Finite Group Databasebeta

← Group #13017703

Character table — Group #13017703

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112244444444555588888888888101016161616161616161616161620202020404040404040404040404040404040404040404040
order12222244445101010444444444101020202020442020202020202020202020202244222444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-11-1-111111111-1-1-1-11111-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111-1-11-1-111111111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1iiii−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
χ711111111111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii−i−iii
χ811111111111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−iii−i−i
χ911111111-1-1111111111-1-11-111-1-1-1-11111-1-111-1-111-1-111-1-1-11-11-111-1-111-1-11111-1-1-1-1
χ1011111111-1-1111111111-1-11-111-1-1-1-11111-1-111-1-111-1-111-1-1-11-11-1-1-111-1-111-1-1-1-11111
χ1111111111-1-111111111-11-1-1111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-1111-1-111-1-1-1-1-1-11111
χ1211111111-1-111111111-11-1-1111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-11-1-111-1-1111111-1-1-1-1
χ1311111111-1-11111-1-1-1-11-1-11-111-1-1-1-1-1-111-1-111-1-111-1-1-1-1111-11-11ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-11111-1-1-1-11-1-11-111-1-1-1-1-1-111-1-111-1-111-1-1-1-1111-11-11−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-11111-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-11-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-11111-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-11-1−i−iiiii−i−iii−i−i−i−iii
χ17222222-2-2222222222200-200222222220000-2-2-2-20000-2-222-200000000000000000000
χ18222222-2-2222222-2-2-2-200-200222222-2-20000-2-2-2-2000022-2-2200000000000000000000
χ19222222-2-2-2-2222222220020022-2-2-2-2220000-2-2220000-2-2-2-2200000000000000000000
χ20222222-2-2-2-22222-2-2-2-20020022-2-2-2-2-2-20000-2-22200002222-200000000000000000000
χ212222-2-22-200222222220200-2-2-20000-2-200222-20000-2-22-20000-2020000000000000000
χ222222-2-22-200222222220-2002-2-20000-2-200-2-22-20000222-2000020-20000000000000000
χ232222-2-22-2002222-2-2-2-20200-2-2-200002200222-20000-2-2-22000020-20000000000000000
χ242222-2-22-2002222-2-2-2-20-2002-2-200002200-2-22-2000022-220000-2020000000000000000
χ252222-2-2-220022222222200-20-2-20000-2-22200-2200-2-200-22000-20200000000000000000
χ262222-2-2-220022222222-20020-2-20000-2-2-2-200-22002200-2200020-200000000000000000
χ272222-2-2-22002222-2-2-2-2200-20-2-20000222200-2200-2-2002-200020-200000000000000000
χ282222-2-2-22002222-2-2-2-2-20020-2-2000022-2-200-220022002-2000-20200000000000000000
χ292-2-222-2002-222-2-22i−2i2i−2i000002-222-2-22i−2i000000000000002i−2i000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ302-2-222-2002-222-2-22i−2i2i−2i000002-222-2-22i−2i000000000000002i−2i00000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ312-2-222-2002-222-2-2−2i2i−2i2i000002-222-2-2−2i2i00000000000000−2i2i000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ322-2-222-2002-222-2-2−2i2i−2i2i000002-222-2-2−2i2i00000000000000−2i2i00000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ332-2-222-200-2222-2-22i−2i2i−2i000002-2-2-2222i−2i00000000000000−2i2i000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ342-2-222-200-2222-2-22i−2i2i−2i000002-2-2-2222i−2i00000000000000−2i2i00000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ352-2-222-200-2222-2-2−2i2i−2i2i000002-2-2-222−2i2i000000000000002i−2i000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ362-2-222-200-2222-2-2−2i2i−2i2i000002-2-2-222−2i2i000000000000002i−2i00000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ374444444444-1-1-1-1000044444-1-1-1-1-1-100-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000
χ384444444444-1-1-1-10000-4-44-4-4-1-1-1-1-1-1001111-1-1-1-111110000000000000000000000000
χ3944444444-4-4-1-1-1-100004-4-44-4-1-1111100-1-111-1-111-1-1110000000000000000000000000
χ4044444444-4-4-1-1-1-10000-44-4-44-1-111110011-1-1-1-11111-1-10000000000000000000000000
χ41444444-4-444-1-1-1-1000000-400-1-1-1-1-1-1005−55−511115−55−50000000000000000000000000
χ42444444-4-444-1-1-1-1000000-400-1-1-1-1-1-100−55−551111−55−550000000000000000000000000
χ43444444-4-4-4-4-1-1-1-1000000400-1-11111005−5−5511-1-15−5−550000000000000000000000000
χ44444444-4-4-4-4-1-1-1-1000000400-1-1111100−555−511-1-1−555−50000000000000000000000000
χ454444-4-44-400-1-1-1-100000400-4115−55−5005−5-1-1-115−5−55110000000000000000000000000
χ464444-4-44-400-1-1-1-100000400-411−55−5500−55-1-1-11−555−5110000000000000000000000000
χ474444-4-44-400-1-1-1-100000-4004115−55−500−5511-115−55−5-1-10000000000000000000000000
χ484444-4-44-400-1-1-1-100000-400411−55−55005−511-11−55−55-1-10000000000000000000000000
χ494444-4-4-4400-1-1-1-10000400-40115−55−500-1-15−51-1−5511−550000000000000000000000000
χ504444-4-4-4400-1-1-1-10000400-4011−55−5500-1-1−551-15−5115−50000000000000000000000000
χ514444-4-4-4400-1-1-1-10000-40040115−55−50011−551-1−55-1-15−50000000000000000000000000
χ524444-4-4-4400-1-1-1-10000-4004011−55−5500115−51-15−5-1-1−550000000000000000000000000
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
χ574-44-40000004-4-4444-4-40000000000000000000000000000000000000000002i−2i2i−2i0000
χ584-44-40000004-4-4444-4-4000000000000000000000000000000000000000000−2i2i−2i2i0000
χ594-44-40000004-4-44-4-4440000000000000000000000000000000000000000002-2-220000
χ604-44-40000004-4-44-4-444000000000000000000000000000000000000000000-222-20000
χ614-4-44-44000044-4-44i−4i4i−4i00000-440000−4i4i0000000000000000000000000000000000000
χ624-4-44-44000044-4-4−4i4i−4i4i00000-4400004i−4i0000000000000000000000000000000000000
χ638-8-888-8008-8-2-222000000000-22-2-222000000000000000000000000000000000000000
χ648-8-888-800-88-2-222000000000-2222-2-2000000000000000000000000000000000000000
χ658-8-88-880000-2-2220000000002-225−25−2525000000000000000000000000000000000000000
χ668-8-88-880000-2-2220000000002-2−252525−25000000000000000000000000000000000000000
χ671616-16-16000000-44-44000000000000000000000000000000000000000000000000000000
χ6816-1616-16000000-444-4000000000000000000000000000000000000000000000000000000

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