−1+51−50−22220000−ζ42−ζ58+ζ62+ζ78ζ42+ζ58−ζ62−ζ78−ζ42−ζ58+ζ62+ζ78ζ42+ζ58−ζ62−ζ78ζ14−ζ26+ζ46−ζ74−ζ14+ζ26−ζ46+ζ74ζ14−ζ26+ζ46−ζ74−ζ14+ζ26−ζ46+ζ740000000000000000000000
χ6144-4-4-44−1−5−1+51+51+51−51−5−1−5−1+500-40041+51−50000−1−5−1+5000000001+5−1−51−5−1+50000000−ζ42+ζ58+ζ62−ζ78ζ42−ζ58−ζ62+ζ78ζ42−ζ58−ζ62+ζ78−ζ42+ζ58+ζ62−ζ78−ζ14−ζ26+ζ46+ζ74ζ14+ζ26−ζ46−ζ74ζ14+ζ26−ζ46−ζ74−ζ14−ζ26+ζ46+ζ740000000000000000000000
χ6244-4-4-44−1−5−1+51+51+51−51−5−1−5−1+500-40041+51−50000−1−5−1+5000000001+5−1−51−5−1+50000000ζ42−ζ58−ζ62+ζ78−ζ42+ζ58+ζ62−ζ78−ζ42+ζ58+ζ62−ζ78ζ42−ζ58−ζ62+ζ78ζ14+ζ26−ζ46−ζ74−ζ14−ζ26+ζ46+ζ74−ζ14−ζ26+ζ46+ζ74ζ14+ζ26−ζ46−ζ740000000000000000000000
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χ6788-8-88-8−2+25−2−252−252−252+252+25−2+25−2−25000000−2+25−2−2500002−252+250000000000000000000000000000000000000000000000000
χ6888-8-88-8−2−25−2+252+252+252−252−25−2−25−2+25000000−2−25−2+2500002+252−250000000000000000000000000000000000000000000000000
χ698-88-80088-88-88-8-8000000000000000000000000000000000000000000000000000000000000000
χ708-88-800−2+25−2−252−25−2+252+25−2−252−252+25000000004ζ24−4ζ56−4ζ24+4ζ56−4ζ8+4ζ724ζ8−4ζ72000000000000000000000000000000000000000000000000000
χ718-88-800−2+25−2−252−25−2+252+25−2−252−252+2500000000−4ζ24+4ζ564ζ24−4ζ564ζ8−4ζ72−4ζ8+4ζ72000000000000000000000000000000000000000000000000000
χ728-88-800−2−25−2+252+25−2−252−25−2+252+252−2500000000−4ζ8+4ζ724ζ8−4ζ72−4ζ24+4ζ564ζ24−4ζ56000000000000000000000000000000000000000000000000000
χ738-88-800−2−25−2+252+25−2−252−25−2+252+252−25000000004ζ8−4ζ72−4ζ8+4ζ724ζ24−4ζ56−4ζ24+4ζ56000000000000000000000000000000000000000000000000000
χ748-8-8800−2+25−2−25−2+252−25−2−252+252−252+2500042−420000000000000−2ζ14+2ζ26−2ζ46+2ζ742ζ14−2ζ26+2ζ46−2ζ742ζ42+2ζ58−2ζ62−2ζ78−2ζ42−2ζ58+2ζ62+2ζ7800000000000000000000000000000000000000000
χ758-8-8800−2+25−2−25−2+252−25−2−252+252−252+25000−424200000000000002ζ14−2ζ26+2ζ46−2ζ74−2ζ14+2ζ26−2ζ46+2ζ74−2ζ42−2ζ58+2ζ62+2ζ782ζ42+2ζ58−2ζ62−2ζ7800000000000000000000000000000000000000000
χ768-8-8800−2−25−2+25−2−252+25−2+252−252+252−2500042−4200000000000002ζ42+2ζ58−2ζ62−2ζ78−2ζ42−2ζ58+2ζ62+2ζ78−2ζ14+2ζ26−2ζ46+2ζ742ζ14−2ζ26+2ζ46−2ζ7400000000000000000000000000000000000000000
χ778-8-8800−2−25−2+25−2−252+25−2+252−252+252−25000−42420000000000000−2ζ42−2ζ58+2ζ62+2ζ782ζ42+2ζ58−2ζ62−2ζ782ζ14−2ζ26+2ζ46−2ζ74−2ζ14+2ζ26−2ζ46+2ζ7400000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.