Finite Group Databasebeta

← Group #13013844

Character table — Group #13013844

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112244444444555588888888888101016161616161616161616161620202020404040404040404040404040404040404040404040
order12222244445101010444448888101020202020442020202040404040404040402244488888888888888888888
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−i11-1-1-1-11111-1-1iiii−i−i−i−i-1-1-1-11ii−i−i1111-1-1-1-1ii−i−iii−i−i
χ10111111-1-1-1-1111111111ii−i−i11-1-1-1-11111-1-1iiii−i−i−i−i-1-1-1-11ii−i−i-1-1-1-11111−i−iii−i−iii
χ11111111-1-1-1-1111111111−i−iii11-1-1-1-11111-1-1−i−i−i−iiiii-1-1-1-11−i−iii1111-1-1-1-1−i−iii−i−iii
χ12111111-1-1-1-1111111111−i−iii11-1-1-1-11111-1-1−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−i11-1-1-1-1-1-111-1-1iiii−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−i11-1-1-1-1-1-111-1-1iiii−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−iii11-1-1-1-1-1-111-1-1−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−iii11-1-1-1-1-1-111-1-1−i−i−i−iiiii1111-1ii−i−i−i−iiiii−i−i-1-11111-1-1
χ1722222222-2-222222222-2000022-2-2-2-222-2-22200000000-2-222-200000000000000000000
χ1822222222-2-22222-2-2-2-2-2000022-2-2-2-2-2-2-2-2220000000022-2-2200000000000000000000
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
χ212-22-22-2002-22-22-222-2-2000002-222-2-22-20000000000002-20000000000000002−22−22−22−2
χ222-22-22-2002-22-22-222-2-2000002-222-2-22-20000000000002-2000000000000000−22−22−22−22
χ232-22-22-2002-22-22-2-2-222000002-222-2-2-22000000000000-22000000000000000i2−i2i2−i2−i2i2−i2i2
χ242-22-22-2002-22-22-2-2-222000002-222-2-2-22000000000000-22000000000000000−i2i2−i2i2i2−i2i2−i2
χ252-22-22-200-222-22-222-2-2000002-2-2-2222-2000000000000-22000000000000000i2−i2−i2i2i2−i2−i2i2
χ262-22-22-200-222-22-222-2-2000002-2-2-2222-2000000000000-22000000000000000−i2i2i2−i2−i2i2i2−i2
χ272-22-22-200-222-22-2-2-222000002-2-2-222-220000000000002-20000000000000002−2−22−222−2
χ282-22-22-200-222-22-2-2-222000002-2-2-222-220000000000002-2000000000000000−222−22−2−22
χ292-22-2-222i−2i002-22-222-2-201+i−1−i1−i−1+i-220000-22002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i002i−2i01+i−1−i1−i−1+i0000000000000000
χ302-22-2-222i−2i002-22-222-2-20−1−i1+i−1+i1−i-220000-22002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i002i−2i0−1−i1+i−1+i1−i0000000000000000
χ312-22-2-222i−2i002-22-2-2-22201+i−1−i1−i−1+i-2200002-2002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00−2i2i0−1−i1+i−1+i1−i0000000000000000
χ322-22-2-222i−2i002-22-2-2-2220−1−i1+i−1+i1−i-2200002-2002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−2i2i01+i−1−i1−i−1+i0000000000000000
χ332-22-2-22−2i2i002-22-222-2-201−i−1+i1+i−1−i-220000-2200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00−2i2i01−i−1+i1+i−1−i0000000000000000
χ342-22-2-22−2i2i002-22-222-2-20−1+i1−i−1−i1+i-220000-2200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00−2i2i0−1+i1−i−1−i1+i0000000000000000
χ352-22-2-22−2i2i002-22-2-2-22201−i−1+i1+i−1−i-2200002-200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i002i−2i0−1+i1−i−1−i1+i0000000000000000
χ362-22-2-22−2i2i002-22-2-2-2220−1+i1−i−1−i1+i-2200002-200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i002i−2i01−i−1+i1+i−1−i0000000000000000
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
