Finite Group Databasebeta

← Group #65254

Character table — Group #65254

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222444444444444441010101020201111222222222244444444444444101010102020
order1222445510101010101044202020202020202020202020888822222244101010101010101044202020202020202020202020888822
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1
χ311111111111111-1-11111-1-1-1-1-1-1-1-11111-1-111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ51-11-11-111-1-111-1-1i−i11-1-1iiii−i−i−i−iii−i−i1-11-11-11-111-1-111-1-1i−i11-1-1iiii−i−i−i−iii−i−i1-1
χ61-11-11-111-1-111-1-1i−i11-1-1iiii−i−i−i−i−i−iii-111-11-11-111-1-111-1-1i−i11-1-1iiii−i−i−i−i−i−iii-11
χ71-11-11-111-1-111-1-1−ii11-1-1−i−i−i−iiiiiii−i−i-111-11-11-111-1-111-1-1−ii11-1-1−i−i−i−iiiiiii−i−i-11
χ81-11-11-111-1-111-1-1−ii11-1-1−i−i−i−iiiii−i−iii1-11-11-11-111-1-111-1-1−ii11-1-1−i−i−i−iiiii−i−iii1-1
χ9222222−1+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+52−1−52−1−52000000222222−1+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+52−1−52−1−52000000
χ10222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52000000222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52000000
χ11222222−1−52−1+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+52−1−52−1−52−1+52−1+52000000222222−1−52−1+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+52−1−52−1−52−1+52−1+52000000
χ12222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52000000222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52000000
χ132222-2-22222222200-2-2-2-2000000000000002222-2-22222222200-2-2-2-200000000000000
χ142222-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52001−521+521−521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000002222-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52001−521+521−521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000
χ152222-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52001−521+521−521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000002222-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52001−521+521−521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000
χ162222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52001+521−521+521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000002222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52001+521−521+521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000
χ172222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52001+521−521+521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000002222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52001+521−521+521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000
χ1822-2-2002222-2-2-2-200000000000000i2−i2i2−i20022-2-2002222-2-2-2-200000000000000i2−i2i2−i200
χ1922-2-2002222-2-2-2-200000000000000−i2i2−i2i20022-2-2002222-2-2-2-200000000000000−i2i2−i2i200
χ202-22-22-2−1+52−1−521−521+52−1+52−1−521−521+522i−2i−1+52−1−521−521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ140000002-22-22-2−1+52−1−521−521+52−1+52−1−521−521+522i−2i−1+52−1−521−521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14000000
χ212-22-22-2−1+52−1−521−521+52−1+52−1−521−521+52−2i2i−1+52−1−521−521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ140000002-22-22-2−1+52−1−521−521+52−1+52−1−521−521+52−2i2i−1+52−1−521−521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14000000
χ222-22-22-2−1−52−1+521+521−52−1−52−1+521+521−522i−2i−1−52−1+521+521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ380000002-22-22-2−1−52−1+521+521−52−1−52−1+521+521−522i−2i−1−52−1+521+521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38000000
χ232-22-22-2−1−52−1+521+521−52−1−52−1+521+521−52−2i2i−1−52−1+521+521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ380000002-22-22-2−1−52−1+521+521−52−1−52−1+521+521−52−2i2i−1−52−1+521+521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38000000
χ242-22-2-2222-2-222-2-200-2-222000000000000002-22-2-2222-2-222-2-200-2-22200000000000000
χ252-22-2-22−1+52−1−521−521+52−1+52−1−521−521+52001−521+52−1+52−1−52−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ140000002-22-2-22−1+52−1−521−521+52−1+52−1−521−521+52001−521+52−1+52−1−52−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14000000
χ262-22-2-22−1+52−1−521−521+52−1+52−1−521−521+52001−521+52−1+52−1−52ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ140000002-22-2-22−1+52−1−521−521+52−1+52−1−521−521+52001−521+52−1+52−1−52ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14000000
χ272-22-2-22−1−52−1+521+521−52−1−52−1+521+521−52001+521−52−1−52−1+52ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ380000002-22-2-22−1−52−1+521+521−52−1−52−1+521+521−52001+521−52−1−52−1+52ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38000000
χ282-22-2-22−1−52−1+521+521−52−1−52−1+521+521−52001+521−52−1−52−1+52−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ380000002-22-2-22−1−52−1+521+521−52−1−52−1+521+521−52001+521−52−1−52−1+52−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38000000
χ292-2-220022-2-2-2-222000000000000002−2−22002-2-220022-2-2-2-222000000000000002−2−2200
χ302-2-220022-2-2-2-22200000000000000−222−2002-2-220022-2-2-2-22200000000000000−222−200
χ3144-4-400−1+5−1−5−1+5−1−51−51+51−51+50000000000000000000044-4-400−1+5−1−5−1+5−1−51−51+51−51+500000000000000000000
χ3244-4-400−1−5−1+5−1−5−1+51+51−51+51−50000000000000000000044-4-400−1−5−1+5−1−5−1+51+51−51+51−500000000000000000000
χ334-4-4400−1+5−1−51−51+51−51+5−1+5−1−5000000000000000000004-4-4400−1+5−1−51−51+51−51+5−1+5−1−500000000000000000000
χ344-4-4400−1−5−1+51+51−51+51−5−1−5−1+5000000000000000000004-4-4400−1−5−1+51+51−51+51−5−1−5−1+500000000000000000000
