Finite Group Databasebeta

← Group #10604953

Character table — Group #10604953

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111222244444444488888888888888101010101010202020202020202020404040404040
order12222244451010101010101022101010101010101020202020444444488888888228888
χ11111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i
χ41111111111111111111111111111111-1-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii
χ511111111111111111-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1
χ611111111111111111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ811111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ9111111-1-1-1111111111-11111-1-1-1-1-1-1-1-111-1-1-1-11ii−i−iii−i−i1-1i−ii−i
χ10111111-1-1-1111111111-11111-1-1-1-1-1-1-1-111-1-1-1-11−i−iii−i−iii1-1−ii−ii
χ11111111-1-1-1111111111-11111-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-111-111-1-11
χ12111111-1-1-1111111111-11111-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-11-111-1
χ13111111-1-1-111111111-11-1-1-1-11111-1-1-1-111-1-1-1-11ii−i−iii−i−i-11−ii−ii
χ14111111-1-1-111111111-11-1-1-1-11111-1-1-1-111-1-1-1-11−i−iii−i−iii-11i−ii−i
χ15111111-1-1-111111111-11-1-1-1-11111-1-1-1-1-1-11111-111-1-1-1-1111-1-111-1
χ16111111-1-1-111111111-11-1-1-1-11111-1-1-1-1-1-11111-1-1-11111-1-11-11-1-11
χ172222-2-222-2222-2-2-2-22000000000022-2-222-222-2-200000000000000
χ182222-2-222-2222-2-2-2-22000000000022-2-2-2-22-2-22200000000000000
χ192222-2-2-2-22222-2-2-2-220000000000-2-222222-2-22-200000000000000
χ202222-2-2-2-22222-2-2-2-220000000000-2-222-2-2-222-2200000000000000
χ212-22-22-200022-222-2-2-2000000000000000022-2-20002i−2i2i−2i00000000
χ222-22-22-200022-222-2-2-2000000000000000022-2-2000−2i2i−2i2i00000000
χ232-22-22-200022-222-2-2-20000000000000000-2-2220002-2-2200000000
χ242-22-22-200022-222-2-2-20000000000000000-2-222000-222-200000000
χ252-22-2-2200022-2-2-222-200000000000000002-22-202i−2i00002i−2i000000
χ262-22-2-2200022-2-2-222-200000000000000002-22-20−2i2i0000−2i2i000000
χ272-22-2-2200022-2-2-222-20000000000000000-22-2202-20000-22000000
χ282-22-2-2200022-2-2-222-20000000000000000-22-220-2200002-2000000
χ29444444444-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000
χ30444444444-1-1-1-1-1-1-1-1-4-411111111-1-1-1-1000000000000000000000
χ31444444-4-4-4-1-1-1-1-1-1-1-14-4-1-1-1-111111111000000000000000000000
χ32444444-4-4-4-1-1-1-1-1-1-1-1-441111-1-1-1-11111000000000000000000000
χ334444-4-444-4-1-1-11111-10055−5−555−5−5-1-111000000000000000000000
χ344444-4-444-4-1-1-11111-100−5−555−5−555-1-111000000000000000000000
χ354444-4-4-4-44-1-1-11111-10055−5−5−5−55511-1-1000000000000000000000
χ364444-4-4-4-44-1-1-11111-100−5−55555−5−511-1-1000000000000000000000
χ3744-4-4004-404-4-40000400000000004-400000000000000000000000
χ3844-4-4004-40-1115−55−5-100−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18-115−5000000000000000000000
χ3944-4-4004-40-1115−55−5-100ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18-115−5000000000000000000000
χ4044-4-4004-40-111−55−55-100−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18-11−55000000000000000000000
χ4144-4-4004-40-111−55−55-100ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18-11−55000000000000000000000
χ4244-4-400-4404-4-4000040000000000-4400000000000000000000000
χ4344-4-400-440-1115−55−5-100−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ181-1−55000000000000000000000
χ4444-4-400-440-1115−55−5-100ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ181-1−55000000000000000000000
χ4544-4-400-440-111−55−55-100−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ181-15−5000000000000000000000
χ4644-4-400-440-111−55−55-100ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ181-15−5000000000000000000000
χ474-4-44000004-440000-4000000000000004-40000000000000000000
χ484-4-44000004-440000-400000000000000-440000000000000000000
χ498-88-88-8000-2-22-2-222200000000000000000000000000000000000
χ508-88-8-88000-2-2222-2-2200000000000000000000000000000000000
χ518-8-8800000-22-225−25−2525200000000000000000000000000000000000
χ528-8-8800000-22-2−252525−25200000000000000000000000000000000000

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