Finite Group Databasebeta

← Group #10604619

Character table — Group #10604619

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43
size1122244444488888888101010101616161620202020202020202020404040404040
order12244225101010242020202020202244101010104488888888244444
χ11111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111-1-1-1-11111-1-1iiii−i−i−i−i-1-1ii−i−i
χ41111111111111111111-1-1-1-11111-1-1−i−i−i−iiiii-1-1−i−iii
χ511111111111-1-111-1-1-1-1111111-1-11111111111-1-1-1-1-1-1
χ611111111111-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111
χ711111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1iiii−i−i−i−i11−i−iii
χ811111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1−i−i−i−iiiii11ii−i−i
χ911111-1-111111-111-1-1-1-11111-1-111-1-111-1-111-1-11-11-11-1
χ1011111-1-111111-111-1-1-1-11111-1-111-1-1-1-111-1-1111-1-11-11
χ1111111-1-111111-111-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii-11i−i−ii
χ1211111-1-111111-111-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i-11−iii−i
χ1311111-1-11111-111111111111-1-1-1-1-1-111-1-111-1-1-11-11-11
χ1411111-1-11111-111111111111-1-1-1-1-1-1-1-111-1-111-111-11-1
χ1511111-1-11111-11111111-1-1-1-1-1-1-1-111ii−i−i−i−iii1-1−iii−i
χ1611111-1-11111-11111111-1-1-1-1-1-1-1-111−i−iiiii−i−i1-1i−i−ii
χ17222-2-22-2222200-2-2000022-2-22-2002-200000000000000
χ18222-2-22-2222200-2-20000-2-2222-200-2200000000000000
χ19222-2-2-22222200-2-2000022-2-2-2200-2200000000000000
χ20222-2-2-22222200-2-20000-2-222-22002-200000000000000
χ2122-22-20022-2-2002-200002-22-2000000002i−2i002i−2i000000
χ2222-22-20022-2-2002-200002-22-200000000−2i2i00−2i2i000000
χ2322-22-20022-2-2002-20000-22-22000000002-200-22000000
χ2422-22-20022-2-2002-20000-22-2200000000-22002-2000000
χ2522-2-220022-2-200-2200002-2-220000002-2002-200000000
χ2622-2-220022-2-200-2200002-2-22000000-2200-2200000000
χ2722-2-220022-2-200-220000-222-20000002i−2i00−2i2i00000000
χ2822-2-220022-2-200-220000-222-2000000−2i2i002i−2i00000000
χ294444444-1-1-1-144-1-1-1-1-1-10000-1-1-1-10000000000000000
χ304444444-1-1-1-1-4-4-1-111110000-1-1110000000000000000
χ3144444-4-4-1-1-1-14-4-1-11111000011-1-10000000000000000
χ3244444-4-4-1-1-1-1-44-1-1-1-1-1-1000011110000000000000000
χ33444-4-44-4-1-1-1-1001155−5−50000-115−50000000000000000
χ34444-4-44-4-1-1-1-10011−5−5550000-11−550000000000000000
χ35444-4-4-44-1-1-1-1001155−5−500001-1−550000000000000000
χ36444-4-4-44-1-1-1-10011−5−55500001-15−50000000000000000
χ3788-88-800-2-22200-220000000000000000000000000000
χ3888-8-8800-2-222002-20000000000000000000000000000
χ398-8000008-80000000000000000000000000000000000
χ408-800000-2225−2500002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18000000000000000000000000
χ418-800000-2225−250000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ18000000000000000000000000
χ428-800000-22−25250000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000
χ438-800000-22−252500002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000

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