Finite Group Databasebeta

← Group #13026905

Character table — Group #13026905

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1124444444558888881016161616161616161620202020202020202020202020323232404040404040408080808080
order12222444510442441010104410101020202020202224488888888202020244888844488
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-1
χ3111111111111-1-111111-11-1-1111-1-111111111111111-1-1-1-111111-1-1-1-1-1
χ4111111111111-1-111111-11-1-1111-1-111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-11111
χ51111111111-1-1111111-1111111111-1-1-1-1-1ii−i−iii−i−i111-1-1-1i−ii−i-1i−ii−i
χ61111111111-1-1111111-1111111111-1-1-1-1-1−i−iii−i−iii111-1-1-1−ii−ii-1−ii−ii
χ71111111111-1-1-1-11111-1-11-1-1111-1-1-1-1-1-1-1ii−i−iii−i−i1-1-111-1i−ii−i1−ii−ii
χ81111111111-1-1-1-11111-1-11-1-1111-1-1-1-1-1-1-1−i−iii−i−iii1-1-111-1−ii−ii1i−ii−i
χ9111111-1-1111111-11111-11111-1-111-1-11111111-1-1-1-1-1-1-111-1-1-111-1-1-111
χ10111111-1-1111111-11111-11111-1-111-1-1111-1-1-1-11111-1-1-111-111-1-1-111-1-1
χ11111111-1-11111-1-1-1111111-1-11-1-1-1-1-1-11111111-1-1-1-1-111-1-1-1-1-111111-1-1
χ12111111-1-11111-1-1-1111111-1-11-1-1-1-1-1-1111-1-1-1-11111-111-1-1-111-1-11-1-111
χ13111111-1-111-1-111-1111-1-11111-1-11111-1-1-1ii−i−i−i−iii-1-1-1-1-11−iii−i1−iii−i
χ14111111-1-111-1-111-1111-1-11111-1-11111-1-1-1−i−iiiii−i−i-1-1-1-1-11i−i−ii1i−i−ii
χ15111111-1-111-1-1-1-1-1111-111-1-11-1-1-1-111-1-1-1ii−i−i−i−iii-111111−iii−i-1i−i−ii
χ16111111-1-111-1-1-1-1-1111-111-1-11-1-1-1-111-1-1-1−i−iiiii−i−i-111111i−i−ii-1−iii−i
χ172222-2-20022220002-2-220200-2000000-2-222222000000000000-2-200000
χ182222-2-20022220002-2-220200-2000000-2-22-2-2-2-20000000000002200000
χ192222-2-20022-2-20002-2-2-20200-200000022-22i2i−2i−2i000000000000−2i2i00000
χ202222-2-20022-2-20002-2-2-20200-200000022-2−2i−2i2i2i0000000000002i−2i00000
χ21222-22-222222200-222220-200-2220022-22-200000000-20000-2000000000
χ22222-22-22222-2-200-2222-20-200-22200-2-22-2200000000-200002000000000
χ23222-22-2-2-2222200222220-200-2-2-200-2-2-22-200000000200002000000000
χ24222-22-2-2-222-2-2002222-20-200-2-2-200222-220000000020000-2000000000
χ25222-2-220022220002-2-220-20020000002-2-200002222000000-2-20000000
χ26222-2-220022220002-2-220-20020000002-2-20000-2-2-2-2000000220000000
χ27222-2-220022-2-20002-2-2-20-2002000000-22200002i2i−2i−2i000000−2i2i0000000
χ28222-2-220022-2-20002-2-2-20-2002000000-2220000−2i−2i2i2i0000002i−2i0000000
χ2944444444-1-100444-1-1-104-1-1-1-1-1-1-1-10000000000000-1-1-1000000000000
χ3044444444-1-100-4-44-1-1-10-4-111-1-1-1110000000000000-111000000000000
χ31444444-4-4-1-10044-4-1-1-10-4-1-1-1-111-1-10000000000000111000000000000
χ32444444-4-4-1-100-4-4-4-1-1-104-111-1111100000000000001-1-1000000000000
χ33444-44-444-1-10000-4-1-1-10015−51-1-15−5000000000000015−5000000000000
χ34444-44-444-1-10000-4-1-1-1001−551-1-1−5500000000000001−55000000000000
χ35444-44-4-4-4-1-100004-1-1-10015−51115−50000000000000-1−55000000000000
χ36444-44-4-4-4-1-100004-1-1-1001−55111−550000000000000-15−5000000000000
χ3744-40000044442-20-400-40022000-2-20000000000000000-220000000000
χ3844-4000004444-220-400-400-2-20002200000000000000002-20000000000
χ3944-40000044-4-42-20-40040022000-2-200000000000000002-20000000000
χ4044-40000044-4-4-220-400400-2-2000220000000000000000-220000000000
χ414-400002i−2i4-44i−4i0000000000002i−2i002-2000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000
χ424-400002i−2i4-44i−4i0000000000002i−2i002-20002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000
χ434-400002i−2i4-4−4i4i0000000000002i−2i00-22000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000
χ444-400002i−2i4-4−4i4i0000000000002i−2i00-220002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000
χ454-40000−2i2i4-44i−4i000000000000−2i2i00-22000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000
χ464-40000−2i2i4-44i−4i000000000000−2i2i00-220002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000
χ474-40000−2i2i4-4−4i4i000000000000−2i2i002-2000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000
χ484-40000−2i2i4-4−4i4i000000000000−2i2i002-20002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000
χ498888-8-800-2-200000-22200-200200000000000000000000000000000000
χ50888-8-8800-2-200000-22200200-200000000000000000000000000000000
χ5188-800000-2-2004-40225−25000−1+5−1−50001−51+50000000000000000000000000000
χ5288-800000-2-2004-402−2525000−1−5−1+50001+51−50000000000000000000000000000
χ5388-800000-2-200-440225−250001−51+5000−1+5−1−50000000000000000000000000000
χ5488-800000-2-200-4402−25250001+51−5000−1−5−1+50000000000000000000000000000
χ5516-1600008i−8i-4400000000000000−2i2i000000000000000000000000000000
χ5616-160000−8i8i-44000000000000002i−2i000000000000000000000000000000

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