Finite Group Databasebeta

← Group #65249

Character table — Group #65249

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222222222224444444444444444444444444444442020202020202020
order1222222255101010101010101010101010101022444410101010101010102020202020202020202020202020202022224444
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ922222222−1+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+52−1−52−1−52−1−52−1−5200000000
χ1022222222−1+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+5200000000
χ1122222222−1+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+5200000000
χ1222222222−1+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+52−1−52−1−52−1−52−1−5200000000
χ1322222222−1−52−1+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+5200000000
χ1422222222−1−52−1+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+521−521−521−521−5200000000
χ1522222222−1−52−1+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+521−521−521−521−5200000000
χ1622222222−1−52−1+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+5200000000
χ172222-2-2-2-222222-2-2222-2-2-2-2-2-200002i−2i00000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ182222-2-2-2-222222-2-2222-2-2-2-2-2-20000−2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ192222-2-2-2-2−1+52−1−52−1+52−1+52−1+521−521−52−1−52−1−52−1−521+521+521−521−521+521+5200002i−2iζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ700000000
χ202222-2-2-2-2−1+52−1−52−1+52−1+52−1+521−521−52−1−52−1−52−1−521+521+521−521−521+521+5200002i−2i−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ700000000
χ212222-2-2-2-2−1+52−1−52−1+52−1+52−1+521−521−52−1−52−1−52−1−521+521+521−521−521+521+520000−2i2iζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ700000000
χ222222-2-2-2-2−1+52−1−52−1+52−1+52−1+521−521−52−1−52−1−52−1−521+521+521−521−521+521+520000−2i2i−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ700000000
χ232222-2-2-2-2−1−52−1+52−1−52−1−52−1−521+521+52−1+52−1+52−1+521−521−521+521+521−521−5200002i−2i−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ1900000000
χ242222-2-2-2-2−1−52−1+52−1−52−1−52−1−521+521+52−1+52−1+52−1+521−521−521+521+521−521−5200002i−2iζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ1900000000
χ252222-2-2-2-2−1−52−1+52−1−52−1−52−1−521+521+52−1+52−1+52−1+521−521−521+521+521−521−520000−2i2i−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ11−ζ1900000000
χ262222-2-2-2-2−1−52−1+52−1−52−1−52−1−521+521+52−1+52−1+52−1+521−521−521+521+521−521−520000−2i2iζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ11−ζ1900000000
χ2722-2-222-2-2222-2-2-2-22-2-2-2-22222002-200000000002-22-22-22-20000000000000000
χ2822-2-222-2-2222-2-2-2-22-2-2-2-2222200-220000000000-22-22-22-220000000000000000
χ2922-2-222-2-2−1+52−1−52−1+521−521−521−521−52−1−521+521+521+521+52−1+52−1+52−1−52−1−52002-200ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−1+521−52−1+521−52−1−521+52−1−521+52ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ1800000000
χ3022-2-222-2-2−1+52−1−52−1+521−521−521−521−52−1−521+521+521+521+52−1+52−1+52−1−52−1−52002-200−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18−1+521−52−1+521−52−1−521+52−1−521+52−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ1800000000
χ3122-2-222-2-2−1+52−1−52−1+521−521−521−521−52−1−521+521+521+521+52−1+52−1+52−1−52−1−5200-2200ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ181−52−1+521−52−1+521+52−1−521+52−1−52−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ1800000000
χ3222-2-222-2-2−1+52−1−52−1+521−521−521−521−52−1−521+521+521+521+52−1+52−1+52−1−52−1−5200-2200−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ181−52−1+521−52−1+521+52−1−521+52−1−52ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ1800000000
χ3322-2-222-2-2−1−52−1+52−1−521+521+521+521+52−1+521−521−521−521−52−1−52−1−52−1+52−1+52002-200−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14−1−521+52−1−521+52−1+521−52−1+521−52−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ1400000000