χ351111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ361111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ3711111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111
χ3811111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1
χ391-11-11-111-1-111-1-1i−i11-1-1iiii−i−i−i−iii−i−i1-1-11-11-11-1-111-1-111−ii-1-111−i−i−i−iiiii−i−iii-11
χ401-11-11-111-1-111-1-1i−i11-1-1iiii−i−i−i−i−i−iii-11-11-11-11-1-111-1-111−ii-1-111−i−i−i−iiiiiii−i−i1-1
χ411-11-11-111-1-111-1-1−ii11-1-1−i−i−i−iiiiiii−i−i-11-11-11-11-1-111-1-111i−i-1-111iiii−i−i−i−i−i−iii1-1
χ421-11-11-111-1-111-1-1−ii11-1-1−i−i−i−iiiii−i−iii1-1-11-11-11-1-111-1-111i−i-1-111iiii−i−i−i−iii−i−i-11
χ43222222−1+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+52−1−52−1−52000000-2-2-2-2-2-21−521+521−521+521−521+521−521+52-2-21−521+521−521+521−521−521+521+521−521−521+521+52000000
χ44222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52000000-2-2-2-2-2-21−521+521−521+521−521+521−521+52221−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000
χ45222222−1−52−1+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+52−1−52−1−52−1+52−1+52000000-2-2-2-2-2-21+521−521+521−521+521−521+521−52-2-21+521−521+521−521+521+521−521−521+521+521−521−52000000
χ46222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52000000-2-2-2-2-2-21+521−521+521−521+521−521+521−52221+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000
χ472222-2-22222222200-2-2-2-200000000000000-2-2-2-222-2-2-2-2-2-2-2-200222200000000000000
χ482222-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52001−521+521−521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000-2-2-2-2221−521+521−521+521−521+521−521+5200−1+52−1−52−1+52−1−52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000
χ492222-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52001−521+521−521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000-2-2-2-2221−521+521−521+521−521+521−521+5200−1+52−1−52−1+52−1−52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000
χ502222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52001+521−521+521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000-2-2-2-2221+521−521+521−521+521−521+521−5200−1−52−1+52−1−52−1+52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000
χ512222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52001+521−521+521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000-2-2-2-2221+521−521+521−521+521−521+521−5200−1−52−1+52−1−52−1+52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000
χ5222-2-2002222-2-2-2-200000000000000i2−i2i2−i200-2-22200-2-2-2-2222200000000000000−i2i2−i2i200
χ5322-2-2002222-2-2-2-200000000000000−i2i2−i2i200-2-22200-2-2-2-2222200000000000000i2−i2i2−i200
χ542-22-22-2−1+52−1−521−521+52−1+52−1−521−521+522i−2i−1+52−1−521−521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14000000-22-22-221−521+52−1+52−1−521−521+52−1+52−1−52−2i2i1−521+52−1+52−1−52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14000000
χ552-22-22-2−1+52−1−521−521+52−1+52−1−521−521+52−2i2i−1+52−1−521−521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14000000-22-22-221−521+52−1+52−1−521−521+52−1+52−1−522i−2i1−521+52−1+52−1−52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14000000
χ562-22-22-2−1−52−1+521+521−52−1−52−1+521+521−522i−2i−1−52−1+521+521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38000000-22-22-221+521−52−1−52−1+521+521−52−1−52−1+52−2i2i1+521−52−1−52−1+52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38000000
χ572-22-22-2−1−52−1+521+521−52−1−52−1+521+521−52−2i2i−1−52−1+521+521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38000000-22-22-221+521−52−1−52−1+521+521−52−1−52−1+522i−2i1+521−52−1−52−1+52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38000000
χ582-22-2-2222-2-222-2-200-2-22200000000000000-22-222-2-2-222-2-2220022-2-200000000000000
χ592-22-2-22−1+52−1−521−521+52−1+52−1−521−521+52001−521+52−1+52−1−52−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14000000-22-222-21−521+52−1+52−1−521−521+52−1+52−1−5200−1+52−1−521−521+52ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14000000
χ602-22-2-22−1+52−1−521−521+52−1+52−1−521−521+52001−521+52−1+52−1−52ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14000000-22-222-21−521+52−1+52−1−521−521+52−1+52−1−5200−1+52−1−521−521+52−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14000000
χ612-22-2-22−1−52−1+521+521−52−1−52−1+521+521−52001+521−52−1−52−1+52ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38000000-22-222-21+521−52−1−52−1+521+521−52−1−52−1+5200−1−52−1+521+521−52−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38000000
χ622-22-2-22−1−52−1+521+521−52−1−52−1+521+521−52001+521−52−1−52−1+52−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38000000-22-222-21+521−52−1−52−1+521+521−52−1−52−1+5200−1−52−1+521+521−52ζ6−ζ14−ζ6+ζ14−ζ22+ζ38ζ22−ζ38−ζ6+ζ14ζ6−ζ14ζ22−ζ38−ζ22+ζ38000000
χ632-2-220022-2-2-2-222000000000000002−2−2200-222-200-2-22222-2-200000000000000−222−200
χ642-2-220022-2-2-2-22200000000000000−222−200-222-200-2-22222-2-2000000000000002−2−2200
χ6544-4-400−1+5−1−5−1+5−1−51−51+51−51+500000000000000000000-4-444001−51+51−51+5−1+5−1−5−1+5−1−500000000000000000000
χ6644-4-400−1−5−1+5−1−5−1+51+51−51+51−500000000000000000000-4-444001+51−51+51−5−1−5−1+5−1−5−1+500000000000000000000
χ674-4-4400−1+5−1−51−51+51−51+5−1+5−1−500000000000000000000-444-4001−51+5−1+5−1−5−1+5−1−51−51+500000000000000000000
χ684-4-4400−1−5−1+51+51−51+51−5−1−5−1+500000000000000000000-444-4001+51−5−1−5−1+5−1−5−1+51+51−500000000000000000000

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