Finite Group Databasebeta

← Group #64992

Character table — Group #64992

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222222222222244444444444444444444444444444440404040
order1222445510101010101020202020202020204488882020202020202020404040404040404040404040404040404444
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1
χ3111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1
χ61111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1
χ9222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52222222−1+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+52−1−52−1−52−1−52−1−520000
χ10222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222-2-2-2-2−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+520000
χ11222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-222-2-21−521−521−521−521+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+520000
χ12222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2-2-2221−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000
χ13222222−1−52−1+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+52222222−1−52−1−52−1−52−1−52−1+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+520000
χ14222222−1−52−1+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+5222-2-2-2-2−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−520000
χ15222222−1−52−1+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+52-2-222-2-21+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+521−521−521−521−520000
χ16222222−1−52−1+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+52-2-2-2-2221+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+520000
χ172222-2-222222222-2-2-2-2-2-2-2-22-2000022-2-222-2-200000000000000000000
χ182222-2-222222222-2-2-2-2-2-2-2-2-220000-2-222-2-22200000000000000000000
χ192222-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+522-20000−1+52−1+521−521−52−1−52−1−521+521+52−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ70000
χ202222-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+522-20000−1+52−1+521−521−52−1−52−1−521+521+52ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ70000
χ212222-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+52-2200001−521−52−1+52−1+521+521+52−1−52−1−52−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ70000
χ222222-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+52-2200001−521−52−1+52−1+521+521+52−1−52−1−52ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ70000
χ232222-2-2−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−522-20000−1−52−1−521+521+52−1+52−1+521−521−52ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ190000
χ242222-2-2−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−522-20000−1−52−1−521+521+52−1+52−1+521−521−52−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ190000
χ252222-2-2−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−52-2200001+521+52−1−52−1−521−521−52−1+52−1+52ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ190000
χ262222-2-2−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−52-2200001+521+52−1−52−1−521−521−52−1+52−1+52−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ190000
χ272-2-222-2222-2-22-2-222-2-222-2-200002i−2i00000000000000002i−2i2i−2i2i−2i2i−2i0000
χ282-2-222-2222-2-22-2-222-2-222-2-20000−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i0000
χ292-2-222-2−1+52−1−52−1+521−521−52−1−521+521+52−1+52−1+521−521−52−1−52−1−521+521+5200002i−2i−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ11−ζ19ζ11+ζ19−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7−ζ3−ζ7ζ3+ζ70000
χ302-2-222-2−1+52−1−52−1+521−521−52−1−521+521+52−1+52−1+521−521−52−1−52−1−521+521+5200002i−2iζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18−ζ11−ζ19ζ11+ζ19−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7−ζ3−ζ7ζ3+ζ70000
χ312-2-222-2−1+52−1−52−1+521−521−52−1−521+521+52−1+52−1+521−521−52−1−52−1−521+521+520000−2i2i−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ7−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ11+ζ19−ζ11−ζ19ζ11+ζ19−ζ11−ζ19ζ3+ζ7−ζ3−ζ7ζ3+ζ7−ζ3−ζ70000
χ322-2-222-2−1+52−1−52−1+521−521−52−1−521+521+52−1+52−1+521−521−52−1−52−1−521+521+520000−2i2iζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3−ζ7ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18ζ11+ζ19−ζ11−ζ19ζ11+ζ19−ζ11−ζ19ζ3+ζ7−ζ3−ζ7ζ3+ζ7−ζ3−ζ70000
χ332-2-222-2−1−52−1+52−1−521+521+52−1+521−521−52−1−52−1−521+521+52−1+52−1+521−521−5200002i−2iζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ3−ζ7ζ3+ζ7−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19−ζ11−ζ19ζ11+ζ190000
