Finite Group Databasebeta

← Group #13013944

Character table — Group #13013944

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112244444444555588888888888101016161616161616161616161620202020404040404040404040404040404040404040404040
order12222244445101010444448888101020202020442020202040404040404040402244288888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i
χ611111111111111-1-1-1-111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii
χ711111111111111-1-1-1-11-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiii
χ811111111111111-1-1-1-11-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iiiiiii−i−i−i−i
χ9111111-1-1-1-1111111111ii−i−i11-1-1-1-111-1-111iiii−i−i−i−i-1-1-1-11ii−i−i1111-1-1-1-1ii−i−iii−i−i
χ10111111-1-1-1-1111111111ii−i−i11-1-1-1-111-1-111iiii−i−i−i−i-1-1-1-11ii−i−i-1-1-1-11111−i−iii−i−iii
χ11111111-1-1-1-1111111111−i−iii11-1-1-1-111-1-111−i−i−i−iiiii-1-1-1-11−i−iii1111-1-1-1-1−i−iii−i−iii
χ12111111-1-1-1-1111111111−i−iii11-1-1-1-111-1-111−i−i−i−iiiii-1-1-1-11−i−iii-1-1-1-11111ii−i−iii−i−i
χ13111111-1-1-1-11111-1-1-1-11ii−i−i11-1-1-1-1-1-1-1-111iiii−i−i−i−i1111-1−i−iiiii−i−i−i−iii-1-11111-1-1
χ14111111-1-1-1-11111-1-1-1-11ii−i−i11-1-1-1-1-1-1-1-111iiii−i−i−i−i1111-1−i−iii−i−iiiii−i−i11-1-1-1-111
χ15111111-1-1-1-11111-1-1-1-11−i−iii11-1-1-1-1-1-1-1-111−i−i−i−iiiii1111-1ii−i−iii−i−i−i−iii11-1-1-1-111
χ16111111-1-1-1-11111-1-1-1-11−i−iii11-1-1-1-1-1-1-1-111−i−i−i−iiiii1111-1ii−i−i−i−iiiii−i−i-1-11111-1-1
χ1722222222-2-222222222-2000022-2-2-2-22222-2-200000000-2-222-200000000000000000000
χ1822222222-2-22222-2-2-2-2-2000022-2-2-2-2-2-222-2-20000000022-2-2200000000000000000000
χ19222222-2-22222222222-2000022222222-2-2-2-20000000022-2-2-200000000000000000000
χ20222222-2-2222222-2-2-2-2-20000222222-2-2-2-2-2-200000000-2-222200000000000000000000
χ2122-2-22-2002i−2i2-22-22i−2i2i−2i000002-22i2i−2i−2i2i−2i0000000000002-2000000000000000i2−i22−22−2i2−i2
χ2222-2-22-2002i−2i2-22-22i−2i2i−2i000002-22i2i−2i−2i2i−2i0000000000002-2000000000000000−i2i2−22−22−i2i2
χ2322-2-22-2002i−2i2-22-2−2i2i−2i2i000002-22i2i−2i−2i−2i2i000000000000-220000000000000002−2−i2i2i2−i2−22
χ2422-2-22-2002i−2i2-22-2−2i2i−2i2i000002-22i2i−2i−2i−2i2i000000000000-22000000000000000−22i2−i2−i2i22−2
χ2522-2-22-200−2i2i2-22-22i−2i2i−2i000002-2−2i−2i2i2i2i−2i000000000000-220000000000000002−2i2−i2−i2i2−22
χ2622-2-22-200−2i2i2-22-22i−2i2i−2i000002-2−2i−2i2i2i2i−2i000000000000-22000000000000000−22−i2i2i2−i22−2
χ2722-2-22-200−2i2i2-22-2−2i2i−2i2i000002-2−2i−2i2i2i−2i2i0000000000002-2000000000000000i2−i2−22−22i2−i2
χ2822-2-22-200−2i2i2-22-2−2i2i−2i2i000002-2−2i−2i2i2i−2i2i0000000000002-2000000000000000−i2i22−22−2−i2i2
χ2922-2-2-222-2002-22-22i−2i2i−2i0i2−i2i2−i2-220000−2i2i2-200i2i2−i2−i2i2i2−i2−i2002i−2i02−22−20000000000000000
χ3022-2-2-222-2002-22-22i−2i2i−2i0−i2i2−i2i2-220000−2i2i2-200−i2−i2i2i2−i2−i2i2i2002i−2i0−22−220000000000000000
χ3122-2-2-222-2002-22-2−2i2i−2i2i0i2−i2i2−i2-2200002i−2i2-200i2i2−i2−i2i2i2−i2−i200−2i2i0−22−220000000000000000
χ3222-2-2-222-2002-22-2−2i2i−2i2i0−i2i2−i2i2-2200002i−2i2-200−i2−i2i2i2−i2−i2i2i200−2i2i02−22−20000000000000000
χ3322-2-2-22-22002-22-22i−2i2i−2i02−2−22-220000−2i2i-220022−2−2−2−22200−2i2i0−i2i2i2−i20000000000000000
χ3422-2-2-22-22002-22-22i−2i2i−2i0−222−2-220000−2i2i-2200−2−22222−2−200−2i2i0i2−i2−i2i20000000000000000
χ3522-2-2-22-22002-22-2−2i2i−2i2i02−2−22-2200002i−2i-220022−2−2−2−222002i−2i0i2−i2−i2i20000000000000000
