Finite Group Databasebeta

← Group #65841

Character table — Group #65841

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222222222222222222222244444444444444444444444444410101010202020202020
order1222224444445510101010101010101010101010104442020202020202020202020202020202020202020202020202244224444
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111-1-1-1-111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ411111111-1-1-1-111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111-1-111-1-11111111111111111-11-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-11-1
χ6111111-1-111-1-11111111111111111-11-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-11
χ7111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-11-1-1-11
χ8111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1111-1
χ91111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1111
χ101111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111-1-1-1
χ111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-11-1-1
χ121111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11-111
χ131111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-11-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-111-11-1
χ141111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111-1-11-11
χ151111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-11-11-1-11
χ161111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-11-111-1
χ17222222222222−1+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+52−1−52222−1+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+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000
χ18222222222222−1−52−1+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+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+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000
χ1922222222-2-2-2-2−1+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+52−1−522-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+520000000000
χ2022222222-2-2-2-2−1−52−1+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+522-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−520000000000
χ21222222-2-222-2-2−1+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+52−1−52-22-21−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+520000000000
χ22222222-2-222-2-2−1−52−1+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+52-22-21+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−520000000000
χ23222222-2-2-2-222−1+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+52−1−52-2-221−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000
χ24222222-2-2-2-222−1−52−1+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+52-2-221+521+521−521−521+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+520000000000
χ252222-2-2222222−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1−52−1+52−1−52-2-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+520000000000
χ262222-2-2222222−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1+52−1−52−1+52-2-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−520000000000
χ272222-2-222-2-2-2-2−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1−52−1+52−1−52-222−1+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+52−1+52−1+52−1−52−1−520000000000
χ282222-2-222-2-2-2-2−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1+52−1−52−1+52-222−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+520000000000
χ292222-2-2-2-222-2-2−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1−52−1+52−1−522-221−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−520000000000
χ302222-2-2-2-222-2-2−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1+52−1−52−1+522-221+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+520000000000
χ312222-2-2-2-2-2-222−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1−52−1+52−1−5222-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000000000
χ322222-2-2-2-2-2-222−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1+52−1−52−1+5222-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000000000
χ332-22-2002-22i−2i2i−2i22-2-20000000022-2-20002-22-200002i−2i2i−2i00002i−2i2i−2i00000000000000
χ342-22-2002-22i−2i2i−2i−1+52−1−521−521+52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−1+52−1−521−521+52000−1+521−52−1−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ70000000000
χ352-22-2002-22i−2i2i−2i−1+52−1−521−521+52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18−1+52−1−521−521+52000−1+521−52−1−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ70000000000
χ362-22-2002-22i−2i2i−2i−1−52−1+521+521−52−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14−1−52−1+521+521−52000−1−521+52−1+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ190000000000
χ372-22-2002-22i−2i2i−2i−1−52−1+521+521−52ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−1−52−1+521+521−52000−1−521+52−1+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ190000000000
χ382-22-2002-2−2i2i−2i2i22-2-20000000022-2-20002-22-20000−2i2i−2i2i0000−2i2i−2i2i00000000000000
