Finite Group Databasebeta

← Group #13017958

Character table — Group #13017958

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11114444444888888888888888888101016161616161616161620202040404040404040404040808080808080
order12224445101010444444202020202020202020202020442020202020202020202442224448888448888
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
χ51111111111111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-11111-1-1-11-1111111-1-1-1-1
χ61111111111111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-11111-1-1-11-1-1-1-1-1-1-11111
χ71111111111111-1-1-1-1111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-1-1111-11ii−i−ii−i−ii−ii
χ81111111111111-1-1-1-1111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-1-1111-11−i−iii−iii−ii−i
χ911111111111-1-111-1-111-1-1-1-1111111111-1-111-1-1-1-1111-1-1-11-111111-1-1-1-111
χ1011111111111-1-111-1-111-1-1-1-1111111111-1-111-1-1-1-1111-1-1-11-11-1-1-1-11111-1-1
χ1111111111111-1-111-1-111-1-1-1-1111111-1-11-1-111-1-1-1-1-1-1-1111-11-1ii−i−i−ii−iii−i
χ1211111111111-1-111-1-111-1-1-1-1111111-1-11-1-111-1-1-1-1-1-1-1111-11-1−i−iiii−ii−i−ii
χ1311111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-11111111-111-1-1-11111-1-111-1-1
χ1411111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-11111111-111-1-1-1-1-1-1-111-1-111
χ1511111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-1-1-1-11111-1-1-11-1-1111ii−i−i−iii−i−ii
χ1611111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-1-1-1-11111-1-1-11-1-1111−i−iiii−i−iii−i
χ1722222-2-222222-200002222220000-2-222-2-2-2000000-2-222000-200000000000
χ1822222-2-222222-200002222220000-2-2-2-2-2-2-200000022-2-2000200000000000
χ1922222-2-22222-22000022-2-2-2-20000-2-222-222000000-2-22-2000200000000000
χ2022222-2-22222-22000022-2-2-2-20000-2-2-2-2-22200000022-22000-200000000000
χ212222-22-2222200002-2-2-200000000-2-2222000022-2-2-22-202-20000000000000
χ222222-22-2222200002-2-2-200000000-2-2-2-22000022-2-22-220-220000000000000
χ232222-22-222220000-22-2-200000000-2-22220000-2-222-22-20-220000000000000
χ242222-22-222220000-22-2-200000000-2-2-2-220000-2-2222-2202-20000000000000
χ252222-2-222222002-200-2-2000022222222-200-2-200002-2-2000-2020000000000
χ262222-2-222222002-200-2-20000222222-2-2-200-2-20000-22200020-20000000000
χ272222-2-22222200-2200-2-20000-2-2-2-22222-2002200002-2-200020-20000000000
χ282222-2-22222200-2200-2-20000-2-2-2-222-2-2-200220000-222000-2020000000000
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
χ304444444-1-1-1-144-4-4-4-4-1-1-1-1-1-11111-1-100-1-1-11111110000000000000000000
χ314444444-1-1-1-1-4-444-4-4-1-11111-1-1-1-1-1-100-111-1-111110000000000000000000
χ324444444-1-1-1-1-4-4-4-444-1-111111111-1-100-11111-1-1-1-10000000000000000000
χ3344444-4-4-1-1-1-14-40000-1-1-1-1-1-155−5−511001115−55−55−50000000000000000000
χ3444444-4-4-1-1-1-14-40000-1-1-1-1-1-1−5−5551100111−55−55−550000000000000000000
χ3544444-4-4-1-1-1-1-440000-1-1111155−5−511001-1-15−5−55−550000000000000000000
χ3644444-4-4-1-1-1-1-440000-1-11111−5−55511001-1-1−555−55−50000000000000000000
χ374444-44-4-1-1-1-100004-41155−5−555−5−51100-15−5−55-1-1110000000000000000000
χ384444-44-4-1-1-1-100004-411−5−555−5−5551100-1−555−5-1-1110000000000000000000
χ394444-44-4-1-1-1-10000-441155−5−5−5−5551100-15−55−511-1-10000000000000000000
χ404444-44-4-1-1-1-10000-4411−5−55555−5−51100-1−55−5511-1-10000000000000000000
χ414444-4-44-1-1-1-1004-4001155−5−5-1-1-1-1-1-1001−55115−5−550000000000000000000
χ424444-4-44-1-1-1-1004-40011−5−555-1-1-1-1-1-10015−511−555−50000000000000000000
χ434444-4-44-1-1-1-100-44001155−5−51111-1-1001−55-1-1−555−50000000000000000000
χ444444-4-44-1-1-1-100-440011−5−5551111-1-10015−5-1-15−5−550000000000000000000
χ454-44-40004-44-40000000000000000004i−4i000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000
χ464-44-40004-44-40000000000000000004i−4i0000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000
χ474-44-40004-44-4000000000000000000−4i4i000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000
χ484-44-40004-44-4000000000000000000−4i4i0000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000
χ4988-8-800088-8-8000000000000000000000000000000000000000000000000
χ5088-8-8000-2-22200000025−25−2ζ4+2ζ12−2ζ28+2ζ362ζ4−2ζ12+2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ36000000000000000000000000000000000000
χ5188-8-8000-2-22200000025−252ζ4−2ζ12+2ζ28−2ζ36−2ζ4+2ζ12−2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ36000000000000000000000000000000000000
χ5288-8-8000-2-222000000−2525−2ζ4−2ζ12+2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ362ζ4−2ζ12+2ζ28−2ζ36−2ζ4+2ζ12−2ζ28+2ζ36000000000000000000000000000000000000
χ5388-8-8000-2-222000000−25252ζ4+2ζ12−2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ36−2ζ4+2ζ12−2ζ28+2ζ362ζ4−2ζ12+2ζ28−2ζ36000000000000000000000000000000000000
χ548-8-880008-8-88000000000000000000000000000000000000000000000000
χ558-8-88000-222-2000000000000−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ3825−25000000000000000000000000000000
χ568-8-88000-222-20000000000002ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38−2525000000000000000000000000000000
χ578-8-88000-222-20000000000002ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ3825−25000000000000000000000000000000
χ588-8-88000-222-2000000000000−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ38−2525000000000000000000000000000000
χ5916-1616-16000-44-44000000000000000000000000000000000000000000000000

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