Finite Group Databasebeta

← Group #13017702

Character table — Group #13017702

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112244444444555588888888888101016161616161616161616161620202020404040404040404040404040404040404040404040
order12222244445101010444422444101020202020441010101020202020202020202244244444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-11-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-11-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−iii−i−i
χ611111111111111-1-1-1-111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii−i−iii
χ711111111111111-1-1-1-11-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111-11iiii−i−i−i−i−i−iii−i−iii
χ811111111111111-1-1-1-11-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111-11−i−i−i−iiiiiii−i−iii−i−i
χ9111111-1-11111111111-11-11-111-1-1-1-111-1-1111111-1-1-1-111-1-1-11-1-1111-1-111-1-11111-1-1-1-1
χ10111111-1-11111111111-11-11-111-1-1-1-111-1-1111111-1-1-1-111-1-1-11-1-11-1-111-1-111-1-1-1-11111
χ11111111-1-11111111111-1-11-1111-1-1-1-111-1-1-1-1-1-111111111-1-11-11-1-111-1-111-1-1-1-1-1-11111
χ12111111-1-11111111111-1-11-1111-1-1-1-111-1-1-1-1-1-111111111-1-11-11-1-1-1-111-1-1111111-1-1-1-1
χ13111111-1-1111111-1-1-1-1-11-11-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-111-1ii−i−i−i−iiiii−i−i−i−iii
χ14111111-1-1111111-1-1-1-1-11-11-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-111-1−i−iiiii−i−i−i−iiiii−i−i
χ15111111-1-1111111-1-1-1-1-1-11-1111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-11-111ii−i−i−i−iii−i−iiiii−i−i
χ16111111-1-1111111-1-1-1-1-1-11-1111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-11-111−i−iiiii−i−iii−i−i−i−iii
χ1722222222-2-222222222-2000022222222-2-20000-2-20000-2-222000-200000000000000000
χ1822222222-2-22222-2-2-2-2-20000222222-2-2-2-20000-2-2000022-2-2000200000000000000000
χ19222222-2-2-2-2222222222000022-2-2-2-222220000-2-20000-2-2-2-2000200000000000000000
χ20222222-2-2-2-22222-2-2-2-22000022-2-2-2-2-2-2220000-2-200002222000-200000000000000000
χ212222-2-2002-2222222220020-2-2-20000-2-20000002-222-2-22-200-202000000000000000000
χ222222-2-2002-22222222200-202-2-20000-2-20000002-2-2-2222-20020-2000000000000000000
χ232222-2-2002-22222-2-2-2-20020-2-2-20000220000002-222-2-2-220020-2000000000000000000
χ242222-2-2002-22222-2-2-2-200-202-2-20000220000002-2-2-222-2200-202000000000000000000
χ252222-2-200-2222222222020-20-2-20000-2-20022-2-2-220000-22000-20020000000000000000
χ262222-2-200-22222222220-2020-2-20000-2-200-2-222-220000-22000200-20000000000000000
χ272222-2-200-222222-2-2-2-2020-20-2-20000220022-2-2-2200002-2000200-20000000000000000
χ282222-2-200-222222-2-2-2-20-2020-2-200002200-2-222-2200002-2000-20020000000000000000
χ292-22-22-22i−2i0022-2-22i−2i2i−2i000002-22i2i−2i−2i2i−2i000000000000002-2000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ302-22-22-22i−2i0022-2-22i−2i2i−2i000002-22i2i−2i−2i2i−2i000000000000002-200000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ312-22-22-22i−2i0022-2-2−2i2i−2i2i000002-22i2i−2i−2i−2i2i00000000000000-22000001−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000
χ322-22-22-22i−2i0022-2-2−2i2i−2i2i000002-22i2i−2i−2i−2i2i00000000000000-2200000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000
χ332-22-22-2−2i2i0022-2-22i−2i2i−2i000002-2−2i−2i2i2i2i−2i00000000000000-22000001+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000
χ342-22-22-2−2i2i0022-2-22i−2i2i−2i000002-2−2i−2i2i2i2i−2i00000000000000-2200000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000
χ352-22-22-2−2i2i0022-2-2−2i2i−2i2i000002-2−2i−2i2i2i−2i2i000000000000002-2000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ362-22-22-2−2i2i0022-2-2−2i2i−2i2i000002-2−2i−2i2i2i−2i2i000000000000002-200000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ374444444444-1-1-1-1000044444-1-1-1-1-1-100-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000
χ384444444444-1-1-1-100004-4-4-4-4-1-1-1-1-1-100-1-11111-1-111110000000000000000000000000
χ3944444444-4-4-1-1-1-10000-40000-1-1-1-1-1-100115−55−5115−55−50000000000000000000000000
χ4044444444-4-4-1-1-1-10000-40000-1-1-1-1-1-10011−55−5511−55−550000000000000000000000000
χ41444444-4-444-1-1-1-10000-44-44-4-1-111110011-1-1-1-1-1-111110000000000000000000000000
χ42444444-4-444-1-1-1-10000-4-44-44-1-1111100111111-1-1-1-1-1-10000000000000000000000000
χ43444444-4-4-4-4-1-1-1-1000040000-1-1111100-1-15−55−511−55−550000000000000000000000000
χ44444444-4-4-4-4-1-1-1-1000040000-1-1111100-1-1−55−55115−55−50000000000000000000000000
χ454444-4-4004-4-1-1-1-100000040-4115−55−5005−55−5−55-11-1-1110000000000000000000000000
χ464444-4-4004-4-1-1-1-100000040-411−55−5500−55−555−5-11-1-1110000000000000000000000000
χ474444-4-4004-4-1-1-1-1000000-404115−55−5005−5−555−5-1111-1-10000000000000000000000000
χ484444-4-4004-4-1-1-1-1000000-40411−55−5500−555−5−55-1111-1-10000000000000000000000000
χ494444-4-400-44-1-1-1-10000040-40115−55−500−55-1-1111-15−5−550000000000000000000000000
χ504444-4-400-44-1-1-1-10000040-4011−55−55005−5-1-1111-1−555−50000000000000000000000000
χ514444-4-400-44-1-1-1-100000-4040115−55−500−5511-1-11-1−555−50000000000000000000000000
χ524444-4-400-44-1-1-1-100000-404011−55−55005−511-1-11-15−5−550000000000000000000000000
χ5344-4-40000004-44-44i−4i−4i4i0000000000000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37
χ5444-4-40000004-44-44i−4i−4i4i00000000000000000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37
χ5544-4-40000004-44-4−4i4i4i−4i0000000000000000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39
χ5644-4-40000004-44-4−4i4i4i−4i00000000000000000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39
χ574-44-4-44000044-4-44i−4i4i−4i00000-440000−4i4i0000000000000000000000000000000000000
χ584-44-4-44000044-4-4−4i4i−4i4i00000-4400004i−4i0000000000000000000000000000000000000
χ594-4-440000004-4-4444-4-40000000000000000000000000000000000000000002i−2i2i−2i0000
χ604-4-440000004-4-4444-4-4000000000000000000000000000000000000000000−2i2i−2i2i0000
χ614-4-440000004-4-44-4-4440000000000000000000000000000000000000000002-2-220000
χ624-4-440000004-4-44-4-444000000000000000000000000000000000000000000-222-20000
χ638-88-88-88i−8i00-2-222000000000-22−2i−2i2i2i000000000000000000000000000000000000000
χ648-88-88-8−8i8i00-2-222000000000-222i2i−2i−2i000000000000000000000000000000000000000
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.