χ342-2-222-2−1−52−1+52−1−521+521+52−1+521−521−52−1−52−1−521+521+52−1+52−1+521−521−5200002i−2i−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ3−ζ7ζ3+ζ7−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19−ζ11−ζ19ζ11+ζ190000
χ352-2-222-2−1−52−1+52−1−521+521+52−1+521−521−52−1−52−1−521+521+52−1+52−1+521−521−520000−2i2iζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ11+ζ19−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ3+ζ7−ζ3−ζ7ζ3+ζ7−ζ3−ζ7ζ11+ζ19−ζ11−ζ19ζ11+ζ19−ζ11−ζ190000
χ362-2-222-2−1−52−1+52−1−521+521+52−1+521−521−52−1−52−1−521+521+52−1+52−1+521−521−520000−2i2i−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ11−ζ19ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ3+ζ7−ζ3−ζ7ζ3+ζ7−ζ3−ζ7ζ11+ζ19−ζ11−ζ19ζ11+ζ19−ζ11−ζ190000
χ372-2-22-22222-2-22-2-2-2-222-2-222002i−2i00000000002i−2i−2i2i−2i2i2i−2i000000000000
χ382-2-22-22222-2-22-2-2-2-222-2-22200−2i2i0000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ392-2-22-22−1+52−1−52−1+521−521−52−1−521+521+521−521−52−1+52−1+521+521+52−1−52−1−52002i−2i00−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7−ζ11−ζ19ζ11+ζ19ζ11+ζ19−ζ11−ζ19ζ3+ζ7−ζ3−ζ7−ζ3−ζ7ζ3+ζ7−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ180000
χ402-2-22-22−1+52−1−52−1+521−521−52−1−521+521+521−521−52−1+52−1+521+521+52−1−52−1−52002i−2i00ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ11−ζ19ζ11+ζ19ζ11+ζ19−ζ11−ζ19ζ3+ζ7−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ180000
χ412-2-22-22−1+52−1−52−1+521−521−52−1−521+521+521−521−52−1+52−1+521+521+52−1−52−1−5200−2i2i00−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ11+ζ19−ζ11−ζ19−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7ζ3+ζ7−ζ3−ζ7ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ180000
χ422-2-22-22−1+52−1−52−1+521−521−52−1−521+521+521−521−52−1+52−1+521+521+52−1−52−1−5200−2i2i00ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7ζ11+ζ19−ζ11−ζ19−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ180000
χ432-2-22-22−1−52−1+52−1−521+521+52−1+521−521−521+521+52−1−52−1−521−521−52−1+52−1+52002i−2i00ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19−ζ3−ζ7ζ3+ζ7ζ3+ζ7−ζ3−ζ7ζ11+ζ19−ζ11−ζ19−ζ11−ζ19ζ11+ζ19−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ140000
χ442-2-22-22−1−52−1+52−1−521+521+52−1+521−521−521+521+52−1−52−1−521−521−52−1+52−1+52002i−2i00−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ3−ζ7ζ3+ζ7ζ3+ζ7−ζ3−ζ7ζ11+ζ19−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ140000
χ452-2-22-22−1−52−1+52−1−521+521+52−1+521−521−521+521+52−1−52−1−521−521−52−1+52−1+5200−2i2i00ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ3+ζ7−ζ3−ζ7−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19ζ11+ζ19−ζ11−ζ19ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ140000
χ462-2-22-22−1−52−1+52−1−521+521+52−1+521−521−521+521+52−1−52−1−521−521−52−1+52−1+5200−2i2i00−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19ζ3+ζ7−ζ3−ζ7−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ140000
χ4744-4-40044-44-4-44-4000000000000000000000000000000000000000000
χ4844-4-400−1+5−1−51−5−1+51−51+5−1−51+5−2ζ11+2ζ192ζ11−2ζ19−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ3−2ζ7−2ζ3+2ζ70000000000000000000000000000000000
χ4944-4-400−1+5−1−51−5−1+51−51+5−1−51+52ζ11−2ζ19−2ζ11+2ζ192ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ3+2ζ72ζ3−2ζ70000000000000000000000000000000000
χ5044-4-400−1−5−1+51+5−1−51+51−5−1+51−52ζ3−2ζ7−2ζ3+2ζ72ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ11−2ζ19−2ζ11+2ζ190000000000000000000000000000000000
χ5144-4-400−1−5−1+51+5−1−51+51−5−1+51−5−2ζ3+2ζ72ζ3−2ζ7−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ11+2ζ192ζ11−2ζ190000000000000000000000000000000000
χ524-44-40044-4-44-4-44000000000000000000000000000000000000000000
χ534-44-400−1+5−1−51−51−5−1+51+51+5−1−5−2ζ11+2ζ192ζ11−2ζ192ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ3+2ζ72ζ3−2ζ70000000000000000000000000000000000
χ544-44-400−1+5−1−51−51−5−1+51+51+5−1−52ζ11−2ζ19−2ζ11+2ζ19−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ3−2ζ7−2ζ3+2ζ70000000000000000000000000000000000
χ554-44-400−1−5−1+51+51+5−1−51−51−5−1+52ζ3−2ζ7−2ζ3+2ζ7−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ11+2ζ192ζ11−2ζ190000000000000000000000000000000000
χ564-44-400−1−5−1+51+51+5−1−51−51−5−1+5−2ζ3+2ζ72ζ3−2ζ72ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ11−2ζ19−2ζ11+2ζ190000000000000000000000000000000000

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