Finite Group Databasebeta

← Group #13017924

Character table — Group #13017924

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11114444444888888888888888888101016161616161616161620202040404040404040404040808080808080
order12224445101010222244101010101010101020202020441010101020202020202442244444444888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1ii−i−ii−iii−i−i
χ411111111111111111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1−i−iii−ii−i−iii
χ51111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1
χ61111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-11111
χ71111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-1-1-1-1-1-11111-1-1ii−i−ii−i−i−iii
χ81111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-1-1-1-1-1-11111-1-1−i−iii−iiii−i−i
χ911111111111-1-11-11-11111-1-1-1-1111111-1-1-1-1111-1-11111-11-1-1-11111-1-11-11-1
χ1011111111111-1-11-11-11111-1-1-1-1111111-1-1-1-1111-1-11111-11-1-1-1-1-1-1-111-11-11
χ1111111111111-1-11-11-11111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-11-1111ii−i−i−iii−i−ii
χ1211111111111-1-11-11-11111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-11-1111−i−iiii−i−iii−i
χ1311111111111-1-1-11-11-1-1-1-11111111111-1-1-1-11-1-111111-11-11-1-11111-1-1-11-11
χ1411111111111-1-1-11-11-1-1-1-11111111111-1-1-1-11-1-111111-11-11-1-1-1-1-1-1111-11-1
χ1511111111111-1-1-11-11-1-1-1-111111111-1-1-1-1-1-11-1-111-1-1-11-11-111ii−i−i−ii−iii−i
χ1611111111111-1-1-11-11-1-1-1-111111111-1-1-1-1-1-11-1-111-1-1-11-11-111−i−iiii−ii−i−ii
χ1722222-2-2222200020-20000222222-2-2220000-200-2-2-22-2020-2000000000000
χ1822222-2-2222200020-20000222222-2-2-2-20000-200-2-22-220-202000000000000
χ1922222-2-22222000-2020000-2-2-2-222-2-2220000-20022-22-20-202000000000000
χ2022222-2-22222000-2020000-2-2-2-222-2-2-2-20000-200222-22020-2000000000000
χ212222-22-222220020-2022220000-2-222220000-2-2-200-2-2220-20000000000000
χ222222-22-222220020-2022220000-2-222-2-20000-2-2-20022-2-2020000000000000
χ232222-22-2222200-2020-2-2-2-20000-2-222220000-22200-2-22-2020000000000000
χ242222-22-2222200-2020-2-2-2-20000-2-222-2-20000-2220022-220-20000000000000
χ252222-2-2222222-2000000000000-2-2-2-22222-2-2200002-2-200002-20000000000
χ262222-2-2222222-2000000000000-2-2-2-2-2-222-2-220000-2220000-220000000000
χ272222-2-222222-22000000000000-2-2-2-222-2-222200002-2-20000-220000000000
χ282222-2-222222-22000000000000-2-2-2-2-2-2-2-22220000-22200002-20000000000
χ294444444-1-1-1-1444444-1-1-1-1-1-1-1-1-1-1-1-100-1-1-1-1-1-1-1-1-10000000000000000000
χ304444444-1-1-1-144-4-4-4-411111111-1-1-1-100-1-1-1-1-111110000000000000000000
χ314444444-1-1-1-1-4-44-44-4-1-1-1-11111-1-1-1-1001111-1-1-1110000000000000000000
χ324444444-1-1-1-1-4-4-44-441111-1-1-1-1-1-1-1-1001111-111-1-10000000000000000000
χ3344444-4-4-1-1-1-100040-455−5−5-1-1-1-1-1-111005−55−515−5110000000000000000000
χ3444444-4-4-1-1-1-100040-4−5−555-1-1-1-1-1-11100−55−551−55110000000000000000000
χ3544444-4-4-1-1-1-1000-40455−5−51111-1-11100−55−5515−5-1-10000000000000000000
χ3644444-4-4-1-1-1-1000-404−5−5551111-1-111005−55−51−55-1-10000000000000000000
χ374444-44-4-1-1-1-10040-40-1-1-1-155−5−511-1-1005−5−551115−50000000000000000000
χ384444-44-4-1-1-1-10040-40-1-1-1-1−5−55511-1-100−555−5111−550000000000000000000
χ394444-44-4-1-1-1-100-4040111155−5−511-1-100−555−51-1-15−50000000000000000000
χ404444-44-4-1-1-1-100-40401111−5−55511-1-1005−5−551-1-1−550000000000000000000
χ414444-4-44-1-1-1-14-4000055−5−555−5−5111100-1-111-1−55−550000000000000000000
χ424444-4-44-1-1-1-14-40000−5−555−5−555111100-1-111-15−55−50000000000000000000
χ434444-4-44-1-1-1-1-44000055−5−5−5−55511110011-1-1-1−555−50000000000000000000
χ444444-4-44-1-1-1-1-440000−5−55555−5−511110011-1-1-15−5−550000000000000000000
χ454-4-4400044-4-40000000000000000004-40000000000000000002i−2i2i−2i000000
χ464-4-4400044-4-40000000000000000004-4000000000000000000−2i2i−2i2i000000
χ474-4-4400044-4-4000000000000000000-440000000000000000002-2-22000000
χ484-4-4400044-4-4000000000000000000-44000000000000000000-222-2000000
χ4988-8-80008-88-8000000000000000000000000000000000000000000000000
χ5088-8-8000-22-220000000000−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ1825−2500000000000000000000000000000000
χ5188-8-8000-22-220000000000−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ18−252500000000000000000000000000000000
χ5288-8-8000-22-2200000000002ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ1825−2500000000000000000000000000000000
χ5388-8-8000-22-2200000000002ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−252500000000000000000000000000000000
χ548-88-80008-8-88000000000000000000000000000000000000000000000000
χ558-88-8000-222-2000000−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ1800000025−25000000000000000000000000000000
χ568-88-8000-222-2000000−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ18000000−2525000000000000000000000000000000
χ578-88-8000-222-20000002ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ1800000025−25000000000000000000000000000000
χ588-88-8000-222-20000002ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18000000−2525000000000000000000000000000000
χ5916-16-1616000-4-444000000000000000000000000000000000000000000000000

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