Finite Group Databasebeta

← Group #65513

Character table — Group #65513

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222444444444444441010101020201111222222222244444444444444101010102020
order1222445510101010101044202020202020202020202020888844222244101010101010101044202020202020202020202020888844
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
χ51-11-11-111-1-1-1-1111-111-1-11111-1-1-1-1ii−i−ii−i1-11-11-111-1-1-1-1111-111-1-11111-1-1-1-1ii−i−ii−i
χ61-11-11-111-1-1-1-1111-111-1-11111-1-1-1-1−i−iii−ii1-11-11-111-1-1-1-1111-111-1-11111-1-1-1-1−i−iii−ii
χ71-11-11-111-1-1-1-111-1111-1-1-1-1-1-11111ii−i−i−ii1-11-11-111-1-1-1-111-1111-1-1-1-1-1-11111ii−i−i−ii
χ81-11-11-111-1-1-1-111-1111-1-1-1-1-1-11111−i−iiii−i1-11-11-111-1-1-1-111-1111-1-1-1-1-1-11111−i−iiii−i
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
χ1822-2-200222-22-2-2-2000000000000002−22−20022-2-200222-22-2-2-2000000000000002−22−200
χ1922-2-200222-22-2-2-200000000000000−22−220022-2-200222-22-2-2-200000000000000−22−2200
χ202-22-22-2−1+52−1−521−521−521+521+52−1+52−1−522-2−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+520000002-22-22-2−1+52−1−521−521−521+521+52−1+52−1−522-2−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+52000000
χ212-22-22-2−1+52−1−521−521−521+521+52−1+52−1−52-22−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−520000002-22-22-2−1+52−1−521−521−521+521+52−1+52−1−52-22−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−52000000
χ222-22-22-2−1−52−1+521+521+521−521−52−1−52−1+522-2−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−520000002-22-22-2−1−52−1+521+521+521−521−52−1−52−1+522-2−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−52000000
χ232-22-22-2−1−52−1+521+521+521−521−52−1−52−1+52-22−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+520000002-22-22-2−1−52−1+521+521+521−521−52−1−52−1+52-22−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+52000000
χ242-22-2-2222-2-2-2-22200-2-222000000000000002-22-2-2222-2-2-2-22200-2-22200000000000000
χ252-22-2-22−1+52−1−521−521−521+521+52−1+52−1−52001−521+52−1+52−1−52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000002-22-2-22−1+52−1−521−521−521+521+52−1+52−1−52001−521+52−1+52−1−52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000
χ262-22-2-22−1+52−1−521−521−521+521+52−1+52−1−52001−521+52−1+52−1−52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000002-22-2-22−1+52−1−521−521−521+521+52−1+52−1−52001−521+52−1+52−1−52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000
χ272-22-2-22−1−52−1+521+521+521−521−52−1−52−1+52001+521−52−1−52−1+52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000002-22-2-22−1−52−1+521+521+521−521−52−1−52−1+52001+521−52−1−52−1+52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000
χ282-22-2-22−1−52−1+521+521+521−521−52−1−52−1+52001+521−52−1−52−1+52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000002-22-2-22−1−52−1+521+521+521−521−52−1−52−1+52001+521−52−1−52−1+52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000
χ292-2-220022-22-22-2-200000000000000i2−i2−i2i2002-2-220022-22-22-2-200000000000000i2−i2−i2i200
χ302-2-220022-22-22-2-200000000000000−i2i2i2−i2002-2-220022-22-22-2-200000000000000−i2i2i2−i200
χ3144-4-400−1+5−1−5−1+51−5−1−51+51−51+50000000000000000000044-4-400−1+5−1−5−1+51−5−1−51+51−51+500000000000000000000
χ3244-4-400−1−5−1+5−1−51+5−1+51−51+51−50000000000000000000044-4-400−1−5−1+5−1−51+5−1+51−51+51−500000000000000000000
χ334-4-4400−1+5−1−51−5−1+51+5−1−51−51+5000000000000000000004-4-4400−1+5−1−51−5−1+51+5−1−51−51+500000000000000000000
