Finite Group Databasebeta

← Group #13017927

Character table — Group #13017927

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11114444444888888888888888888101016161616161616161620202040404040404040404040808080808080
order12224445101010444444202020202020202020202020442020202020202020202442244444444888888
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
χ5111111111111-11-1-1-111111111-1-1-1-111111-1-1-1-1-1-1111-1-11-11-11111-1-11-11-1
χ6111111111111-11-1-1-111111111-1-1-1-111111-1-1-1-1-1-1111-1-11-11-1-1-1-1-111-11-11
χ7111111111111-11-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-11-11ii−i−i−iii−i−ii
χ8111111111111-11-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-11-11−i−iiii−i−iii−i
χ911111111111-11-11-1-11111-1-1-1-11111111-1-111-1-1-1-1111-1-1-11-111111-1-1-11-11
χ1011111111111-11-11-1-11111-1-1-1-11111111-1-111-1-1-1-1111-1-1-11-11-1-1-1-1111-11-1
χ1111111111111-11-11-1-11111-1-1-1-11111-1-11-1-111-1-1-1-1-1-1-1111-11-1ii−i−i−ii−iii−i
χ1211111111111-11-11-1-11111-1-1-1-11111-1-11-1-111-1-1-1-1-1-1-1111-11-1−i−iiii−ii−i−ii
χ1311111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1
χ1411111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111
χ1511111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-11111ii−i−ii−i−i−iii
χ1611111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-11111−i−iii−iiii−i−i
χ1722222-2-22222020-20022-2-20000222222-200-2-20000-22-200020-20000000000
χ1822222-2-22222020-20022-2-200002222-2-2-200-2-200002-22000-2020000000000
χ1922222-2-222220-2020022-2-20000-2-2-2-222-200220000-22-2000-2020000000000
χ2022222-2-222220-2020022-2-20000-2-2-2-2-2-2-2002200002-2200020-20000000000
χ212222-22-2222220-2000-2-2222222000022-2-2-2000000-2-220020-200000000000
χ222222-22-2222220-2000-2-22222220000-2-2-2-2-200000022-200-20200000000000
χ232222-22-22222-202000-2-222-2-2-2-2000022-222000000-2-2200-20200000000000
χ242222-22-22222-202000-2-222-2-2-2-20000-2-2-22200000022-20020-200000000000
χ252222-2-22222200002-2-2-2-2-200000000222000022-2-22-2-22-200000000000000
χ262222-2-22222200002-2-2-2-2-200000000-2-22000022-2-2-222-2200000000000000
χ272222-2-2222220000-22-2-2-2-2000000002220000-2-2222-2-2-2200000000000000
χ282222-2-2222220000-22-2-2-2-200000000-2-220000-2-222-2222-200000000000000
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
χ304444444-1-1-1-14-44-4-4-4-1-1-1-1-1-1-1-1111100-1-1-11111110000000000000000000
χ314444444-1-1-1-1-44-44-4-4-1-1-1-11111-1-1-1-100-111-1-111110000000000000000000
χ324444444-1-1-1-1-4-4-4-444-1-1-1-11111111100-11111-1-1-1-10000000000000000000
χ3344444-4-4-1-1-1-1040-400-1-11155−5−5-1-1-1-10015−5115−55−50000000000000000000
χ3444444-4-4-1-1-1-1040-400-1-111−5−555-1-1-1-1001−5511−55−550000000000000000000
χ3544444-4-4-1-1-1-10-40400-1-11155−5−511110015−5-1-1−55−550000000000000000000
χ3644444-4-4-1-1-1-10-40400-1-111−5−5551111001−55-1-15−55−50000000000000000000
χ374444-44-4-1-1-1-140-400011-1-1-1-1-1-155−5−5001115−55−5−550000000000000000000
χ384444-44-4-1-1-1-140-400011-1-1-1-1-1-1−5−55500111−55−555−50000000000000000000
χ394444-44-4-1-1-1-1-40400011-1-1111155−5−5001-1-15−5−555−50000000000000000000
χ404444-44-4-1-1-1-1-40400011-1-11111−5−555001-1-1−555−5−550000000000000000000
χ414444-4-44-1-1-1-100004-4111155−5−555−5−500-1−55−55-1-1110000000000000000000
χ424444-4-44-1-1-1-100004-41111−5−555−5−55500-15−55−5-1-1110000000000000000000
χ434444-4-44-1-1-1-10000-44111155−5−5−5−55500-1−555−511-1-10000000000000000000
χ444444-4-44-1-1-1-10000-441111−5−55555−5−500-15−5−5511-1-10000000000000000000
χ454-4-440004-4-440000000000000000004-40000000000000000002i−2i2i−2i000000
χ464-4-440004-4-440000000000000000004-4000000000000000000−2i2i−2i2i000000
χ474-4-440004-4-44000000000000000000-440000000000000000002-2-22000000
χ484-4-440004-4-44000000000000000000-44000000000000000000-222-2000000
χ4988-8-800088-8-8000000000000000000000000000000000000000000000000
χ5088-8-8000-2-22200000025−25000000−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18000000000000000000000000000000
χ5188-8-8000-2-22200000025−250000002ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18000000000000000000000000000000
χ5288-8-8000-2-222000000−2525000000−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ18000000000000000000000000000000
χ5388-8-8000-2-222000000−25250000002ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18000000000000000000000000000000
χ548-88-80008-88-8000000000000000000000000000000000000000000000000
χ558-88-8000-22-220000000025−25−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ180000000000000000000000000000000000
χ568-88-8000-22-220000000025−252ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ180000000000000000000000000000000000
χ578-88-8000-22-2200000000−2525−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ180000000000000000000000000000000000
χ588-88-8000-22-2200000000−25252ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ180000000000000000000000000000000000
χ5916-16-1616000-444-4000000000000000000000000000000000000000000000000

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