Finite Group Databasebeta

← Group #13014439

Character table — Group #13014439

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size112444444455888888888810161616161616161616202020323240404040404040404040808080808080
order12244451010102224888820202020220404040404040404044410202444448888888888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1
χ311111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-1-1-1
χ411111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-1-1-11111
χ51111111111-1-11111111111-1111111111-1-1-111-1ii−i−i-1-1-1-1-1i−iii−i−i
χ61111111111-1-11111111111-1111111111-1-1-111-1−i−iii-1-1-1-1-1−ii−i−iii
χ71111111111-1-111-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-1-111-1ii−i−i-11111i−i−i−iii
χ81111111111-1-111-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-1-111-1−i−iii-11111−iiii−i−i
χ91111-1-11111111-1ii−i−i-1-1-1-111iiii−i−i−i−i-1-111-111111-1ii−i−i-1-1i−ii−i
χ101111-1-11111111-1ii−i−i-1-1-1-111iiii−i−i−i−i-1-111-11-1-1-1-1-1ii−i−i11−ii−ii
χ111111-1-11111111-1−i−iii-1-1-1-111−i−i−i−iiiii-1-111-111111-1−i−iii-1-1−ii−ii
χ121111-1-11111111-1−i−iii-1-1-1-111−i−i−i−iiiii-1-111-11-1-1-1-1-1−i−iii11i−ii−i
χ131111-1-11111-1-11-1ii−i−i-1-1-1-1-11iiii−i−i−i−i11-11-1-1ii−i−i1−i−iii−ii-111-1
χ141111-1-11111-1-11-1ii−i−i-1-1-1-1-11iiii−i−i−i−i11-11-1-1−i−iii1−i−iiii−i1-1-11
χ151111-1-11111-1-11-1−i−iii-1-1-1-1-11−i−i−i−iiiii11-11-1-1ii−i−i1ii−i−i−ii1-1-11
χ161111-1-11111-1-11-1−i−iii-1-1-1-1-11−i−i−i−iiiii11-11-1-1−i−iii1ii−i−ii−i-111-1
χ17222222222222-2-2000022222200000000222-2-2-20000-20000000000
χ182222222222-2-2-2-200002222-2200000000-2-2-2-2-22000020000000000
χ192222-2-2222222-220000-2-2-2-22200000000-2-22-22-2000020000000000
χ202222-2-22222-2-2-220000-2-2-2-2-220000000022-2-2220000-20000000000
χ21444444-1-1-1-100444444-1-1-1-10-1-1-1-1-1-1-1-1-1000-1-10000000000000000
χ22444444-1-1-1-10044-4-4-4-4-1-1-1-10-111111111000-1-10000000000000000
χ23444444-1-1-1-100-4-40000-1-1-1-10-155−5−555−5−5000110000000000000000
χ24444444-1-1-1-100-4-40000-1-1-1-10-1−5−555−5−555000110000000000000000
χ254444-4-4-1-1-1-1004-44i4i−4i−4i11110-1−i−i−i−iiiii000-110000000000000000
χ264444-4-4-1-1-1-1004-4−4i−4i4i4i11110-1iiii−i−i−i−i000-110000000000000000
χ274444-4-4-1-1-1-100-44000011110-1i5i5−i5−i5−i5−i5i5i50001-10000000000000000
χ284444-4-4-1-1-1-100-44000011110-1−i5−i5i5i5i5i5−i5−i50001-10000000000000000
χ29444-40044444400000000004-40000000000-4000000000000000000
χ30444-4004444-4-40000000000-4-400000000004000000000000000000
χ3144-40004-4-44440000000000-40000000000000002-22-200000000000
χ3244-40004-4-44440000000000-4000000000000000-22-2200000000000
χ3344-40004-4-44-4-4000000000040000000000000002i−2i−2i2i00000000000
χ3444-40004-4-44-4-400000000004000000000000000−2i2i2i−2i00000000000
χ354-4002i−2i400-44-4001+i−1−i1−i−1+i2i2i−2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i2i−2i0000000001+i−1−i1−i−1+i000000
