Finite Group Databasebeta

← Group #65512

Character table — Group #65512

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222222222224444444444444444444444444444442020202020202020
order1222222255101010101010101010101010101022224410101010101010101010101010101010202020202020202022444444
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
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
χ172222-2-2-2-222222-2-2-2222-2-2-2-2-20000000000000000000000000000000000002i−2i
χ182222-2-2-2-222222-2-2-2222-2-2-2-2-2000000000000000000000000000000000000−2i2i
χ1922-2-222-2-2222-2-22-2-22-2-22-2-22200002-2000000000000000022-2-222-2-200000000
χ2022-2-222-2-2222-2-22-2-22-2-22-2-2220000-220000000000000000-2-222-2-22200000000
χ2122-2-222-2-2−1+52−1−52−1+521−521−52−1+521−521−52−1−521+521+52−1−521+521+52−1+52−1−5200002-2ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−1+52−1+521−521−52−1−52−1−521+521+5200000000
χ2222-2-222-2-2−1+52−1−52−1+521−521−52−1+521−521−52−1−521+521+52−1−521+521+52−1+52−1−5200002-2−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18−1+52−1+521−521−52−1−52−1−521+521+5200000000
χ2322-2-222-2-2−1+52−1−52−1+521−521−52−1+521−521−52−1−521+521+52−1−521+521+52−1+52−1−520000-22ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ181−521−52−1+52−1+521+521+52−1−52−1−5200000000
χ2422-2-222-2-2−1+52−1−52−1+521−521−52−1+521−521−52−1−521+521+52−1−521+521+52−1+52−1−520000-22−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ181−521−52−1+52−1+521+521+52−1−52−1−5200000000
χ2522-2-222-2-2−1−52−1+52−1−521+521+52−1−521+521+52−1+521−521−52−1+521−521−52−1−52−1+5200002-2−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14−1−52−1−521+521+52−1+52−1+521−521−5200000000
χ2622-2-222-2-2−1−52−1+52−1−521+521+52−1−521+521+52−1+521−521−52−1+521−521−52−1−52−1+5200002-2ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−1−52−1−521+521+52−1+52−1+521−521−5200000000
χ2722-2-222-2-2−1−52−1+52−1−521+521+52−1−521+521+52−1+521−521−52−1+521−521−52−1−52−1+520000-22−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ141+521+52−1−52−1−521−521−52−1+52−1+5200000000
χ2822-2-222-2-2−1−52−1+52−1−521+521+52−1−521+521+52−1+521−521−52−1+521−521−52−1−52−1+520000-22ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ141+521+52−1−52−1−521−521−52−1+52−1+5200000000
χ2922-2-2-2-222222-2-2-2222-2-2-222-2-20000000000000000000000000000002-2000000
χ3022-2-2-2-222222-2-2-2222-2-2-222-2-2000000000000000000000000000000-22000000
χ312-22-22-22-222-22-2-22-2-22-2-22-222002-200000000002-22-22-22-20000000000000000
χ322-22-22-22-222-22-2-22-2-22-2-22-22200-220000000000-22-22-22-220000000000000000
χ332-22-22-22-2−1+52−1−521−52−1+521−521−52−1+521−521+52−1−521+521+52−1−521+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
χ342-22-22-22-2−1+52−1−521−52−1+521−521−52−1+521−521+52−1−521+521+52−1−521+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
χ352-22-22-22-2−1+52−1−521−52−1+521−521−52−1+521−521+52−1−521+521+52−1−521+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
χ362-22-22-22-2−1+52−1−521−52−1+521−521−52−1+521−521+52−1−521+521+52−1−521+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
χ372-22-22-22-2−1−52−1+521+52−1−521+521+52−1−521+521−52−1+521−521−52−1+521−52−1−52−1+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
