Finite Group Databasebeta

← Group #64950

Character table — Group #64950

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222222222224444444444444444444444444444442020202020202020
order1222222255101010101010101010101010101044444420202020202020202020202020202020202020202020202044444444
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
χ17222-22-2-2-22222-2-222-2-22-2-22-2-2002-2000000000022-2-222-2-20000000000000000
χ18222-22-2-2-22222-2-222-2-22-2-22-2-200-220000000000-2-222-2-2220000000000000000
χ19222-22-2-2-2−1+52−1−52−1+52−1+521−521−52−1−52−1−521+521+52−1+521−521−52−1−521+521+52002-200−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7−1+52−1+521−521−52−1−52−1−521+521+52−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ700000000
χ20222-22-2-2-2−1+52−1−52−1+52−1+521−521−52−1−52−1−521+521+52−1+521−521−52−1−521+521+52002-200ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7−1+52−1+521−521−52−1−52−1−521+521+52ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ700000000
χ21222-22-2-2-2−1+52−1−52−1+52−1+521−521−52−1−52−1−521+521+52−1+521−521−52−1−521+521+5200-2200−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ71−521−52−1+52−1+521+521+52−1−52−1−52ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ700000000
χ22222-22-2-2-2−1+52−1−52−1+52−1+521−521−52−1−52−1−521+521+52−1+521−521−52−1−521+521+5200-2200ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ71−521−52−1+52−1+521+521+52−1−52−1−52−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ700000000
χ23222-22-2-2-2−1−52−1+52−1−52−1−521+521+52−1+52−1+521−521−52−1−521+521+52−1+521−521−52002-200ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19−1−52−1−521+521+52−1+52−1+521−521−52ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ1900000000
χ24222-22-2-2-2−1−52−1+52−1−52−1−521+521+52−1+52−1+521−521−52−1−521+521+52−1+521−521−52002-200−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19−1−52−1−521+521+52−1+52−1+521−521−52−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ1900000000
χ25222-22-2-2-2−1−52−1+52−1−52−1−521+521+52−1+52−1+521−521−52−1−521+521+52−1+521−521−5200-2200ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ191+521+52−1−52−1−521−521−52−1+52−1+52−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ1900000000
χ26222-22-2-2-2−1−52−1+52−1−52−1−521+521+52−1+52−1+521−521−52−1−521+521+52−1+521−521−5200-2200−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ191+521+52−1−52−1−521−521−52−1+52−1+52ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ1900000000
χ2722-22-22-2-2222-22-22-22-2-22-2-22-22-200002-22-22-22-2000000000000000000000000
χ2822-22-22-2-2222-22-22-22-2-22-2-22-2-220000-22-22-22-22000000000000000000000000
χ2922-22-22-2-2−1+52−1−52−1+521−52−1+521−52−1−521+52−1−521+521−52−1+521−521+52−1−521+522-20000−1+521−52−1+521−52−1−521+52−1−521+52−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ700000000
χ3022-22-22-2-2−1+52−1−52−1+521−52−1+521−52−1−521+52−1−521+521−52−1+521−521+52−1−521+522-20000−1+521−52−1+521−52−1−521+52−1−521+52ζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3−ζ700000000
χ3122-22-22-2-2−1+52−1−52−1+521−52−1+521−52−1−521+52−1−521+521−52−1+521−521+52−1−521+52-2200001−52−1+521−52−1+521+52−1−521+52−1−52−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3−ζ700000000
χ3222-22-22-2-2−1+52−1−52−1+521−52−1+521−52−1−521+52−1−521+521−52−1+521−521+52−1−521+52-2200001−52−1+521−52−1+521+52−1−521+52−1−52ζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ700000000
χ3322-22-22-2-2−1−52−1+52−1−521+52−1−521+52−1+521−52−1+521−521+52−1−521+521−52−1+521−522-20000−1−521+52−1−521+52−1+521−52−1+521−52ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ11+ζ1900000000
χ3422-22-22-2-2−1−52−1+52−1−521+52−1−521+52−1+521−52−1+521−521+52−1−521+521−52−1+521−522-20000−1−521+52−1−521+52−1+521−52−1+521−52−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ11−ζ1900000000
