Finite Group Databasebeta

← Group #10604982

Character table — Group #10604982

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111222244444444488888888888888101010101010202020202020202020404040404040
order12222244451010101010101044202020202020202020202020222244444444444444444
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
χ511111111111111111-1-11111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1
χ611111111111111111-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ811111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ9111111-1-1-1111111111-1-1-1-1-11111-1-1-1-11111-1-1-111-1-111-1-11-11-11-1
χ10111111-1-1-1111111111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1111-1-11-11
χ11111111-1-1-1111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1111ii−i−i−i−iii-11i−i−ii
χ12111111-1-1-1111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1111−i−iiiii−i−i-11−iii−i
χ13111111-1-1-111111111-11-1-1-1-1-1-1-1-111111111-1-1-111-1-111-1-1-11-11-11
χ14111111-1-1-111111111-11-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-111-111-11-1
χ15111111-1-1-111111111-11-1-1-1-1-1-1-1-11111-1-1-1-1111ii−i−i−i−iii1-1−iii−i
χ16111111-1-1-111111111-11-1-1-1-1-1-1-1-11111-1-1-1-1111−i−iiiii−i−i1-1i−i−ii
χ172222-2-222-2222-2-2-2-220022-2-2000000002-2-22-2-2200000000000000
χ182222-2-222-2222-2-2-2-220022-2-200000000-222-222-200000000000000
χ192222-2-2-2-22222-2-2-2-2200-2-222000000002-2-2222-200000000000000
χ202222-2-2-2-22222-2-2-2-2200-2-22200000000-222-2-2-2200000000000000
χ2122-2-22-200022-222-2-2-20000000000000022-2-2000002-2002-2000000
χ2222-2-22-200022-222-2-2-20000000000000022-2-200000-2200-22000000
χ2322-2-22-200022-222-2-2-200000000000000-2-222000002i−2i00−2i2i000000
χ2422-2-22-200022-222-2-2-200000000000000-2-22200000−2i2i002i−2i000000
χ2522-2-2-2200022-2-2-222-2000000000000002-22-20002-2002-200000000
χ2622-2-2-2200022-2-2-222-2000000000000002-22-2000-2200-2200000000
χ2722-2-2-2200022-2-2-222-200000000000000-22-220002i−2i00−2i2i00000000
χ2822-2-2-2200022-2-2-222-200000000000000-22-22000−2i2i002i−2i00000000
χ29444444444-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000
χ30444444444-1-1-1-1-1-1-1-1-4-4-1-1-1-111111111000000000000000000000
χ31444444-4-4-4-1-1-1-1-1-1-1-14-41111-1-1-1-11111000000000000000000000
χ32444444-4-4-4-1-1-1-1-1-1-1-1-4411111111-1-1-1-1000000000000000000000
χ334444-4-444-4-1-1-11111-100-1-11155−5−555−5−5000000000000000000000
χ344444-4-444-4-1-1-11111-100-1-111−5−555−5−555000000000000000000000
χ354444-4-4-4-44-1-1-11111-10011-1-155−5−5−5−555000000000000000000000
χ364444-4-4-4-44-1-1-11111-10011-1-1−5−55555−5−5000000000000000000000
χ374-44-4004-404-4-400004004-40000000000000000000000000000000
χ384-44-4004-40-1115−55−5-100-115−5−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−ζ18000000000000000000000
χ394-44-4004-40-1115−55−5-100-115−5ζ2−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+ζ18000000000000000000000
χ404-44-4004-40-111−55−55-100-11−55−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+ζ18000000000000000000000
χ414-44-4004-40-111−55−55-100-11−55ζ2+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−ζ18000000000000000000000
χ424-44-400-4404-4-40000400-440000000000000000000000000000000
χ434-44-400-440-1115−55−5-1001-1−55−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+ζ18000000000000000000000
χ444-44-400-440-1115−55−5-1001-1−55ζ2−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−ζ18000000000000000000000
χ454-44-400-440-111−55−55-1001-15−5−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−ζ18000000000000000000000
χ464-44-400-440-111−55−55-1001-15−5ζ2+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+ζ18000000000000000000000
χ474-4-44000004-440000-40000000000000000004i−4i000000000000000
χ484-4-44000004-440000-4000000000000000000−4i4i000000000000000
χ4988-8-88-8000-2-22-2-222200000000000000000000000000000000000
χ5088-8-8-88000-2-2222-2-2200000000000000000000000000000000000
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.