χ382-22-22-22-2−1−52−1+521+52−1−521+521+52−1−521+521−52−1+521−521−52−1+521−52−1−52−1+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
χ392-22-22-22-2−1−52−1+521+52−1−521+521+52−1−521+521−52−1+521−521−52−1+521−52−1−52−1+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
χ402-22-22-22-2−1−52−1+521+52−1−521+521+52−1−521+521−52−1+521−521−52−1+521−52−1−52−1+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
χ412-22-2-22-2222-22-22-22-22-22-22-2-2000000000000000000000000000000002-20000
χ422-22-2-22-2222-22-22-22-22-22-22-2-200000000000000000000000000000000-220000
χ432-2-222-2-2222-2-22-2-22-2-22-2-22222-200002-2-222-2-22000000000000000000000000
χ442-2-222-2-2222-2-22-2-22-2-22-2-2222-220000-222-2-222-2000000000000000000000000
χ452-2-222-2-22−1+52−1−521−521−52−1+521−521−52−1+521+521+52−1−521+521+52−1−52−1+52−1−522-20000−1+521−521−52−1+52−1−521+521+52−1−52ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ1800000000
χ462-2-222-2-22−1+52−1−521−521−52−1+521−521−52−1+521+521+52−1−521+521+52−1−52−1+52−1−522-20000−1+521−521−52−1+52−1−521+521+52−1−52−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ1800000000
χ472-2-222-2-22−1+52−1−521−521−52−1+521−521−52−1+521+521+52−1−521+521+52−1−52−1+52−1−52-2200001−52−1+52−1+521−521+52−1−52−1−521+52ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ1800000000
χ482-2-222-2-22−1+52−1−521−521−52−1+521−521−52−1+521+521+52−1−521+521+52−1−52−1+52−1−52-2200001−52−1+52−1+521−521+52−1−52−1−521+52−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ1800000000
χ492-2-222-2-22−1−52−1+521+521+52−1−521+521+52−1−521−521−52−1+521−521−52−1+52−1−52−1+522-20000−1−521+521+52−1−52−1+521−521−52−1+52−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ1400000000
χ502-2-222-2-22−1−52−1+521+521+52−1−521+521+52−1−521−521−52−1+521−521−52−1+52−1−52−1+522-20000−1−521+521+52−1−52−1+521−521−52−1+52ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ1400000000
χ512-2-222-2-22−1−52−1+521+521+52−1−521+521+52−1−521−521−52−1+521−521−52−1+52−1−52−1+52-2200001+52−1−52−1−521+521−52−1+52−1+521−52−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ1400000000
χ522-2-222-2-22−1−52−1+521+521+52−1−521+521+52−1−521−521−52−1+521−521−52−1+52−1−52−1+52-2200001+52−1−52−1−521+521−52−1+52−1+521−52ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ1400000000
χ532-2-22-222-222-2-2222-2-2-2222-2-2-200000000000000000000000000000000002-200
χ542-2-22-222-222-2-2222-2-2-2222-2-2-20000000000000000000000000000000000-2200
χ554444-4-4-4-4−1+5−1−5−1+5−1+5−1+51−51−51−5−1−5−1−5−1−51+51+51+51−51+500000000000000000000000000000000000000
χ564444-4-4-4-4−1−5−1+5−1−5−1−5−1−51+51+51+5−1+5−1+5−1+51−51−51−51+51−500000000000000000000000000000000000000
χ5744-4-4-4-444−1+5−1−5−1+51−51−51−5−1+5−1+5−1−51+51+51+5−1−5−1−51−51+500000000000000000000000000000000000000
χ5844-4-4-4-444−1−5−1+5−1−51+51+51+5−1−5−1−5−1+51−51−51−5−1+5−1+51+51−500000000000000000000000000000000000000
χ594-44-4-44-44−1+5−1−51−5−1+51−5−1+51−5−1+51+5−1−51+5−1−51+5−1−51−51+500000000000000000000000000000000000000
χ604-44-4-44-44−1−5−1+51+5−1−51+5−1−51+5−1−51−5−1+51−5−1+51−5−1+51+51−500000000000000000000000000000000000000
χ614-4-44-444-4−1+5−1−51−51−5−1+5−1+5−1+51−51+51+5−1−5−1−5−1−51+51−51+500000000000000000000000000000000000000
χ624-4-44-444-4−1−5−1+51+51+5−1−5−1−5−1−51+51−51−5−1+5−1+5−1+51−51+51−500000000000000000000000000000000000000

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