Finite Group Databasebeta

← Group #13018936

Character table — Group #13018936

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112244444444555588888888888101016161616161616161616161620202020404040404040404040404040404040404040404040
order12222244445101010444428888101020202020441010202040404040404040402244488888888888888888888
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−iii−i−iii−i−i
χ611111111111111-1-1-1-111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
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−iii−i−iii
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−iiiii−i−iii−i−i
χ9111111-1-11111111111-111-1-111111111-1-1-1-11111-1-1-1-1-1-111-111-1-11-11-11-11-11111-1-1-1-1
χ10111111-1-11111111111-111-1-111111111-1-1-1-11111-1-1-1-1-1-111-111-1-1-11-11-11-11-1-1-1-11111
χ11111111-1-11111111111-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1111-11-11-11-1-1-1-1-11111
χ12111111-1-11111111111-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1-111-11-11-11-111111-1-1-1-1
χ13111111-1-1111111-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-11-1-111i−i−iii−i−iiii−i−i−i−iii
χ14111111-1-1111111-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-11-1-111−iii−i−iii−i−i−iiiii−i−i
χ15111111-1-1111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1i−i−iii−i−ii−i−iiiii−i−i
χ16111111-1-1111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1−iii−i−iii−iii−i−i−i−iii
χ1722222222-2-222222222-2000022-2-2-2-222-2-2220000000022-2-2-200000000000000000000
χ1822222222-2-22222-2-2-2-2-2000022-2-2-2-2-2-2-2-22200000000-2-222200000000000000000000
χ19222222-2-2-2-2222222222000022-2-2-2-22222-2-200000000-2-2-2-2200000000000000000000
χ20222222-2-2-2-22222-2-2-2-22000022-2-2-2-2-2-222-2-2000000002222-200000000000000000000
χ212222-2-2002-22222222200000-2-222-2-2-2-2000000000000002-2000002020-20-2000000000
χ222222-2-2002-22222222200000-2-222-2-2-2-2000000000000002-200000-20-20202000000000
χ232222-2-2002-22222-2-2-2-200000-2-222-2-22200000000000000-22000002i0−2i0−2i02i000000000
χ242222-2-2002-22222-2-2-2-200000-2-222-2-22200000000000000-2200000−2i02i02i0−2i000000000
χ252222-2-200-222222222200000-2-2-2-222-2-200000000000000-220000002020-20-200000000
χ262222-2-200-222222222200000-2-2-2-222-2-200000000000000-22000000-20-2020200000000
χ272222-2-200-222222-2-2-2-200000-2-2-2-22222000000000000002-20000002i0−2i0−2i02i00000000
χ282222-2-200-222222-2-2-2-200000-2-2-2-22222000000000000002-2000000−2i02i02i0−2i00000000
χ292-22-22-22i−2i0022-2-22i−2i2i−2i0i2−i22−22-200002i−2i002i−2ii2i2−i2−i222−2−22-20002−2i2−i20000000000000000
χ302-22-22-22i−2i0022-2-22i−2i2i−2i0−i2i2−222-200002i−2i002i−2i−i2−i2i2i2−2−2222-2000−22−i2i20000000000000000
χ312-22-22-22i−2i0022-2-2−2i2i−2i2i0i2−i22−22-20000−2i2i002i−2ii2i2−i2−i222−2−2-22000−22−i2i20000000000000000
χ322-22-22-22i−2i0022-2-2−2i2i−2i2i0−i2i2−222-20000−2i2i002i−2i−i2−i2i2i2−2−222-220002−2i2−i20000000000000000
χ332-22-22-2−2i2i0022-2-22i−2i2i−2i0i2−i2−222-200002i−2i00−2i2ii2i2−i2−i2−2−222-220002−2−i2i20000000000000000
χ342-22-22-2−2i2i0022-2-22i−2i2i−2i0−i2i22−22-200002i−2i00−2i2i−i2−i2i2i222−2−2-22000−22i2−i20000000000000000
χ352-22-22-2−2i2i0022-2-2−2i2i−2i2i0i2−i2−222-20000−2i2i00−2i2ii2i2−i2−i2−2−2222-2000−22i2−i20000000000000000
