Finite Group Databasebeta

← Group #4071

Character table — Group #4071

Order 160.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111122222222222222222210101010111122222222222222222210101010
order1222445510101010101020202020202020204444222244101010101010101020202020202020204444
χ11111111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1
χ31111-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-1
χ41111-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-111
χ51-11-11-111-1-1-1-1111111-1-1-1-1i−ii−i1-11-11-111-1-1-1-1111111-1-1-1-1i−ii−i
χ61-11-11-111-1-1-1-1111111-1-1-1-1−ii−ii1-11-11-111-1-1-1-1111111-1-1-1-1−ii−ii
χ71-11-1-1111-1-1-1-111-1-1-1-11111i−i−ii1-11-1-1111-1-1-1-111-1-1-1-11111i−i−ii
χ81-11-1-1111-1-1-1-111-1-1-1-11111−iii−i1-11-1-1111-1-1-1-111-1-1-1-11111−iii−i
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+52−1−52−1−520000222222−1+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+520000222222−1−52−1+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
χ112222-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+5200002222-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+520000
χ122222-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+521−521−5200002222-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+521−521−520000
χ1322-2-200222-22-2-2-200000000000022-2-200222-22-2-2-2000000000000
χ1422-2-200−1+52−1−52−1+521−52−1−521+521−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000022-2-200−1+52−1−52−1+521−52−1−521+521−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ70000
χ1522-2-200−1+52−1−52−1+521−52−1−521+521−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000022-2-200−1+52−1−52−1+521−52−1−521+521−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ70000
χ1622-2-200−1−52−1+52−1−521+52−1+521−521+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000022-2-200−1−52−1+52−1−521+52−1+521−521+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ190000
χ1722-2-200−1−52−1+52−1−521+52−1+521−521+521−52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000022-2-200−1−52−1+52−1−521+52−1+521−521+521−52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ190000
χ182-22-22-2−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+5200002-22-22-2−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000
χ192-22-22-2−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−5200002-22-22-2−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000
χ202-22-2-22−1+52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200002-22-2-22−1+52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000
χ212-22-2-22−1−52−1+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+5200002-22-2-22−1−52−1+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+520000
χ222-2-220022-22-22-2-20000000000002-2-220022-22-22-2-2000000000000
χ232-2-2200−1+52−1−521−52−1+521+52−1−521−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ700002-2-2200−1+52−1−521−52−1+521+52−1−521−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ70000
χ242-2-2200−1+52−1−521−52−1+521+52−1−521−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ700002-2-2200−1+52−1−521−52−1+521+52−1−521−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ70000
χ252-2-2200−1−52−1+521+52−1−521−52−1+521+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ1900002-2-2200−1−52−1+521+52−1−521−52−1+521+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ190000
χ262-2-2200−1−52−1+521+52−1−521−52−1+521+521−52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ1900002-2-2200−1−52−1+521+52−1−521−52−1+521+521−52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ190000
χ2711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ281111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ291111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111
χ301111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1
χ311-11-11-111-1-1-1-1111111-1-1-1-1i−ii−i-11-11-11-1-11111-1-1-1-1-1-11111−ii−ii
χ321-11-11-111-1-1-1-1111111-1-1-1-1−ii−ii-11-11-11-1-11111-1-1-1-1-1-11111i−ii−i
χ331-11-1-1111-1-1-1-111-1-1-1-11111i−i−ii-11-111-1-1-11111-1-11111-1-1-1-1−iii−i
χ341-11-1-1111-1-1-1-111-1-1-1-11111−iii−i-11-111-1-1-11111-1-11111-1-1-1-1i−i−ii
χ35222222−1+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+52−1−52−1−520000-2-2-2-2-2-21−521+521−521−521+521+521−521+521−521−521+521+521−521−521+521+520000
χ36222222−1−52−1+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+520000-2-2-2-2-2-21+521−521+521+521−521−521+521−521+521+521−521−521+521+521−521−520000
χ372222-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+520000-2-2-2-2221−521+521−521−521+521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000
χ382222-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+521−521−520000-2-2-2-2221+521−521+521+521−521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000
χ3922-2-200222-22-2-2-2000000000000-2-22200-2-2-22-2222000000000000
χ4022-2-200−1+52−1−52−1+521−52−1−521+521−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ70000-2-222001−521+521−52−1+521+52−1−52−1+52−1−52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ70000
χ4122-2-200−1+52−1−52−1+521−52−1−521+521−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ70000-2-222001−521+521−52−1+521+52−1−52−1+52−1−52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ70000
χ4222-2-200−1−52−1+52−1−521+52−1+521−521+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ190000-2-222001+521−521+52−1−521−52−1+52−1−52−1+52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ190000
χ4322-2-200−1−52−1+52−1−521+52−1+521−521+521−52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ190000-2-222001+521−521+52−1−521−52−1+52−1−52−1+52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ190000
χ442-22-22-2−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000-22-22-221−521+52−1+52−1+52−1−52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−520000
χ452-22-22-2−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000-22-22-221+521−52−1−52−1−52−1+52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+520000
χ462-22-2-22−1+52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000-22-222-21−521+52−1+52−1+52−1−52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+520000
χ472-22-2-22−1−52−1+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+520000-22-222-21+521−52−1−52−1−52−1+52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−520000
χ482-2-220022-22-22-2-2000000000000-222-200-2-22-22-222000000000000
χ492-2-2200−1+52−1−521−52−1+521+52−1−521−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ70000-222-2001−521+52−1+521−52−1−521+52−1+52−1−52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ70000
χ502-2-2200−1+52−1−521−52−1+521+52−1−521−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ70000-222-2001−521+52−1+521−52−1−521+52−1+52−1−52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ70000
χ512-2-2200−1−52−1+521+52−1−521−52−1+521+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ190000-222-2001+521−52−1−521+52−1+521−52−1−52−1+52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ190000
χ522-2-2200−1−52−1+521+52−1−521−52−1+521+521−52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ190000-222-2001+521−52−1−521+52−1+521−52−1−52−1+52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ190000

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