χ364-4002i−2i400-44-400−1−i1+i−1+i1−i2i2i−2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i2i−2i000000000−1−i1+i−1+i1−i000000
χ374-4002i−2i400-4-44001+i−1−i1−i−1+i2i2i−2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i−2i2i000000000−1−i1+i−1+i1−i000000
χ384-4002i−2i400-4-4400−1−i1+i−1+i1−i2i2i−2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2i2i0000000001+i−1−i1−i−1+i000000
χ394-400−2i2i400-44-4001−i−1+i1+i−1−i−2i−2i2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2i2i0000000001−i−1+i1+i−1−i000000
χ404-400−2i2i400-44-400−1+i1−i−1−i1+i−2i−2i2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2i2i000000000−1+i1−i−1−i1+i000000
χ414-400−2i2i400-4-44001−i−1+i1+i−1−i−2i−2i2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i2i−2i000000000−1+i1−i−1−i1+i000000
χ424-400−2i2i400-4-4400−1+i1−i−1−i1+i−2i−2i2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i2i−2i0000000001−i−1+i1+i−1−i000000
χ43888-800-2-2-2-20000000025−2525−250200000000000000000000000000000
χ44888-800-2-2-2-200000000−2525−25250200000000000000000000000000000
χ458-8004i−4i-225−25200002+2i−2−2i2−2i−2+2i−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ1900−ζ2−ζ3−ζ7−ζ18ζ2+ζ3+ζ7+ζ18−ζ6−ζ11−ζ14−ζ19ζ6+ζ11+ζ14+ζ19−ζ2+ζ3+ζ7−ζ18ζ2−ζ3−ζ7+ζ18−ζ6+ζ11−ζ14+ζ19ζ6−ζ11+ζ14−ζ19000000000000000000000
χ468-8004i−4i-225−2520000−2−2i2+2i−2+2i2−2i−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ1900ζ2+ζ3+ζ7+ζ18−ζ2−ζ3−ζ7−ζ18ζ6+ζ11+ζ14+ζ19−ζ6−ζ11−ζ14−ζ19ζ2−ζ3−ζ7+ζ18−ζ2+ζ3+ζ7−ζ18ζ6−ζ11+ζ14−ζ19−ζ6+ζ11−ζ14+ζ19000000000000000000000
χ478-8004i−4i-2−2525200002+2i−2−2i2−2i−2+2i−2ζ11−2ζ19−2ζ3−2ζ72ζ11+2ζ192ζ3+2ζ700−ζ6−ζ11−ζ14−ζ19ζ6+ζ11+ζ14+ζ19−ζ2−ζ3−ζ7−ζ18ζ2+ζ3+ζ7+ζ18−ζ6+ζ11−ζ14+ζ19ζ6−ζ11+ζ14−ζ19−ζ2+ζ3+ζ7−ζ18ζ2−ζ3−ζ7+ζ18000000000000000000000
χ488-8004i−4i-2−252520000−2−2i2+2i−2+2i2−2i−2ζ11−2ζ19−2ζ3−2ζ72ζ11+2ζ192ζ3+2ζ700ζ6+ζ11+ζ14+ζ19−ζ6−ζ11−ζ14−ζ19ζ2+ζ3+ζ7+ζ18−ζ2−ζ3−ζ7−ζ18ζ6−ζ11+ζ14−ζ19−ζ6+ζ11−ζ14+ζ19ζ2−ζ3−ζ7+ζ18−ζ2+ζ3+ζ7−ζ18000000000000000000000
χ498-800−4i4i-225−25200002−2i−2+2i2+2i−2−2i2ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ1900−ζ2+ζ3+ζ7−ζ18ζ2−ζ3−ζ7+ζ18−ζ6+ζ11−ζ14+ζ19ζ6−ζ11+ζ14−ζ19−ζ2−ζ3−ζ7−ζ18ζ2+ζ3+ζ7+ζ18−ζ6−ζ11−ζ14−ζ19ζ6+ζ11+ζ14+ζ19000000000000000000000
χ508-800−4i4i-225−2520000−2+2i2−2i−2−2i2+2i2ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ1900ζ2−ζ3−ζ7+ζ18−ζ2+ζ3+ζ7−ζ18ζ6−ζ11+ζ14−ζ19−ζ6+ζ11−ζ14+ζ19ζ2+ζ3+ζ7+ζ18−ζ2−ζ3−ζ7−ζ18ζ6+ζ11+ζ14+ζ19−ζ6−ζ11−ζ14−ζ19000000000000000000000
χ518-800−4i4i-2−2525200002−2i−2+2i2+2i−2−2i2ζ11+2ζ192ζ3+2ζ7−2ζ11−2ζ19−2ζ3−2ζ700−ζ6+ζ11−ζ14+ζ19ζ6−ζ11+ζ14−ζ19−ζ2+ζ3+ζ7−ζ18ζ2−ζ3−ζ7+ζ18−ζ6−ζ11−ζ14−ζ19ζ6+ζ11+ζ14+ζ19−ζ2−ζ3−ζ7−ζ18ζ2+ζ3+ζ7+ζ18000000000000000000000
χ528-800−4i4i-2−252520000−2+2i2−2i−2−2i2+2i2ζ11+2ζ192ζ3+2ζ7−2ζ11−2ζ19−2ζ3−2ζ700ζ6−ζ11+ζ14−ζ19−ζ6+ζ11−ζ14+ζ19ζ2−ζ3−ζ7+ζ18−ζ2+ζ3+ζ7−ζ18ζ6+ζ11+ζ14+ζ19−ζ6−ζ11−ζ14−ζ19ζ2+ζ3+ζ7+ζ18−ζ2−ζ3−ζ7−ζ18000000000000000000000
χ531616-16000-444-40000000000000000000000000000000000000000000

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