χ3622-2-2-22-22002-22-2−2i2i−2i2i0−222−2-2200002i−2i-2200−2−22222−2−2002i−2i0−i2i2i2−i20000000000000000
χ374444444444-1-1-1-1000044444-1-1-1-1-1-100-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000
χ384444444444-1-1-1-100004-4-4-4-4-1-1-1-1-1-100-1-1-1-1111111110000000000000000000000000
χ3944444444-4-4-1-1-1-10000-40000-1-1111100-1-111i5−i5i5−i5i5−i5i5−i50000000000000000000000000
χ4044444444-4-4-1-1-1-10000-40000-1-1111100-1-111−i5i5−i5i5−i5i5−i5i50000000000000000000000000
χ41444444-4-444-1-1-1-10000-40000-1-1-1-1-1-10011115−55−5−55−550000000000000000000000000
χ42444444-4-444-1-1-1-10000-40000-1-1-1-1-1-1001111−55−555−55−50000000000000000000000000
χ43444444-4-4-4-4-1-1-1-1000044i4i−4i−4i-1-111110011-1-1−i−i−i−iiiii0000000000000000000000000
χ44444444-4-4-4-4-1-1-1-100004−4i−4i4i4i-1-111110011-1-1iiii−i−i−i−i0000000000000000000000000
χ454444-4-400004444444400000-4-40000-4-40000000000000000000000000000000000000
χ464444-4-400004444-4-4-4-400000-4-40000440000000000000000000000000000000000000
χ4744-4-4-444-400-11-11000002i2−2i22i2−2i21-1i5−i5i5−i500-11i5−i5ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ390000000000000000000000000
χ4844-4-4-444-400-11-11000002i2−2i22i2−2i21-1−i5i5−i5i500-11−i5i5ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ290000000000000000000000000
χ4944-4-4-444-400-11-1100000−2i22i2−2i22i21-1i5−i5i5−i500-11i5−i5−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ390000000000000000000000000
χ5044-4-4-444-400-11-1100000−2i22i2−2i22i21-1−i5i5−i5i500-11−i5i5−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ290000000000000000000000000
χ5144-4-4-44-4400-11-110000022−22−22221-1i5−i5i5−i5001-1−i5i5−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ390000000000000000000000000
χ5244-4-4-44-4400-11-110000022−22−22221-1−i5i5−i5i5001-1i5−i5ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ290000000000000000000000000
χ5344-4-4-44-4400-11-1100000−222222−221-1i5−i5i5−i5001-1−i5i5ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ390000000000000000000000000
χ5444-4-4-44-4400-11-1100000−222222−221-1−i5i5−i5i5001-1i5−i5−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ290000000000000000000000000
χ554-44-400000044-4-44i−4i−4i4i00000000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000
χ564-44-400000044-4-44i−4i−4i4i000000000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000
χ574-44-400000044-4-4−4i4i4i−4i00000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000
χ584-44-400000044-4-4−4i4i4i−4i000000000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000
χ594-4-440000004-4-4444-4-400000000000000000000000000000000002i−2i2i−2i000000000000
χ604-4-440000004-4-4444-4-40000000000000000000000000000000000−2i2i−2i2i000000000000
χ614-4-440000004-4-44-4-44400000000000000000000000000000000002-2-22000000000000
χ624-4-440000004-4-44-4-4440000000000000000000000000000000000-222-2000000000000
χ638888-8-80000-2-2-2-20000000002225−25−2525000000000000000000000000000000000000000
χ648888-8-80000-2-2-2-200000000022−252525−25000000000000000000000000000000000000000
χ6588-8-88-8008i−8i-22-22000000000-22−2i−2i2i2i000000000000000000000000000000000000000
χ6688-8-88-800−8i8i-22-22000000000-222i2i−2i−2i000000000000000000000000000000000000000
χ6716-1616-16000000-4-444000000000000000000000000000000000000000000000000000000
χ6816-16-1616000000-444-4000000000000000000000000000000000000000000000000000000

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