Finite Group Databasebeta

← Group #13017557

Character table — Group #13017557

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122444444448888888888810101010101010101616161616161616161616162020202020202020202040404040404040404080808080
order12222244445101010444441010202020204444444420202020202020202020202044888888882224488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1iiii−i−i−i−i-1-1-1-1-1ii−i−iii−i−i
χ41111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1−i−i−i−iiiii-1-1-1-1-1−i−iii−i−iii
χ5111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-1
χ6111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ7111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i-11111ii−i−i−i−iii
χ8111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii-11111−i−iiiii−i−i
χ911111111-1-11111-11-11-111-1-1-1-11111111111-1-111-1-111-1-1-1-111111111-11-11-1-1-1-1-11-11-1
χ1011111111-1-11111-11-11-111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-11-11
χ1111111111-1-11111-11-11-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111iiii−i−i−i−i1-11-11−i−iiii−i−ii
χ1211111111-1-11111-11-11-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111−i−i−i−iiiii1-11-11ii−i−i−iii−i
χ1311111111-1-11111-1-11-1111-1-1-1-111111111-1-11111-1-1-1-111-1-111111111-1-11-11-1-1-1-1-11-11
χ1411111111-1-11111-1-11-1111-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1111111-11-1
χ1511111111-1-11111-1-11-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i11-11-1−i−iii−iii−i
χ1611111111-1-11111-1-11-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii11-11-1ii−i−ii−i−ii
χ17222222-2-2222222-200002222222222-2-2-2-20000-2-2-2-200002200000000-2000000000000
χ18222222-2-2222222-20000222222-2-2-2-222220000-2-2-2-20000-2-2000000002000000000000
χ19222222-2-2-2-222222000022-2-2-2-22222-2-2-2-20000-2-2220000-2-2000000002000000000000
χ20222222-2-2-2-222222000022-2-2-2-2-2-2-2-222220000-2-22200002200000000-2000000000000
χ212222-2-22-20022220020-2-2-2000022-2-222-2-200-2-22-2000022000000000000-20200000000
χ222222-2-22-20022220020-2-2-20000-2-222-2-22200-2-22-200002200000000000020-200000000
χ232222-2-22-200222200-202-2-2000022-2-222-2-200222-20000-2-200000000000020-200000000
χ242222-2-22-200222200-202-2-20000-2-222-2-22200222-20000-2-2000000000000-20200000000
χ252222-2-2-22002222020-20-2-2000022-2-2-2-222-2-200-220022000000000000020-2000000000
χ262222-2-2-22002222020-20-2-20000-2-22222-2-2-2-200-2200220000000000000-202000000000
χ272222-2-2-220022220-2020-2-2000022-2-2-2-2222200-2200-2-20000000000000-202000000000
χ282222-2-2-220022220-2020-2-20000-2-22222-2-22200-2200-2-2000000000000020-2000000000
χ292-2-222-2002-222-2-2000002-222-2-22i−2i2i−2i00000000000000002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000001+i−1−i1−i−1+i0000
χ302-2-222-2002-222-2-2000002-222-2-22i−2i2i−2i00000000000000002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000−1−i1+i−1+i1−i0000
χ312-2-222-2002-222-2-2000002-222-2-2−2i2i−2i2i0000000000000000−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000001−i−1+i1+i−1−i0000
χ322-2-222-2002-222-2-2000002-222-2-2−2i2i−2i2i0000000000000000−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000−1+i1−i−1−i1+i0000
χ332-2-222-200-2222-2-2000002-2-2-2222i−2i2i−2i0000000000000000−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000−1−i1+i−1+i1−i0000
χ342-2-222-200-2222-2-2000002-2-2-2222i−2i2i−2i0000000000000000−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000001+i−1−i1−i−1+i0000
χ352-2-222-200-2222-2-2000002-2-2-222−2i2i−2i2i00000000000000002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000−1+i1−i−1−i1+i0000
χ362-2-222-200-2222-2-2000002-2-2-222−2i2i−2i2i00000000000000002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000001−i−1+i1+i−1−i0000
χ374444444444-1-1-1-144444-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ384444444444-1-1-1-14-4-4-4-4-1-1-1-1-1-1000000001111-1-1-1-1111100000000000000000000000
χ3944444444-4-4-1-1-1-1-44-44-4-1-1111100000000-1-111-1-111-1-11100000000000000000000000
χ4044444444-4-4-1-1-1-1-4-44-44-1-111110000000011-1-1-1-11111-1-100000000000000000000000
χ41444444-4-444-1-1-1-1-40000-1-1-1-1-1-1000000005−55−511115−55−500000000000000000000000
χ42444444-4-444-1-1-1-1-40000-1-1-1-1-1-100000000−55−551111−55−5500000000000000000000000
χ43444444-4-4-4-4-1-1-1-140000-1-11111000000005−5−5511-1-15−5−5500000000000000000000000
χ44444444-4-4-4-4-1-1-1-140000-1-1111100000000−555−511-1-1−555−500000000000000000000000
χ454444-4-44-400-1-1-1-10040-4115−55−5000000005−511-115−5−55-1-100000000000000000000000
χ464444-4-44-400-1-1-1-10040-411−55−5500000000−5511-11−555−5-1-100000000000000000000000
χ474444-4-44-400-1-1-1-100-404115−55−500000000−55-1-1-115−55−51100000000000000000000000
χ484444-4-44-400-1-1-1-100-40411−55−55000000005−5-1-1-11−55−551100000000000000000000000
χ494444-4-4-4400-1-1-1-1040-40115−55−500000000115−51-1−55-1-1−5500000000000000000000000
χ504444-4-4-4400-1-1-1-1040-4011−55−550000000011−551-15−5-1-15−500000000000000000000000
χ514444-4-4-4400-1-1-1-10-4040115−55−500000000-1-1−551-1−55115−500000000000000000000000
χ524444-4-4-4400-1-1-1-10-404011−55−5500000000-1-15−51-15−511−5500000000000000000000000
χ5344-4-40000004-4-440000000000000004i−4i0000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000000
χ5444-4-40000004-4-440000000000000004i−4i00000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000000
χ5544-4-40000004-4-44000000000000000−4i4i0000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000000
χ5644-4-40000004-4-44000000000000000−4i4i00000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000000
χ574-44-40000004-44-4000000000000000004i−4i00000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000000
χ584-44-40000004-44-4000000000000000004i−4i000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000000
χ594-44-40000004-44-400000000000000000−4i4i00000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000000
χ604-44-40000004-44-400000000000000000−4i4i000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000000
χ614-4-44-44000044-4-400000-4400004i−4i−4i4i000000000000000000000000000000000000000
χ624-4-44-44000044-4-400000-440000−4i4i4i−4i000000000000000000000000000000000000000
χ638-8-888-8008-8-2-22200000-22-2-2220000000000000000000000000000000000000000000
χ648-8-888-800-88-2-22200000-2222-2-20000000000000000000000000000000000000000000
χ658-8-88-880000-2-222000002-225−25−25250000000000000000000000000000000000000000000
χ668-8-88-880000-2-222000002-2−252525−250000000000000000000000000000000000000000000
χ671616-16-16000000-444-4000000000000000000000000000000000000000000000000000000
χ6816-1616-16000000-44-44000000000000000000000000000000000000000000000000000000

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