Finite Group Databasebeta

← Group #13014018

Character table — Group #13014018

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1122244444444444488888888888881616161616161616161620202020404080808080808080808080
order12222222251010101010101021010101010101010101010104420202020202020204444224488888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i
χ911111-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1i−iiiii−i−i−i−i11-1-11-1i−i1-1i−i1-1i−i
χ1011111-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1i−iiiii−i−i−i−i11-1-11-1i−i-11−ii-11−ii
χ1111111-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1i−iiiii−i−i−i−i-1-111-11−iii−i-11−ii1-1
χ1211111-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1i−iiiii−i−i−i−i-1-111-11−ii−ii1-1i−i-11
χ1311111-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1−ii−i−i−i−iiiii11-1-11-1−ii1-1−ii1-1−ii
χ1411111-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1−ii−i−i−i−iiiii11-1-11-1−ii-11i−i-11i−i
χ1511111-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1−ii−i−i−i−iiiii-1-111-11i−ii−i1-1−ii-11
χ1611111-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1−ii−i−i−i−iiiii-1-111-11i−i−ii-11i−i1-1
χ172222222-2-22222-2-2-2-2-222-2-2-2-22222-2-200000000002222-2-20000000000
χ182222222-2-22222-2-2-2-2-222-2-2-2-22222-2-20000000000-2-2-2-2220000000000
χ1922222-2-22222222222-222-2-2-2-2-2-2-2-222000000000022-2-2-220000000000
χ2022222-2-22222222222-222-2-2-2-2-2-2-2-2220000000000-2-2222-20000000000
χ21444444444-1-1-1-1-1-1-1-14-1-1-1-1-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-10000000000000000
χ22444444444-1-1-1-1-1-1-1-14-1-1-1-1-1-1-1-1-1-1-1-1-4-4111111110000000000000000
χ234444444-4-4-1-1-1-11111-4-1-11111-1-1-1-11100i5i5−i5−i5i5i5−i5−i50000000000000000
χ244444444-4-4-1-1-1-11111-4-1-11111-1-1-1-11100−i5−i5i5i5−i5−i5i5i50000000000000000
χ2544444-4-444-1-1-1-1-1-1-1-1-4-1-111111111-1-10055−5−5−5−5550000000000000000
χ2644444-4-444-1-1-1-1-1-1-1-1-4-1-111111111-1-100−5−55555−5−50000000000000000
χ2744444-4-4-4-4-1-1-1-111114-1-1-1-1-1-11111114i−4i−i−i−i−iiiii0000000000000000
χ2844444-4-4-4-4-1-1-1-111114-1-1-1-1-1-1111111−4i4iiiii−i−i−i−i0000000000000000
χ29444-4-4000044-4-4000004-400000000000000000000004-4000000000000
χ30444-4-4000044-4-4000004-40000000000000000000000-44000000000000
χ3144-44-4000044-4-400000-44000000000000000000004-400000000000000
χ3244-44-4000044-4-400000-4400000000000000000000-4400000000000000
χ3344-4-44004-4444444440-4-400000000-4-400000000000000000000000000
χ3444-4-44004-4-1-1-1-1-1-1-1-101155−5−555−5−51100−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−ζ180000000000000000
χ3544-4-44004-4-1-1-1-1-1-1-1-101155−5−555−5−51100ζ2−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+ζ180000000000000000
χ3644-4-44004-4-1-1-1-1-1-1-1-1011−5−555−5−5551100−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−ζ180000000000000000
χ3744-4-44004-4-1-1-1-1-1-1-1-1011−5−555−5−5551100ζ2+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+ζ180000000000000000
χ3844-4-4400-444444-4-4-4-40-4-4000000004400000000000000000000000000
χ3944-4-4400-44-1-1-1-1111101155−5−5−5−555-1-100−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ190000000000000000
χ4044-4-4400-44-1-1-1-1111101155−5−5−5−555-1-100ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ190000000000000000
χ4144-4-4400-44-1-1-1-11111011−5−55555−5−5-1-100ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ190000000000000000
χ4244-4-4400-44-1-1-1-11111011−5−55555−5−5-1-100−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ190000000000000000
χ43888-8-80000-2-2222525−25−250-220000000025−2500000000000000000000000000
χ44888-8-80000-2-222−25−2525250-2200000000−252500000000000000000000000000
χ4588-88-80000-2-2222525−25−2502-200000000−252500000000000000000000000000
χ4688-88-80000-2-222−25−25252502-20000000025−2500000000000000000000000000
χ478-80004-4008-800000000000004-44-40000000000000000000000000000
χ488-80004-400-2225−25−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18000−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ14−1−51+5−1+51−50000000000000000000000000000
χ498-80004-400-2225−252ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ180002ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ14−1−51+5−1+51−50000000000000000000000000000
χ508-80004-400-22−2525−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ18000−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ18−1+51−5−1−51+50000000000000000000000000000
χ518-80004-400-22−25252ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ180002ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ18−1+51−5−1−51+50000000000000000000000000000
χ528-8000-44008-80000000000000-44-440000000000000000000000000000
χ538-8000-4400-2225−25−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ180002ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ141+5−1−51−5−1+50000000000000000000000000000
χ548-8000-4400-2225−252ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18000−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ141+5−1−51−5−1+50000000000000000000000000000
χ558-8000-4400-22−2525−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ180002ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ181−5−1+51+5−1−50000000000000000000000000000
χ568-8000-4400-22−25252ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18000−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ181−5−1+51+5−1−50000000000000000000000000000

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