Finite Group Databasebeta

← Group #65521

Character table — Group #65521

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222222222222244444444444444444444444444442020202020202020
order1222224444551010101010102020202020202020224410101010101010101010101020202020202020202020202044448888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-1-11-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ61111-1-11-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ71111-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111
χ81111-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1
χ91-11-11-111-1-111-1-1-1-1111111-1-1-1-11-11-111-1-11111-1-1-1-111-1-11111-1-1-1-1i−ii−ii−ii−i
χ101-11-11-111-1-111-1-1-1-1111111-1-1-1-11-11-111-1-11111-1-1-1-111-1-11111-1-1-1-1−ii−ii−ii−ii
χ111-11-11-111-1-111-1-1-1-1111111-1-1-1-1-11-1111-1-1-1-1-1-1111111-1-1-1-1-1-11111i−ii−i−ii−ii
χ121-11-11-111-1-111-1-1-1-1111111-1-1-1-1-11-1111-1-1-1-1-1-1111111-1-1-1-1-1-11111−ii−iii−ii−i
χ131-11-1-111-11-111-1-1-1-111-1-1-1-111111-1-11-1-1111111-1-1-1-111-1-1-1-1-1-11111i−i−iii−i−ii
χ141-11-1-111-11-111-1-1-1-111-1-1-1-111111-1-11-1-1111111-1-1-1-111-1-1-1-1-1-11111−iii−i−iii−i
χ151-11-1-111-11-111-1-1-1-111-1-1-1-11111-111-1-1-111-1-1-1-1111111-1-11111-1-1-1-1i−i−ii−iii−i
χ161-11-1-111-11-111-1-1-1-111-1-1-1-11111-111-1-1-111-1-1-1-1111111-1-11111-1-1-1-1−iii−ii−i−ii
χ172222222222−1+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+52−1−52−1−5200000000
χ182222222222−1+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+52−1−52−1−52-2-2-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+5200000000
χ192222222222−1−52−1+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+52−1−52−1−52−1+52−1+5200000000
χ202222222222−1−52−1+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+52-2-2-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−5200000000
χ21222222-2-2-2-222222222-2-2-2-2-2-2-2-20000222200000000-2-2-2-20000000000000000
χ22222222-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+520000−1+52−1−52−1+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521+521−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ1800000000
χ23222222-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+520000−1+52−1−52−1+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521+521−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ1800000000
χ24222222-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+521−521−520000−1−52−1+52−1−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521−521+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ1400000000
χ25222222-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+521−521−520000−1−52−1+52−1−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521−521+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ1400000000
χ262222-2-22-2-22−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+5222-2-21−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+5200000000
χ272222-2-22-2-22−1+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+521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000
χ282222-2-22-2-22−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+521−521−5222-2-21+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−5200000000
χ292222-2-22-2-22−1−52−1+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+521−521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000
χ302222-2-2-222-222222222222222220000-2-2-2-200000000-2-2-2-20000000000000000
χ312222-2-2-222-2−1+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+52−1−52−1−5200001−521+521−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521+521−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ1800000000
χ322222-2-2-222-2−1+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+52−1−52−1−5200001−521+521−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521+521−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ1800000000
χ332222-2-2-222-2−1−52−1+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+5200001+521−521+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521−521+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ1400000000
χ342222-2-2-222-2−1−52−1+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+5200001+521−521+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521−521+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ1400000000
χ352-22-22-222-2-2−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+522-22-2−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+5200000000
χ362-22-22-222-2-2−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52-22-22−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−5200000000
χ372-22-22-222-2-2−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−522-22-2−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−5200000000
χ382-22-22-222-2-2−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−52-22-22−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+5200000000
χ392-22-22-2-2-22222-2-2-2-222-2-2-2-22222000022-2-200000000-2-2220000000000000000
χ402-22-22-2-2-222−1+52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000−1+52−1−521−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521+52−1+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ1800000000
χ412-22-22-2-2-222−1+52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000−1+52−1−521−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521+52−1+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ1800000000
χ422-22-22-2-2-222−1−52−1+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+520000−1−52−1+521+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521−52−1−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ1400000000
χ432-22-22-2-2-222−1−52−1+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+520000−1−52−1+521+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521−52−1−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ1400000000
χ442-22-2-222-22-2−1+52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−522-2-221−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−5200000000
χ452-22-2-222-22-2−1+52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52-222-21−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+5200000000
χ462-22-2-222-22-2−1−52−1+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+522-2-221+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+5200000000
χ472-22-2-222-22-2−1−52−1+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52-222-21+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−5200000000
χ482-22-2-22-22-2222-2-2-2-2222222-2-2-2-20000-2-22200000000-2-2220000000000000000
χ492-22-2-22-22-22−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+5200001−521+52−1+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521+52−1+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ1800000000
χ502-22-2-22-22-22−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+5200001−521+52−1+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521+52−1+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ1800000000
χ512-22-2-22-22-22−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−5200001+521−52−1−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521−52−1−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ1400000000
χ522-22-2-22-22-22−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−5200001+521−52−1−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521−52−1−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ1400000000
χ5344-4-4000000444-44-4-4-400000000000000000000000000000000000000000000
χ5444-4-4000000−1+5−1−5−1+51−5−1−51+51−51+5−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ7000000000000000000000000000000000000
χ5544-4-4000000−1+5−1−5−1+51−5−1−51+51−51+52ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ7000000000000000000000000000000000000
χ5644-4-4000000−1−5−1+5−1−51+5−1+51−51+51−52ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ19000000000000000000000000000000000000
χ5744-4-4000000−1−5−1+5−1−51+5−1+51−51+51−5−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19000000000000000000000000000000000000
χ584-4-4400000044-44-44-4-400000000000000000000000000000000000000000000
χ594-4-44000000−1+5−1−51−5−1+51+5−1−51−51+5−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ7000000000000000000000000000000000000
χ604-4-44000000−1+5−1−51−5−1+51+5−1−51−51+52ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ7000000000000000000000000000000000000
χ614-4-44000000−1−5−1+51+5−1−51−5−1+51+51−52ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19000000000000000000000000000000000000
χ624-4-44000000−1−5−1+51+5−1−51−5−1+51+51−5−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ19000000000000000000000000000000000000

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