Finite Group Databasebeta

← Group #65815

Character table — Group #65815

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222444444444444441010101020201111222222222244444444444444101010102020
order1222225510101010101044101010102020202020202020444444222222101010101010101044101010102020202020202020444444
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
χ51111-1-1111111111-1-1-1-1-11111-1-1-1-111-1-11-11111-1-1111111111-1-1-1-1-11111-1-1-1-111-1-11-1
χ61111-1-1111111111-1-1-1-1-11111-1-1-1-1-1-111-111111-1-1111111111-1-1-1-1-11111-1-1-1-1-1-111-11
χ71111-1-111111111-11-1-1-1-1-1-1-1-1111111-1-1-111111-1-111111111-11-1-1-1-1-1-1-1-1111111-1-1-11
χ81111-1-111111111-11-1-1-1-1-1-1-1-11111-1-1111-11111-1-111111111-11-1-1-1-1-1-1-1-11111-1-1111-1
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
χ132222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+520000002222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000
χ142222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−520000002222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52000000
χ152222-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−520000002222-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000000
χ162222-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+520000002222-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52000000
χ1722-2-22-22222-2-2-2-2002-22-20000000000000022-2-22-22222-2-2-2-2002-22-200000000000000
χ1822-2-22-2−1+52−1−52−1+52−1−521−521−521+521+5200−1+521−52−1−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ700000022-2-22-2−1+52−1−52−1+52−1−521−521−521+521+5200−1+521−52−1−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000
χ1922-2-22-2−1+52−1−52−1+52−1−521−521−521+521+5200−1+521−52−1−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ700000022-2-22-2−1+52−1−52−1+52−1−521−521−521+521+5200−1+521−52−1−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000
χ2022-2-22-2−1−52−1+52−1−52−1+521+521+521−521−5200−1−521+52−1+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ1900000022-2-22-2−1−52−1+52−1−52−1+521+521+521−521−5200−1−521+52−1+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000
χ2122-2-22-2−1−52−1+52−1−52−1+521+521+521−521−5200−1−521+52−1+521−52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ1900000022-2-22-2−1−52−1+52−1−52−1+521+521+521−521−5200−1−521+52−1+521−52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000
χ2222-2-2-222222-2-2-2-200-22-220000000000000022-2-2-222222-2-2-2-200-22-2200000000000000
χ2322-2-2-22−1+52−1−52−1+52−1−521−521−521+521+52001−52−1+521+52−1−52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ700000022-2-2-22−1+52−1−52−1+52−1−521−521−521+521+52001−52−1+521+52−1−52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000
χ2422-2-2-22−1+52−1−52−1+52−1−521−521−521+521+52001−52−1+521+52−1−52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ700000022-2-2-22−1+52−1−52−1+52−1−521−521−521+521+52001−52−1+521+52−1−52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000
χ2522-2-2-22−1−52−1+52−1−52−1+521+521+521−521−52001+52−1−521−52−1+52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ1900000022-2-2-22−1−52−1+52−1−52−1+521+521+521−521−52001+52−1−521−52−1+52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000
χ2622-2-2-22−1−52−1+52−1−52−1+521+521+521−521−52001+52−1−521−52−1+52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ1900000022-2-2-22−1−52−1+52−1−52−1+521+521+521−521−52001+52−1−521−52−1+52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000
χ272-22-20022-2-22-22-200000000000000002i−2i002-22-20022-2-22-22-200000000000000002i−2i00
χ282-22-20022-2-22-22-20000000000000000−2i2i002-22-20022-2-22-22-20000000000000000−2i2i00
χ292-2-220022-2-2-22-22000000000000002-200002-2-220022-2-2-22-22000000000000002-20000
χ302-2-220022-2-2-22-2200000000000000-2200002-2-220022-2-2-22-2200000000000000-220000
χ314-44-400−1+5−1−51−51+5−1+51−5−1−51+5000000000000000000004-44-400−1+5−1−51−51+5−1+51−5−1−51+500000000000000000000
χ324-44-400−1−5−1+51+51−5−1−51+5−1+51−5000000000000000000004-44-400−1−5−1+51+51−5−1−51+5−1+51−500000000000000000000
χ334-4-4400−1+5−1−51−51+51−5−1+51+5−1−5000000000000000000004-4-4400−1+5−1−51−51+51−5−1+51+5−1−500000000000000000000