χ41444444-4-444-1-1-1-10000-40000-1-1-1-1-1-10011115−55−5−55−550000000000000000000000000
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-1-1111100-1-111−i−i−i−iiiii0000000000000000000000000
χ44444444-4-4-4-4-1-1-1-100004−4i−4i4i4i-1-1111100-1-111iiii−i−i−i−i0000000000000000000000000
χ454444-4-400004444444400000-4-40000-4-40000000000000000000000000000000000000
χ464444-4-400004444-4-4-4-400000-4-40000440000000000000000000000000000000000000
χ4744-4-40000004-4-444i−4i4i−4i0000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ4844-4-40000004-4-444i−4i4i−4i00000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ4944-4-40000004-4-44−4i4i−4i4i0000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ5044-4-40000004-4-44−4i4i−4i4i00000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ514-44-4-444i−4i00-11-11000002+2i−2−2i2−2i−2+2i1-15−55−500i5−i5−ii−ζ6−ζ12−ζ14−ζ28−ζ4−ζ22−ζ36−ζ38ζ6+ζ12+ζ14+ζ28ζ4+ζ22+ζ36+ζ38−ζ4+ζ22−ζ36+ζ38ζ6−ζ12+ζ14−ζ28ζ4−ζ22+ζ36−ζ38−ζ6+ζ12−ζ14+ζ280000000000000000000000000
χ524-44-4-444i−4i00-11-11000002+2i−2−2i2−2i−2+2i1-1−55−5500−i5i5−ii−ζ4−ζ22−ζ36−ζ38−ζ6−ζ12−ζ14−ζ28ζ4+ζ22+ζ36+ζ38ζ6+ζ12+ζ14+ζ28ζ6−ζ12+ζ14−ζ28−ζ4+ζ22−ζ36+ζ38−ζ6+ζ12−ζ14+ζ28ζ4−ζ22+ζ36−ζ380000000000000000000000000
χ534-44-4-444i−4i00-11-1100000−2−2i2+2i−2+2i2−2i1-15−55−500i5−i5−iiζ6+ζ12+ζ14+ζ28ζ4+ζ22+ζ36+ζ38−ζ6−ζ12−ζ14−ζ28−ζ4−ζ22−ζ36−ζ38ζ4−ζ22+ζ36−ζ38−ζ6+ζ12−ζ14+ζ28−ζ4+ζ22−ζ36+ζ38ζ6−ζ12+ζ14−ζ280000000000000000000000000
χ544-44-4-444i−4i00-11-1100000−2−2i2+2i−2+2i2−2i1-1−55−5500−i5i5−iiζ4+ζ22+ζ36+ζ38ζ6+ζ12+ζ14+ζ28−ζ4−ζ22−ζ36−ζ38−ζ6−ζ12−ζ14−ζ28−ζ6+ζ12−ζ14+ζ28ζ4−ζ22+ζ36−ζ38ζ6−ζ12+ζ14−ζ28−ζ4+ζ22−ζ36+ζ380000000000000000000000000
χ554-44-4-44−4i4i00-11-11000002−2i−2+2i2+2i−2−2i1-15−55−500−i5i5i−iζ6−ζ12+ζ14−ζ28−ζ4+ζ22−ζ36+ζ38−ζ6+ζ12−ζ14+ζ28ζ4−ζ22+ζ36−ζ38−ζ4−ζ22−ζ36−ζ38−ζ6−ζ12−ζ14−ζ28ζ4+ζ22+ζ36+ζ38ζ6+ζ12+ζ14+ζ280000000000000000000000000
χ564-44-4-44−4i4i00-11-11000002−2i−2+2i2+2i−2−2i1-1−55−5500i5−i5i−i−ζ4+ζ22−ζ36+ζ38ζ6−ζ12+ζ14−ζ28ζ4−ζ22+ζ36−ζ38−ζ6+ζ12−ζ14+ζ28−ζ6−ζ12−ζ14−ζ28−ζ4−ζ22−ζ36−ζ38ζ6+ζ12+ζ14+ζ28ζ4+ζ22+ζ36+ζ380000000000000000000000000
χ574-44-4-44−4i4i00-11-1100000−2+2i2−2i−2−2i2+2i1-15−55−500−i5i5i−i−ζ6+ζ12−ζ14+ζ28ζ4−ζ22+ζ36−ζ38ζ6−ζ12+ζ14−ζ28−ζ4+ζ22−ζ36+ζ38ζ4+ζ22+ζ36+ζ38ζ6+ζ12+ζ14+ζ28−ζ4−ζ22−ζ36−ζ38−ζ6−ζ12−ζ14−ζ280000000000000000000000000
χ584-44-4-44−4i4i00-11-1100000−2+2i2−2i−2−2i2+2i1-1−55−5500i5−i5i−iζ4−ζ22+ζ36−ζ38−ζ6+ζ12−ζ14+ζ28−ζ4+ζ22−ζ36+ζ38ζ6−ζ12+ζ14−ζ28ζ6+ζ12+ζ14+ζ28ζ4+ζ22+ζ36+ζ38−ζ6−ζ12−ζ14−ζ28−ζ4−ζ22−ζ36−ζ380000000000000000000000000
χ594-4-4400000044-4-44i−4i−4i4i00000000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000
χ604-4-4400000044-4-44i−4i−4i4i000000000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000
χ614-4-4400000044-4-4−4i4i4i−4i00000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000
χ624-4-4400000044-4-4−4i4i4i−4i000000000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000
χ638888-8-80000-2-2-2-20000000002225−25−2525000000000000000000000000000000000000000
χ648888-8-80000-2-2-2-200000000022−252525−25000000000000000000000000000000000000000
χ658-88-88-8008-8-22-22000000000-22-2-222000000000000000000000000000000000000000
χ668-88-88-800-88-22-22000000000-2222-2-2000000000000000000000000000000000000000
χ671616-16-16000000-444-4000000000000000000000000000000000000000000000000000000
χ6816-16-1616000000-4-444000000000000000000000000000000000000000000000000000000

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