Finite Group Databasebeta

← Group #4098

Character table — Group #4098

Order 160.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111122222222222222222210101010111122222222222222222210101010
order1222225510101010101010101010101010104444222222101010101010101010101010101010104444
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
χ511-1-11-11111-1-1-1-11111-1-1-1-1i−ii−i11-1-11-11111-1-1-1-11111-1-1-1-1i−ii−i
χ611-1-11-11111-1-1-1-11111-1-1-1-1−ii−ii11-1-11-11111-1-1-1-11111-1-1-1-1−ii−ii
χ711-1-1-111111-1-1-1-1-1-1-1-11111i−i−ii11-1-1-111111-1-1-1-1-1-1-1-11111i−i−ii
χ811-1-1-111111-1-1-1-1-1-1-1-11111−iii−i11-1-1-111111-1-1-1-1-1-1-1-11111−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
χ1322-2-22-2−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000022-2-22-2−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+520000
χ1422-2-22-2−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000022-2-22-2−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−520000
χ1522-2-2-22−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52000022-2-2-22−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−520000
χ1622-2-2-22−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52000022-2-2-22−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+520000
χ172-22-20022-2-22-22-20000000000002-22-20022-2-22-22-2000000000000
χ182-22-200−1+52−1−521−521+52−1+521−52−1−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ1800002-22-200−1+52−1−521−521+52−1+521−52−1−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000
χ192-22-200−1+52−1−521−521+52−1+521−52−1−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ1800002-22-200−1+52−1−521−521+52−1+521−52−1−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000
χ202-22-200−1−52−1+521+521−52−1−521+52−1+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ1400002-22-200−1−52−1+521+521−52−1−521+52−1+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ140000
χ212-22-200−1−52−1+521+521−52−1−521+52−1+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ1400002-22-200−1−52−1+521+521−52−1−521+52−1+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000
χ222-2-220022-2-2-22-220000000000002-2-220022-2-2-22-22000000000000
χ232-2-2200−1+52−1−521−521+521−52−1+521+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ1800002-2-2200−1+52−1−521−521+521−52−1+521+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000
χ242-2-2200−1+52−1−521−521+521−52−1+521+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ1800002-2-2200−1+52−1−521−521+521−52−1+521+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000
χ252-2-2200−1−52−1+521+521−521+52−1−521−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ1400002-2-2200−1−52−1+521+521−521+52−1−521−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000
χ262-2-2200−1−52−1+521+521−521+52−1−521−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ1400002-2-2200−1−52−1+521+521−521+52−1−521−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ140000
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
χ3111-1-11-11111-1-1-1-11111-1-1-1-1i−ii−i-1-111-11-1-1-1-11111-1-1-1-11111−ii−ii
χ3211-1-11-11111-1-1-1-11111-1-1-1-1−ii−ii-1-111-11-1-1-1-11111-1-1-1-11111i−ii−i
χ3311-1-1-111111-1-1-1-1-1-1-1-11111i−i−ii-1-1111-1-1-1-1-111111111-1-1-1-1−iii−i
χ3411-1-1-111111-1-1-1-1-1-1-1-11111−iii−i-1-1111-1-1-1-1-111111111-1-1-1-1i−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
χ3922-2-22-2−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+520000-2-222-221−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000
χ4022-2-22-2−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−520000-2-222-221+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+520000
χ4122-2-2-22−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−520000-2-2222-21−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000
χ4222-2-2-22−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+520000-2-2222-21+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000
χ432-22-20022-2-22-22-2000000000000-22-2200-2-222-22-22000000000000
χ442-22-200−1+52−1−521−521+52−1+521−52−1−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000-22-22001−521+52−1+52−1−521−52−1+521+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000
χ452-22-200−1+52−1−521−521+52−1+521−52−1−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000-22-22001−521+52−1+52−1−521−52−1+521+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000
χ462-22-200−1−52−1+521+521−52−1−521+52−1+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ140000-22-22001+521−52−1−52−1+521+52−1−521−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000
χ472-22-200−1−52−1+521+521−52−1−521+52−1+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000-22-22001+521−52−1−52−1+521+52−1−521−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ140000
χ482-2-220022-2-2-22-22000000000000-222-200-2-2222-22-2000000000000
χ492-2-2200−1+52−1−521−521+521−52−1+521+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000-222-2001−521+52−1+52−1−52−1+521−52−1−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000
χ502-2-2200−1+52−1−521−521+521−52−1+521+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000-222-2001−521+52−1+52−1−52−1+521−52−1−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000
χ512-2-2200−1−52−1+521+521−521+52−1−521−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000-222-2001+521−52−1−52−1+52−1−521+52−1+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ140000
χ522-2-2200−1−52−1+521+521−521+52−1−521−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ140000-222-2001+521−52−1−52−1+52−1−521+52−1+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000

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