Finite Group Databasebeta

← Group #13017925

Character table — Group #13017925

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11114444444888888888888888888101016161616161616161620202040404040404040404040808080808080
order12224445101010224444202020202020202020202020441010101020202020202442222444444888888
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
χ5111111111111-1-1-11-111111111-1-1-1-11111-1-11-1-1-1-11111-1-1-11-11111-1-11-11-1
χ6111111111111-1-1-11-111111111-1-1-1-11111-1-11-1-1-1-11111-1-1-11-1-1-1-1-111-11-11
χ7111111111111-1-1-11-111111111-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-1111-11ii−i−i−iii−i−ii
χ8111111111111-1-1-11-111111111-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-1111-11−i−iiii−i−iii−i
χ911111111111-11-1-1-111111-1-1-1-1111111-1-1111-1-1-1-1111-11-1-1-111111-1-1-11-11
χ1011111111111-11-1-1-111111-1-1-1-1111111-1-1111-1-1-1-1111-11-1-1-11-1-1-1-1111-11-1
χ1111111111111-11-1-1-111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1-11-1111-1ii−i−i−ii−iii−i
χ1211111111111-11-1-1-111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1-11-1111-1−i−iiii−ii−i−ii
χ1311111111111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ1411111111111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111
χ1511111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-111ii−i−ii−i−i−iii
χ1611111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-111−i−iii−iiii−i−i
χ1722222-2-22222002-200-2-2-2-200000000220000222-2-22-2-2002-2000000000000
χ1822222-2-22222002-200-2-2-2-200000000-2-20000222-2-2-22200-22000000000000
χ1922222-2-2222200-2200-2-2-2-2000000002200002-2-2222-2-200-22000000000000
χ2022222-2-2222200-2200-2-2-2-200000000-2-200002-2-222-222002-2000000000000
χ212222-22-2222202000-222-2-20000-2-2-2-2220022-20000-22-202000-20000000000
χ222222-22-2222202000-222-2-20000-2-2-2-2-2-20022-200002-220-200020000000000
χ232222-22-222220-2000222-2-2000022222200-2-2-20000-22-20-200020000000000
χ242222-22-222220-2000222-2-200002222-2-200-2-2-200002-2202000-20000000000
χ252222-2-2222222000-20-2-222-2-2-2-20000222200-20000-2-222000-200000000000
χ262222-2-2222222000-20-2-222-2-2-2-20000-2-22200-2000022-2-2000200000000000
χ272222-2-222222-200020-2-2222222000022-2-200-20000-2-22-2000200000000000
χ282222-2-222222-200020-2-22222220000-2-2-2-200-2000022-22000-200000000000
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
χ304444444-1-1-1-14-4-4-44-4-1-1-1-1-1-1-1-1111100-1-111-111110000000000000000000
χ314444444-1-1-1-1-44-4-4-44-1-1-1-11111-1-1-1-10011-1-1-111110000000000000000000
χ324444444-1-1-1-1-4-444-4-4-1-1-1-111111111001111-1-1-1-1-10000000000000000000
χ3344444-4-4-1-1-1-1004-400111155−5−555−5−5005−55−5-1-1-1110000000000000000000
χ3444444-4-4-1-1-1-1004-4001111−5−555−5−55500−55−55-1-1-1110000000000000000000
χ3544444-4-4-1-1-1-100-4400111155−5−5−5−555005−5−55-111-1-10000000000000000000
χ3644444-4-4-1-1-1-100-44001111−5−55555−5−500−555−5-111-1-10000000000000000000
χ374444-44-4-1-1-1-104000-4-1-11155−5−5111100−55-1-115−55−50000000000000000000
χ384444-44-4-1-1-1-104000-4-1-111−5−5551111005−5-1-11−55−550000000000000000000
χ394444-44-4-1-1-1-10-40004-1-11155−5−5-1-1-1-100−55111−55−550000000000000000000
χ404444-44-4-1-1-1-10-40004-1-111−5−555-1-1-1-1005−51115−55−50000000000000000000
χ414444-4-44-1-1-1-14000-4011-1-1111155−5−500-1-1−5515−5−550000000000000000000
χ424444-4-44-1-1-1-14000-4011-1-11111−5−55500-1-15−51−555−50000000000000000000
χ434444-4-44-1-1-1-1-40004011-1-1-1-1-1-155−5−50011−551−555−50000000000000000000
χ444444-4-44-1-1-1-1-40004011-1-1-1-1-1-1−5−55500115−515−5−550000000000000000000
χ4544-4-40004-4-440000000000000000004-40000000000000000002i−2i2i−2i000000
χ4644-4-40004-4-440000000000000000004-4000000000000000000−2i2i−2i2i000000
χ4744-4-40004-4-44000000000000000000-440000000000000000002-2-22000000
χ4844-4-40004-4-44000000000000000000-44000000000000000000-222-2000000
χ498-88-800088-8-8000000000000000000000000000000000000000000000000
χ508-88-8000-2-22200000025−25000000−2ζ3+2ζ7−2ζ11+2ζ192ζ3−2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ19000000000000000000000000000000
χ518-88-8000-2-22200000025−250000002ζ3−2ζ7+2ζ11−2ζ19−2ζ3+2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ19000000000000000000000000000000
χ528-88-8000-2-222000000−25250000002ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7+2ζ11−2ζ19−2ζ3+2ζ7−2ζ11+2ζ19000000000000000000000000000000
χ538-88-8000-2-222000000−2525000000−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7−2ζ11+2ζ192ζ3−2ζ7+2ζ11−2ζ19000000000000000000000000000000
χ548-8-880008-88-8000000000000000000000000000000000000000000000000
χ558-8-88000-22-220000000025−25−2ζ3+2ζ7−2ζ11+2ζ192ζ3−2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ190000000000000000000000000000000000
χ568-8-88000-22-220000000025−252ζ3−2ζ7+2ζ11−2ζ19−2ζ3+2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ190000000000000000000000000000000000
χ578-8-88000-22-2200000000−25252ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7+2ζ11−2ζ19−2ζ3+2ζ7−2ζ11+2ζ190000000000000000000000000000000000
χ588-8-88000-22-2200000000−2525−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7−2ζ11+2ζ192ζ3−2ζ7+2ζ11−2ζ190000000000000000000000000000000000
χ591616-16-16000-444-4000000000000000000000000000000000000000000000000

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