χ3422-2-222-2-2−1−52−1+52−1−521+521+521+521+52−1+521−521−521−521−52−1−52−1−52−1+52−1+52002-200ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−1−521+52−1−521+52−1+521−52−1+521−52ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ1400000000
χ3522-2-222-2-2−1−52−1+52−1−521+521+521+521+52−1+521−521−521−521−52−1−52−1−52−1+52−1+5200-2200−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ141+52−1−521+52−1−521−52−1+521−52−1+52ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ1400000000
χ3622-2-222-2-2−1−52−1+52−1−521+521+521+521+52−1+521−521−521−521−52−1−52−1−52−1+52−1+5200-2200ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ141+52−1−521+52−1−521−52−1+521−52−1+52−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ1400000000
χ3722-2-2-2-222222-2-2222-2-222-2-2-2-22-200002-2-222-2-22000000000000000000000000
χ3822-2-2-2-222222-2-2222-2-222-2-2-2-2-220000-222-2-222-2000000000000000000000000
χ3922-2-2-2-222−1+52−1−52−1+521−521−52−1+52−1+52−1−521+521+52−1−52−1−521−521−521+521+522-20000−1+521−521−52−1+52−1−521+521+52−1−52−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ700000000
χ4022-2-2-2-222−1+52−1−52−1+521−521−52−1+52−1+52−1−521+521+52−1−52−1−521−521−521+521+522-20000−1+521−521−52−1+52−1−521+521+52−1−52ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ700000000
χ4122-2-2-2-222−1+52−1−52−1+521−521−52−1+52−1+52−1−521+521+52−1−52−1−521−521−521+521+52-2200001−52−1+52−1+521−521+52−1−52−1−521+52−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ700000000
χ4222-2-2-2-222−1+52−1−52−1+521−521−52−1+52−1+52−1−521+521+52−1−52−1−521−521−521+521+52-2200001−52−1+52−1+521−521+52−1−52−1−521+52ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ700000000
χ4322-2-2-2-222−1−52−1+52−1−521+521+52−1−52−1−52−1+521−521−52−1+52−1+521+521+521−521−522-20000−1−521+521+52−1−52−1+521−521−52−1+52ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ1900000000
χ4422-2-2-2-222−1−52−1+52−1−521+521+52−1−52−1−52−1+521−521−52−1+52−1+521+521+521−521−522-20000−1−521+521+52−1−52−1+521−521−52−1+52−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ1900000000
χ4522-2-2-2-222−1−52−1+52−1−521+521+52−1−52−1−52−1+521−521−52−1+52−1+521+521+521−521−52-2200001+52−1−52−1−521+521−52−1+52−1+521−52ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ1900000000
χ4622-2-2-2-222−1−52−1+52−1−521+521+52−1−52−1−52−1+521−521−52−1+52−1+521+521+521−521−52-2200001+52−1−52−1−521+521−52−1+52−1+521−52−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ1900000000
χ472-22-22-22-222-22-22-2-22-22-22-22-2000000000000000000000000000000002-20000
χ482-22-22-22-222-22-22-2-22-22-22-22-200000000000000000000000000000000-220000
χ492-22-2-22-2222-22-2-22-22-2-22-22-2200000000000000000000000000000000002-200
χ502-22-2-22-2222-22-2-22-22-2-22-22-220000000000000000000000000000000000-2200
χ512-2-222-2-2222-2-22-22-2-22-222-22-20000000000000000000000000000002-2000000
χ522-2-222-2-2222-2-22-22-2-22-222-22-2000000000000000000000000000000-22000000
χ532-2-22-222-222-2-222-2-2-222-2-22-220000000000000000000000000000000000002-2
χ542-2-22-222-222-2-222-2-2-222-2-22-22000000000000000000000000000000000000-22
χ554-44-44-44-4−1+5−1−51−5−1+51−5−1+51−51+5−1−51+5−1−51+5−1+51−5−1−51+500000000000000000000000000000000000000
χ564-44-44-44-4−1−5−1+51+5−1−51+5−1−51+51−5−1+51−5−1+51−5−1−51+5−1+51−500000000000000000000000000000000000000
χ574-44-4-44-44−1+5−1−51−5−1+51−51−5−1+51+5−1−51+51+5−1−51−5−1+51+5−1−500000000000000000000000000000000000000
χ584-44-4-44-44−1−5−1+51+5−1−51+51+5−1−51−5−1+51−51−5−1+51+5−1−51−5−1+500000000000000000000000000000000000000
χ594-4-444-4-44−1+5−1−51−51−5−1+51−5−1+51+51+5−1−51+5−1−5−1+51−5−1−51+500000000000000000000000000000000000000
χ604-4-444-4-44−1−5−1+51+51+5−1−51+5−1−51−51−5−1+51−5−1+5−1−51+5−1+51−500000000000000000000000000000000000000
χ614-4-44-444-4−1+5−1−51−51−5−1+5−1+51−51+51+5−1−5−1−51+51−5−1+51+5−1−500000000000000000000000000000000000000
χ624-4-44-444-4−1−5−1+51+51+5−1−5−1−51+51−51−5−1+5−1+51−51+5−1−51−5−1+500000000000000000000000000000000000000

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