χ362-22-22-2−2i2i0022-2-2−2i2i−2i2i0−i2i22−22-20000−2i2i00−2i2i−i2−i2i2i222−2−22-20002−2−i2i20000000000000000
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
χ3944444444-4-4-1-1-1-10000-40000-1-111110011-1-1i5−i5i5−i5i5−i5i5−i50000000000000000000000000
χ4044444444-4-4-1-1-1-10000-40000-1-111110011-1-1−i5i5−i5i5−i5i5−i5i50000000000000000000000000
χ41444444-4-444-1-1-1-10000-444-4-4-1-1-1-1-1-1001111-1-1-1-111110000000000000000000000000
χ42444444-4-444-1-1-1-10000-4-4-444-1-1-1-1-1-10011111111-1-1-1-10000000000000000000000000
χ43444444-4-4-4-4-1-1-1-1000040000-1-1111100-1-111i5−i5i5−i5−i5i5−i5i50000000000000000000000000
χ44444444-4-4-4-4-1-1-1-1000040000-1-1111100-1-111−i5i5−i5i5i5−i5i5−i50000000000000000000000000
χ4544-4-40000004-44-44i−4i−4i4i000000000000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000
χ4644-4-40000004-44-44i−4i−4i4i0000000000000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000
χ4744-4-40000004-44-4−4i4i4i−4i000000000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000
χ4844-4-40000004-44-4−4i4i4i−4i0000000000000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000
χ494-44-44-44i−4i00-1-111000002i2−2i222−22-11i5−i5i5−i5005−5−iiζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ290000000000000000000000000
χ504-44-44-44i−4i00-1-111000002i2−2i222−22-11−i5i5−i5i500−55−iiζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ390000000000000000000000000
χ514-44-44-44i−4i00-1-11100000−2i22i2−2222-11i5−i5i5−i5005−5−ii−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ290000000000000000000000000
χ524-44-44-44i−4i00-1-11100000−2i22i2−2222-11−i5i5−i5i500−55−ii−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ390000000000000000000000000
χ534-44-44-4−4i4i00-1-111000002i2−2i2−2222-11i5−i5i5−i500−55i−iζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ290000000000000000000000000
χ544-44-44-4−4i4i00-1-111000002i2−2i2−2222-11−i5i5−i5i5005−5i−iζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ390000000000000000000000000
χ554-44-44-4−4i4i00-1-11100000−2i22i222−22-11i5−i5i5−i500−55i−i−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ290000000000000000000000000
χ564-44-44-4−4i4i00-1-11100000−2i22i222−22-11−i5i5−i5i5005−5i−i−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ390000000000000000000000000
χ574-44-4-44000044-4-44i−4i4i−4i00000-440000−4i4i0000000000000000000000000000000000000
χ584-44-4-44000044-4-4−4i4i−4i4i00000-4400004i−4i0000000000000000000000000000000000000
χ594-4-440000004-4-4444-4-400000000000000000000000000000000000000000000002i−2i2i−2i
χ604-4-440000004-4-4444-4-40000000000000000000000000000000000000000000000−2i2i−2i2i
χ614-4-440000004-4-44-4-44400000000000000000000000000000000000000000000002-2-22
χ624-4-440000004-4-44-4-4440000000000000000000000000000000000000000000000-222-2
χ638888-8-8008-8-2-2-2-200000000022-2-222000000000000000000000000000000000000000
χ648888-8-800-88-2-2-2-20000000002222-2-2000000000000000000000000000000000000000
χ658-88-8-880000-2-2220000000002-22i5−2i5−2i52i5000000000000000000000000000000000000000
χ668-88-8-880000-2-2220000000002-2−2i52i52i5−2i5000000000000000000000000000000000000000
χ671616-16-16000000-44-44000000000000000000000000000000000000000000000000000000
χ6816-16-1616000000-444-4000000000000000000000000000000000000000000000000000000

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