χ344-4-4400−1−5−1+51+5−1−51−5−1+51+51−5000000000000000000004-4-4400−1−5−1+51+5−1−51−5−1+51+51−500000000000000000000
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
χ391-11-11-111-1-1-1-1111-111-1-11111-1-1-1-1ii−i−ii−i-11-11-11-1-11111-1-1-11-1-111-1-1-1-11111−i−iii−ii
χ401-11-11-111-1-1-1-1111-111-1-11111-1-1-1-1−i−iii−ii-11-11-11-1-11111-1-1-11-1-111-1-1-1-11111ii−i−ii−i
χ411-11-11-111-1-1-1-111-1111-1-1-1-1-1-11111ii−i−i−ii-11-11-11-1-11111-1-11-1-1-1111111-1-1-1-1−i−iiii−i
χ421-11-11-111-1-1-1-111-1111-1-1-1-1-1-11111−i−iiii−i-11-11-11-1-11111-1-11-1-1-1111111-1-1-1-1ii−i−i−ii
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
χ5222-2-200222-22-2-2-2000000000000002−22−200-2-22200-2-2-22-222200000000000000−22−2200
χ5322-2-200222-22-2-2-200000000000000−22−2200-2-22200-2-2-22-2222000000000000002−22−200
χ542-22-22-2−1+52−1−521−521−521+521+52−1+52−1−522-2−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+52000000-22-22-221−521+52−1+52−1+52−1−52−1−521−521+52-221−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000000
χ552-22-22-2−1+52−1−521−521−521+521+52−1+52−1−52-22−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−52000000-22-22-221−521+52−1+52−1+52−1−52−1−521−521+522-21−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52000000
χ562-22-22-2−1−52−1+521+521+521−521−52−1−52−1+522-2−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−52000000-22-22-221+521−52−1−52−1−52−1+52−1+521+521−52-221+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52000000
χ572-22-22-2−1−52−1+521+521+521−521−52−1−52−1+52-22−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+52000000-22-22-221+521−52−1−52−1−52−1+52−1+521+521−522-21+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−52000000
χ582-22-2-2222-2-2-2-22200-2-22200000000000000-22-222-2-2-22222-2-20022-2-200000000000000
χ592-22-2-22−1+52−1−521−521−521+521+52−1+52−1−52001−521+52−1+52−1−52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000-22-222-21−521+52−1+52−1+52−1−52−1−521−521+5200−1+52−1−521−521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000
χ602-22-2-22−1+52−1−521−521−521+521+52−1+52−1−52001−521+52−1+52−1−52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000-22-222-21−521+52−1+52−1+52−1−52−1−521−521+5200−1+52−1−521−521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000
χ612-22-2-22−1−52−1+521+521+521−521−52−1−52−1+52001+521−52−1−52−1+52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000-22-222-21+521−52−1−52−1−52−1+52−1+521+521−5200−1−52−1+521+521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000
χ622-22-2-22−1−52−1+521+521+521−521−52−1−52−1+52001+521−52−1−52−1+52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000-22-222-21+521−52−1−52−1−52−1+52−1+521+521−5200−1−52−1+521+521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000
χ632-2-220022-22-22-2-200000000000000i2−i2−i2i200-222-200-2-22-22-22200000000000000−i2i2i2−i200
χ642-2-220022-22-22-2-200000000000000−i2i2i2−i200-222-200-2-22-22-22200000000000000i2−i2−i2i200
χ6544-4-400−1+5−1−5−1+51−5−1−51+51−51+500000000000000000000-4-444001−51+51−5−1+51+5−1−5−1+5−1−500000000000000000000
χ6644-4-400−1−5−1+5−1−51+5−1+51−51+51−500000000000000000000-4-444001+51−51+5−1−51−5−1+5−1−5−1+500000000000000000000
χ674-4-4400−1+5−1−51−5−1+51+5−1−51−51+500000000000000000000-444-4001−51+5−1+51−5−1−51+5−1+5−1−500000000000000000000
χ684-4-4400−1−5−1+51+5−1−51−5−1+51+51−500000000000000000000-444-4001+51−5−1−51+5−1+51−5−1−5−1+500000000000000000000

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