Finite Group Databasebeta

← Group #10604994

Character table — Group #10604994

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111222244444444488888888888888101010101010202020202020202020404040404040
order12222244451010102020202024101010101010202020202020444444488888888248888
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
χ511111111111111111-1-111-1-1-1-111-1-1-1-1111111111111111-1-1-1-1-1-1
χ611111111111111111-1-111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ811111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ91111-1-1-1-111111-1-1-1-11-1-1-1111111-1-1-1-111-1-1-1-11ii−i−iii−i−i1-1i−ii−i
χ101111-1-1-1-111111-1-1-1-11-1-1-1111111-1-1-1-111-1-1-1-11−i−iii−i−iii1-1−ii−ii
χ111111-1-1-1-111111-1-1-1-11-1-1-1111111-1-1-1-1-1-11111-111-1-1-1-111-111-1-11
χ121111-1-1-1-111111-1-1-1-11-1-1-1111111-1-1-1-1-1-11111-1-1-11111-1-1-11-111-1
χ131111-1-1-1-111111-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-11ii−i−iii−i−i-11−ii−ii
χ141111-1-1-1-111111-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-11−i−iii−i−iii-11i−ii−i
χ151111-1-1-1-111111-1-1-1-1-11-1-1-1-1-1-1111111-1-11111-111-1-1-1-1111-1-111-1
χ161111-1-1-1-111111-1-1-1-1-11-1-1-1-1-1-1111111-1-11111-1-1-11111-1-11-11-1-11
χ17222222-2-2-22222-2-2-2-200220000-2-200002222-2-2-200000000000000
χ18222222-2-2-22222-2-2-2-200220000-2-20000-2-2-2-222200000000000000
χ192222-2-222-22222222200-2-20000-2-2000022-2-222-200000000000000
χ202222-2-222-22222222200-2-20000-2-20000-2-222-2-2200000000000000
χ2122-2-2002i−2i022-2-22i2i−2i−2i000000000000002-2002i−2i01+i−1−i1−i−1+i1+i−1−i1−i−1+i000000
χ2222-2-2002i−2i022-2-22i2i−2i−2i000000000000002-2002i−2i0−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000
χ2322-2-2002i−2i022-2-22i2i−2i−2i00000000000000-2200−2i2i01−i−1+i−1−i1+i−1+i1−i1+i−1−i000000
χ2422-2-2002i−2i022-2-22i2i−2i−2i00000000000000-2200−2i2i0−1+i1−i1+i−1−i1−i−1+i−1−i1+i000000
χ2522-2-200−2i2i022-2-2−2i−2i2i2i000000000000002-200−2i2i01−i−1+i1+i−1−i1−i−1+i1+i−1−i000000
χ2622-2-200−2i2i022-2-2−2i−2i2i2i000000000000002-200−2i2i0−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000
χ2722-2-200−2i2i022-2-2−2i−2i2i2i00000000000000-22002i−2i01+i−1−i−1+i1−i−1−i1+i1−i−1+i000000
χ2822-2-200−2i2i022-2-2−2i−2i2i2i00000000000000-22002i−2i0−1−i1+i1−i−1+i1+i−1−i−1+i1−i000000
χ29444444444-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000
χ30444444444-1-1-1-1-1-1-1-1-4-4-1-11111-1-11111000000000000000000000
χ31444444-4-4-4-1-1-1-1111100-1-155−5−51155−5−5000000000000000000000
χ32444444-4-4-4-1-1-1-1111100-1-1−5−55511−5−555000000000000000000000
χ334444-4-444-4-1-1-1-1-1-1-1-1001155−5−511−5−555000000000000000000000
χ344444-4-444-4-1-1-1-1-1-1-1-10011−5−5551155−5−5000000000000000000000
χ354444-4-4-4-44-1-1-1-111114-411-1-1-1-1-1-11111000000000000000000000
χ364444-4-4-4-44-1-1-1-11111-44111111-1-1-1-1-1-1000000000000000000000
χ374-44-4000004-44-4000000000000000000004i−4i00000000000000000
χ384-44-4000004-44-400000000000000000000−4i4i00000000000000000
χ394-4-444-40004-4-440000004-40000000000000000000000000000000
χ404-4-444-4000-111-15−55−500-11−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ185−5−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18000000000000000000000
χ414-4-444-4000-111-15−55−500-11ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ185−5ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18000000000000000000000
χ424-4-444-4000-111-1−55−5500-11−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−55−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18000000000000000000000
χ434-4-444-4000-111-1−55−5500-11ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−55ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18000000000000000000000
χ444-4-44-440004-4-44000000-440000000000000000000000000000000
χ454-4-44-44000-111-15−55−5001-1−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−55ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18000000000000000000000
χ464-4-44-44000-111-15−55−5001-1ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−55−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18000000000000000000000
χ474-4-44-44000-111-1−55−55001-1−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ185−5ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18000000000000000000000
χ484-4-44-44000-111-1−55−55001-1ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ185−5−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18000000000000000000000
χ4988-8-8008i−8i0-2-222−2i−2i2i2i00000000000000000000000000000000000
χ5088-8-800−8i8i0-2-2222i2i−2i−2i00000000000000000000000000000000000
χ518-88-800000-22-222i5−2i5−2i52i500000000000000000000000000000000000
χ528-88-800000-22-22−2i52i52i5−2i500000000000000000000000000000000000

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