χ392-22-2002-2−2i2i−2i2i−1+52−1−521−521+52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−1+52−1−521−521+52000−1+521−52−1−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ11+ζ19−ζ11−ζ19ζ3+ζ7−ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11+ζ19−ζ11−ζ19ζ3+ζ7−ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ70000000000
χ402-22-2002-2−2i2i−2i2i−1+52−1−521−521+52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18−1+52−1−521−521+52000−1+521−52−1−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ11+ζ19−ζ11−ζ19ζ3+ζ7−ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11+ζ19−ζ11−ζ19ζ3+ζ7−ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ70000000000
χ412-22-2002-2−2i2i−2i2i−1−52−1+521+521−52−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14−1−52−1+521+521−52000−1−521+52−1+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ3+ζ7−ζ3−ζ7ζ11+ζ19−ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3+ζ7−ζ3−ζ7ζ11+ζ19−ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ190000000000
χ422-22-2002-2−2i2i−2i2i−1−52−1+521+521−52ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−1−52−1+521+521−52000−1−521+52−1+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ3+ζ7−ζ3−ζ7ζ11+ζ19−ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3+ζ7−ζ3−ζ7ζ11+ζ19−ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ190000000000
χ432-22-200-222i−2i−2i2i22-2-20000000022-2-2000-22-2200002i−2i2i−2i0000−2i2i−2i2i00000000000000
χ442-22-200-222i−2i−2i2i−1+52−1−521−521+52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−1+52−1−521−521+520001−52−1+521+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11+ζ19−ζ11−ζ19ζ3+ζ7−ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ70000000000
χ452-22-200-222i−2i−2i2i−1+52−1−521−521+52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18−1+52−1−521−521+520001−52−1+521+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11+ζ19−ζ11−ζ19ζ3+ζ7−ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ70000000000
χ462-22-200-222i−2i−2i2i−1−52−1+521+521−52−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14−1−52−1+521+521−520001+52−1−521−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3+ζ7−ζ3−ζ7ζ11+ζ19−ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ190000000000
χ472-22-200-222i−2i−2i2i−1−52−1+521+521−52ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−1−52−1+521+521−520001+52−1−521−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3+ζ7−ζ3−ζ7ζ11+ζ19−ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ190000000000
χ482-22-200-22−2i2i2i−2i22-2-20000000022-2-2000-22-220000−2i2i−2i2i00002i−2i2i−2i00000000000000
χ492-22-200-22−2i2i2i−2i−1+52−1−521−521+52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−1+52−1−521−521+520001−52−1+521+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ11+ζ19−ζ11−ζ19ζ3+ζ7−ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ70000000000
χ502-22-200-22−2i2i2i−2i−1+52−1−521−521+52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18−1+52−1−521−521+520001−52−1+521+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ11+ζ19−ζ11−ζ19ζ3+ζ7−ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ70000000000
χ512-22-200-22−2i2i2i−2i−1−52−1+521+521−52−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14−1−52−1+521+521−520001+52−1−521−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ3+ζ7−ζ3−ζ7ζ11+ζ19−ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ190000000000
χ522-22-200-22−2i2i2i−2i−1−52−1+521+521−52ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−1−52−1+521+521−520001+52−1−521−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ3+ζ7−ζ3−ζ7ζ11+ζ19−ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ190000000000
χ532-2-222-200000022-2-22-22-22-22-2-2-2220000000000000000000000000002-22-2000000
χ542-2-222-200000022-2-22-22-22-22-2-2-222000000000000000000000000000-22-22000000
χ552-2-22-2200000022-2-2-22-22-22-22-2-2220000000000000000000000000002-2-22000000
χ562-2-22-2200000022-2-2-22-22-22-22-2-222000000000000000000000000000-222-2000000
χ5744-4-400000000444400000000-4-4-4-40000000000000000000000000000000000000
χ5844-4-400000000−1+5−1−5−1+5−1−52ζ6−2ζ14−2ζ6+2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ182ζ2−2ζ18−2ζ2+2ζ181−51+51−51+50000000000000000000000000000000000000
χ5944-4-400000000−1+5−1−5−1+5−1−5−2ζ6+2ζ142ζ6−2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ18−2ζ2+2ζ182ζ2−2ζ181−51+51−51+50000000000000000000000000000000000000
χ6044-4-400000000−1−5−1+5−1−5−1+5−2ζ2+2ζ182ζ2−2ζ182ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ142ζ6−2ζ14−2ζ6+2ζ141+51−51+51−50000000000000000000000000000000000000
χ6144-4-400000000−1−5−1+5−1−5−1+52ζ2−2ζ18−2ζ2+2ζ18−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ14−2ζ6+2ζ142ζ6−2ζ141+51−51+51−50000000000000000000000000000000000000
χ624-4-444-4000000−1+5−1−51−51+5−1+51−5−1+51−5−1−51+5−1−51+51−51+5−1+5−1−50000000000000000000000000000000000000
χ634-4-444-4000000−1−5−1+51+51−5−1−51+5−1−51+5−1+51−5−1+51−51+51−5−1−5−1+50000000000000000000000000000000000000
χ644-4-44-44000000−1+5−1−51−51+51−5−1+51−5−1+51+5−1−51+5−1−51−51+5−1+5−1−50000000000000000000000000000000000000
χ654-4-44-44000000−1−5−1+51+51−51+5−1−51+5−1−51−5−1+51−5−1+51+51−5−1−5−1+50000000000000000000000000000000000000

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