χ344-4-4400−1−5−1+51+51−51+5−1−51−5−1+5000000000000000000004-4-4400−1−5−1+51+51−51+5−1−51−5−1+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
χ391111-1-1111111111-1-1-1-1-11111-1-1-1-111-1-11-1-1-1-1-111-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-111-11
χ401111-1-1111111111-1-1-1-1-11111-1-1-1-1-1-111-11-1-1-1-111-1-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-11-1
χ411111-1-111111111-11-1-1-1-1-1-1-1-1111111-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1111-1
χ421111-1-111111111-11-1-1-1-1-1-1-1-11111-1-1111-1-1-1-1-111-1-1-1-1-1-1-1-11-111111111-1-1-1-111-1-1-11
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
χ472222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000-2-2-2-2221−521+521−521+521−521−521+521+52-22−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000000
χ482222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52000000-2-2-2-2221−521+521−521+521−521−521+521+522-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52000000
χ492222-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000000-2-2-2-2221+521−521+521−521+521+521−521−52-22−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52000000
χ502222-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52000000-2-2-2-2221+521−521+521−521+521+521−521−522-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52000000
χ5122-2-22-22222-2-2-2-2002-22-200000000000000-2-222-22-2-2-2-2222200-22-2200000000000000
χ5222-2-22-2−1+52−1−52−1+52−1−521−521−521+521+5200−1+521−52−1−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000-2-222-221−521+521−521+52−1+52−1+52−1−52−1−52001−52−1+521+52−1−52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000
χ5322-2-22-2−1+52−1−52−1+52−1−521−521−521+521+5200−1+521−52−1−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000-2-222-221−521+521−521+52−1+52−1+52−1−52−1−52001−52−1+521+52−1−52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000
χ5422-2-22-2−1−52−1+52−1−52−1+521+521+521−521−5200−1−521+52−1+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000-2-222-221+521−521+521−52−1−52−1−52−1+52−1+52001+52−1−521−52−1+52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000
χ5522-2-22-2−1−52−1+52−1−52−1+521+521+521−521−5200−1−521+52−1+521−52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000-2-222-221+521−521+521−52−1−52−1−52−1+52−1+52001+52−1−521−52−1+52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000
χ5622-2-2-222222-2-2-2-200-22-2200000000000000-2-2222-2-2-2-2-22222002-22-200000000000000
χ5722-2-2-22−1+52−1−52−1+52−1−521−521−521+521+52001−52−1+521+52−1−52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000-2-2222-21−521+521−521+52−1+52−1+52−1−52−1−5200−1+521−52−1−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000
χ5822-2-2-22−1+52−1−52−1+52−1−521−521−521+521+52001−52−1+521+52−1−52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000-2-2222-21−521+521−521+52−1+52−1+52−1−52−1−5200−1+521−52−1−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000
χ5922-2-2-22−1−52−1+52−1−52−1+521+521+521−521−52001+52−1−521−52−1+52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000-2-2222-21+521−521+521−52−1−52−1−52−1+52−1+5200−1−521+52−1+521−52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000
χ6022-2-2-22−1−52−1+52−1−52−1+521+521+521−521−52001+52−1−521−52−1+52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000-2-2222-21+521−521+521−52−1−52−1−52−1+52−1+5200−1−521+52−1+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000
χ612-22-20022-2-22-22-200000000000000002i−2i00-22-2200-2-222-22-220000000000000000−2i2i00
χ622-22-20022-2-22-22-20000000000000000−2i2i00-22-2200-2-222-22-2200000000000000002i−2i00
χ632-2-220022-2-2-22-22000000000000002-20000-222-200-2-2222-22-200000000000000-220000
χ642-2-220022-2-2-22-2200000000000000-220000-222-200-2-2222-22-2000000000000002-20000
χ654-44-400−1+5−1−51−51+5−1+51−5−1−51+500000000000000000000-44-44001−51+5−1+5−1−51−5−1+51+5−1−500000000000000000000
χ664-44-400−1−5−1+51+51−5−1−51+5−1+51−500000000000000000000-44-44001+51−5−1−5−1+51+5−1−51−5−1+500000000000000000000
χ674-4-4400−1+5−1−51−51+51−5−1+51+5−1−500000000000000000000-444-4001−51+5−1+5−1−5−1+51−5−1−51+500000000000000000000
χ684-4-4400−1−5−1+51+51−51+5−1−51−5−1+500000000000000000000-444-4001+51−5−1−5−1+5−1−51+5−1+51−500000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.