Finite Group Databasebeta

← Group #13017708

Character table — Group #13017708

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112244444444555588888888888101016161616161616161616161620202020404040404040404040404040404040404040404040
order12222244445101010444424444101020202020441010202020202020202020204444244448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-11-111111111-1-1-1-111-1-111-1-11111-1-11-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111-1-1-11-111111111-1-1-1-111-1-111-1-11111-1-11-1-1-1-1-1-1-1-1-1-111111111
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
χ711111111111111-1-1-1-1-1-1-11-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-111-111ii−i−iii−i−i−i−i−i−iiiii
χ811111111111111-1-1-1-1-1-1-11-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-111-111−i−iii−i−iiiiiii−i−i−i−i
χ911111111-1-1111111111-1-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-111-11-11-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1111111111-1-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-111-11-11-1-1-1-1-11111-1-111-1-111
χ1111111111-1-111111111-111-1-111-1-1-1-111-1-111-1-1-1-11111-1-1111-1-1-111111-1-1-1-1-1-111-1-111
χ1211111111-1-111111111-111-1-111-1-1-1-111-1-111-1-1-1-11111-1-1111-1-1-11-1-1-1-1111111-1-111-1-1
χ1311111111-1-11111-1-1-1-11-1-1-1111-1-1-1-1-1-111-1-1-1-11111-1-111-1-11-11-11ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-11111-1-1-1-11-1-1-1111-1-1-1-1-1-111-1-1-1-11111-1-111-1-11-11-11−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-11111-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1111-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-11111-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1111-1−i−iiiii−i−iii−i−i−i−iii
χ17222222-2-22222222222000-20222222220000-2-200-2-20022-2-200-2000000000000000000
χ18222222-2-2222222-2-2-2-2000-20222222-2-20000-2-200-2-200-2-222002000000000000000000
χ19222222-2-2-2-2222222220002022-2-2-2-22200002200-2-200-2-2-2-2002000000000000000000
χ20222222-2-2-2-22222-2-2-2-20002022-2-2-2-2-2-200002200-2-200222200-2000000000000000000
χ212222-2-22-2002222222202-200-2-20000-2-2002200002-2-2-2002-22000-20000000000000000
χ222222-2-22-200222222220-2200-2-20000-2-200-2-200002-222002-2-200020000000000000000
χ232222-2-22-2002222-2-2-2-202-200-2-2000022002200002-2-2-200-22-200020000000000000000
χ242222-2-22-2002222-2-2-2-20-2200-2-200002200-2-200002-22200-222000-20000000000000000
χ252222-2-2-2200222222222000-2-2-20000-2-2220000-2-2-220000-22020-200000000000000000
χ262222-2-2-220022222222-20002-2-20000-2-2-2-2000022-220000-220-20200000000000000000
χ272222-2-2-22002222-2-2-2-22000-2-2-2000022220000-2-2-2200002-20-20200000000000000000
χ282222-2-2-22002222-2-2-2-2-20002-2-2000022-2-2000022-2200002-2020-200000000000000000
χ292-2-222-2002i−2i2-22-22i−2i2i−2i000002-22i2i−2i−2i2i−2i0000000000002-20000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ302-2-222-2002i−2i2-22-22i−2i2i−2i000002-22i2i−2i−2i2i−2i0000000000002-2000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ312-2-222-2002i−2i2-22-2−2i2i−2i2i000002-22i2i−2i−2i−2i2i000000000000-220000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i
χ322-2-222-2002i−2i2-22-2−2i2i−2i2i000002-22i2i−2i−2i−2i2i000000000000-22000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i
χ332-2-222-200−2i2i2-22-22i−2i2i−2i000002-2−2i−2i2i2i2i−2i000000000000-220000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i
χ342-2-222-200−2i2i2-22-22i−2i2i−2i000002-2−2i−2i2i2i2i−2i000000000000-22000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i
χ352-2-222-200−2i2i2-22-2−2i2i−2i2i000002-2−2i−2i2i2i−2i2i0000000000002-20000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ362-2-222-200−2i2i2-22-2−2i2i−2i2i000002-2−2i−2i2i2i−2i2i0000000000002-2000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ374444444444-1-1-1-1000044444-1-1-1-1-1-100-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000
χ384444444444-1-1-1-10000-4-4-44-4-1-1-1-1-1-1001111-1-111-1-1110000000000000000000000000
χ3944444444-4-4-1-1-1-100004-4-4-44-1-1111100-1-11111-1-1-1-1110000000000000000000000000
χ4044444444-4-4-1-1-1-10000-444-4-4-1-111110011-1-11111-1-1-1-10000000000000000000000000
χ41444444-4-444-1-1-1-10000000-40-1-1-1-1-1-1005−55−5115−5115−50000000000000000000000000
χ42444444-4-444-1-1-1-10000000-40-1-1-1-1-1-100−55−5511−5511−550000000000000000000000000
χ43444444-4-4-4-4-1-1-1-1000000040-1-11111005−5−55-1-15−511−550000000000000000000000000
χ44444444-4-4-4-4-1-1-1-1000000040-1-1111100−555−5-1-1−55115−50000000000000000000000000
χ454444-4-44-400-1-1-1-1000004-400115−55−5005−5-1-15−5−55-11110000000000000000000000000
χ464444-4-44-400-1-1-1-1000004-40011−55−5500−55-1-1−555−5-11110000000000000000000000000
χ474444-4-44-400-1-1-1-100000-4400115−55−500−55115−55−5-11-1-10000000000000000000000000
χ484444-4-44-400-1-1-1-100000-440011−55−55005−511−55−55-11-1-10000000000000000000000000
χ494444-4-4-4400-1-1-1-100004000-4115−55−500-1-15−5−55111-1−550000000000000000000000000
χ504444-4-4-4400-1-1-1-100004000-411−55−5500-1-1−555−5111-15−50000000000000000000000000
χ514444-4-4-4400-1-1-1-10000-40004115−55−50011−55−55-1-11-15−50000000000000000000000000
χ524444-4-4-4400-1-1-1-10000-4000411−55−5500115−55−5-1-11-1−550000000000000000000000000
χ5344-4-400000044-4-444-4-4000000000000000000000000000000000000002-22-200000000
χ5444-4-400000044-4-444-4-400000000000000000000000000000000000000-22-2200000000
χ5544-4-400000044-4-4-4-444000000000000000000000000000000000000002i−2i−2i2i00000000
χ5644-4-400000044-4-4-4-44400000000000000000000000000000000000000−2i2i2i−2i00000000
χ574-44-40000004-4-444i−4i−4i4i0000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ584-44-40000004-4-444i−4i−4i4i00000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ594-44-40000004-4-44−4i4i4i−4i0000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ604-44-40000004-4-44−4i4i4i−4i00000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ614-4-44-4400004-44-44i−4i4i−4i00000-440000−4i4i0000000000000000000000000000000000000
χ624-4-44-4400004-44-4−4i4i−4i4i00000-4400004i−4i0000000000000000000000000000000000000
χ638-8-888-8008i−8i-22-22000000000-22−2i−2i2i2i000000000000000000000000000000000000000
χ648-8-888-800−8i8i-22-22000000000-222i2i−2i−2i000000000000000000000000000000000000000
χ658-8-88-880000-22-220000000002-22i5−2i5−2i52i5000000000000000000000000000000000000000
χ668-8-88-880000-22-220000000002-2−2i52i52i5−2i5000000000000000000000000000000000000000
χ671616-16-16000000-4-444000000000000000000000000000000000000000000000000000000
χ6816-1616-16000000-444-4000000000000000000000000000000000000000000000000000000

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