χ3522-22-22-2-2−1−52−1+52−1−521+52−1−521+52−1+521−52−1+521−521+52−1−521+521−52−1+521−52-2200001+52−1−521+52−1−521−52−1+521−52−1+52ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ11−ζ1900000000
χ3622-22-22-2-2−1−52−1+52−1−521+52−1−521+52−1+521−52−1+521−521+52−1−521+521−52−1+521−52-2200001+52−1−521+52−1−521−52−1+521−52−1+52−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ11+ζ1900000000
χ3722-2-2-2-222222-2-222-2-22-2-22-2-2200002-200000000000000002-2-222-2-2200000000
χ3822-2-2-2-222222-2-222-2-22-2-22-2-220000-220000000000000000-222-2-222-200000000
χ3922-2-2-2-222−1+52−1−52−1+521−521−52−1+52−1−521+521+52−1−521−521−52−1+521+521+52−1−5200002-2−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7−1+521−521−52−1+52−1−521+521+52−1−5200000000
χ4022-2-2-2-222−1+52−1−52−1+521−521−52−1+52−1−521+521+52−1−521−521−52−1+521+521+52−1−5200002-2ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7−1+521−521−52−1+52−1−521+521+52−1−5200000000
χ4122-2-2-2-222−1+52−1−52−1+521−521−52−1+52−1−521+521+52−1−521−521−52−1+521+521+52−1−520000-22−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ71−52−1+52−1+521−521+52−1−52−1−521+5200000000
χ4222-2-2-2-222−1+52−1−52−1+521−521−52−1+52−1−521+521+52−1−521−521−52−1+521+521+52−1−520000-22ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ71−52−1+52−1+521−521+52−1−52−1−521+5200000000
χ4322-2-2-2-222−1−52−1+52−1−521+521+52−1−52−1+521−521−52−1+521+521+52−1−521−521−52−1+5200002-2ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19−1−521+521+52−1−52−1+521−521−52−1+5200000000
χ4422-2-2-2-222−1−52−1+52−1−521+521+52−1−52−1+521−521−52−1+521+521+52−1−521−521−52−1+5200002-2−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19−1−521+521+52−1−52−1+521−521−52−1+5200000000
χ4522-2-2-2-222−1−52−1+52−1−521+521+52−1−52−1+521−521−52−1+521+521+52−1−521−521−52−1+520000-22ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ11−ζ191+52−1−52−1−521+521−52−1+52−1+521−5200000000
χ4622-2-2-2-222−1−52−1+52−1−521+521+52−1−52−1+521−521−52−1+521+521+52−1−521−521−52−1+520000-22−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ11+ζ191+52−1−52−1−521+521−52−1+52−1+521−5200000000
χ472-222-2-2-2222-2222-2222-2-2-2-2-2-20000000000000000000000000000002i−2i000000
χ482-222-2-2-2222-2222-2222-2-2-2-2-2-2000000000000000000000000000000−2i2i000000
χ492-22-2-222-222-22-2-2-22-2-2-222-22200000000000000000000000000000000002i−2i00
χ502-22-2-222-222-22-2-2-22-2-2-222-2220000000000000000000000000000000000−2i2i00
χ512-2-222-22-222-2-22-2-2-22-22-222-22000000000000000000000000000000002i−2i0000
χ522-2-222-22-222-2-22-2-2-22-22-222-2200000000000000000000000000000000−2i2i0000
χ532-2-2-222-2222-2-2-22-2-2-2222-222-20000000000000000000000000000000000002-2
χ542-2-2-222-2222-2-2-22-2-2-2222-222-2000000000000000000000000000000000000-22
χ554-444-4-4-44−1+5−1−51−5−1+5−1+5−1+51+5−1−5−1−5−1−51−51−51−51+51+51+500000000000000000000000000000000000000
χ564-444-4-4-44−1−5−1+51+5−1−5−1−5−1−51−5−1+5−1+5−1+51+51+51+51−51−51−500000000000000000000000000000000000000
χ574-44-4-444-4−1+5−1−51−5−1+51−51−51+5−1−51+51+51−5−1+5−1+51+5−1−5−1−500000000000000000000000000000000000000
χ584-44-4-444-4−1−5−1+51+5−1−51+51+51−5−1+51−51−51+5−1−5−1−51−5−1+5−1+500000000000000000000000000000000000000
χ594-4-444-44-4−1+5−1−51−51−5−1+51−51+51+5−1−51+5−1+51−5−1+5−1−51+5−1−500000000000000000000000000000000000000
χ604-4-444-44-4−1−5−1+51+51+5−1−51+51−51−5−1+51−5−1−51+5−1−5−1+51−5−1+500000000000000000000000000000000000000
χ614-4-4-444-44−1+5−1−51−51−51−5−1+51+51+51+5−1−5−1+5−1+51−5−1−5−1−51+500000000000000000000000000000000000000
χ624-4-4-444-44−1−5−1+51+51+51+5−1−51−51−51−5−1+5−1−5−1−51+5−1+5−1+51−500000000000000000000000000000000000000

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