Finite Group Databasebeta

← Group #13017959

Character table — Group #13017959

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11114444444888888888888888888101016161616161616161620202040404040404040404040808080808080
order12224445101010224444202020202020202020202020441010101020202020202442444448888448888
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−ii−ii−i
χ411111111111111111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1−i−iii−ii−ii−ii
χ51111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ61111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-111
χ71111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-111-1-111ii−i−i−iii−i−ii
χ81111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-111-1-111−i−iiii−i−iii−i
χ911111111111-1-111-1-111111111-1-1-1-111-1-1-1-111-1-111111-1-1-11-1111111-1-1-1-1
χ1011111111111-1-111-1-111111111-1-1-1-111-1-1-1-111-1-111111-1-1-11-1-1-1-1-1-1-11111
χ1111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1111-11ii−i−ii−i−ii−ii
χ1211111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1111-11−i−iii−iii−ii−i
χ1311111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1111111-11-1-1-111111-1-1-1-111
χ1411111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1111111-11-1-1-11-1-1-1-11111-1-1
χ1511111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-11-1111-1ii−i−i−ii−iii−i
χ1611111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-11-1111-1−i−iiii−ii−i−ii
χ1722222-2-22222002-20022-2-2-2-2-2-200002200002200-2-2-222000-200000000000
χ1822222-2-22222002-20022-2-2-2-2-2-20000-2-200002200-222-2-2000200000000000
χ1922222-2-2222200-220022-2-222220000220000-2-200-2-2-22-2000200000000000
χ2022222-2-2222200-220022-2-222220000-2-20000-2-200-222-22000-200000000000
χ212222-22-222222-20000-2-2-2-2000000002222-2-200002-22-2002-2000000000000
χ222222-22-222222-20000-2-2-2-200000000-2-222-2-2000022-2200-22000000000000
χ232222-22-22222-220000-2-2-2-20000000022-2-22200002-22-200-22000000000000
χ242222-22-22222-220000-2-2-2-200000000-2-2-2-222000022-22002-2000000000000
χ252222-2-22222200002-2-2-2220000222222000000-2-2-22-2-20-200020000000000
χ262222-2-22222200002-2-2-22200002222-2-2000000-2-2-2-22202000-20000000000
χ272222-2-2222220000-22-2-2220000-2-2-2-22200000022-22-2-202000-20000000000
χ282222-2-2222220000-22-2-2220000-2-2-2-2-2-200000022-2-2220-200020000000000
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
χ304444444-1-1-1-144-4-4-4-4-1-1-1-11111111100-1-1-1-11111-10000000000000000000
χ314444444-1-1-1-1-4-444-4-4-1-1-1-1-1-1-1-11111001111-1-111-10000000000000000000
χ324444444-1-1-1-1-4-4-4-444-1-1-1-11111-1-1-1-100111111-1-1-10000000000000000000
χ3344444-4-4-1-1-1-1004-400-1-111111155−5−5005−55−5-1-15−510000000000000000000
χ3444444-4-4-1-1-1-1004-400-1-1111111−5−55500−55−55-1-1−5510000000000000000000
χ3544444-4-4-1-1-1-100-4400-1-111-1-1-1-155−5−500−55−55115−510000000000000000000
χ3644444-4-4-1-1-1-100-4400-1-111-1-1-1-1−5−555005−55−511−5510000000000000000000
χ374444-44-4-1-1-1-14-40000111155−5−555−5−500-1-1115−5−55-10000000000000000000
χ384444-44-4-1-1-1-14-400001111−5−555−5−55500-1-111−555−5-10000000000000000000
χ394444-44-4-1-1-1-1-440000111155−5−5−5−5550011-1-15−55−5-10000000000000000000
χ404444-44-4-1-1-1-1-4400001111−5−55555−5−50011-1-1−55−55-10000000000000000000
χ414444-4-44-1-1-1-100004-411-1-155−5−5-1-1-1-100−555−5−551110000000000000000000
χ424444-4-44-1-1-1-100004-411-1-1−5−555-1-1-1-1005−5−555−51110000000000000000000
χ434444-4-44-1-1-1-10000-4411-1-155−5−51111005−5−55−55-1-110000000000000000000
χ444444-4-44-1-1-1-10000-4411-1-1−5−555111100−555−55−5-1-110000000000000000000
χ454-44-40004-4-440000000000000000004i−4i000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000
χ464-44-40004-4-440000000000000000004i−4i0000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000
χ474-44-40004-4-44000000000000000000−4i4i000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000
χ484-44-40004-4-44000000000000000000−4i4i0000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000
χ4988-8-800088-8-8000000000000000000000000000000000000000000000000
χ5088-8-8000-2-22200000025−2500−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ380000000000000000000000000000000000
χ5188-8-8000-2-22200000025−25002ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ380000000000000000000000000000000000
χ5288-8-8000-2-222000000−2525002ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ380000000000000000000000000000000000
χ5388-8-8000-2-222000000−252500−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ380000000000000000000000000000000000
χ548-8-880008-88-8000000000000000000000000000000000000000000000000
χ558-8-88000-22-220000000025−250000−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ38000000000000000000000000000000
χ568-8-88000-22-220000000025−2500002ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38000000000000000000000000000000
χ578-8-88000-22-2200000000−252500002ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38000000000000000000000000000000
χ588-8-88000-22-2200000000−25250000−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ38000000000000000000000000000000
χ5916-1616-16000-444-4000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.