Finite Group Databasebeta

← Group #13019947

Character table — Group #13019947

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111122224444444444488888888888888810101010161616161616161616202020202020202040404040404040404040404040808080
order12222244444510101010101010488202020204040404040404040444442020202020202020444488884888888888888488
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1ii−i−i-1-1-1iii−i−i−iii−i−i-1i−i
χ41111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1−i−iii-1-1-1−i−i−iiii−i−iii-1−ii
χ511111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111111-1-1111111-1-1-1-1-1-1-1
χ611111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-11111-111
χ711111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i-111iii−i−i−i−i−iii1−ii
χ811111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii-111−i−i−iiiiii−i−i1i−i
χ9111111111-1-111111111-1111111111111111111-1-1-1-1-1-1-1-1-11-1-111111-1111-1-11-1-11111-1-1-1
χ10111111111-1-111111111-1111111111111111111-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-111-111-111-1-1-1-1-111
χ11111111111-1-111111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1ii−i−i1-1-1i−i−i−iiiii−i−i1−ii
χ12111111111-1-111111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1−i−iii1-1-1−iiii−i−i−i−iii1i−i
χ13111111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-111111-1-1-11-1-11-1-1-1-1-1-1111
χ14111111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-111-11111111-1-1
χ15111111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111-1ii−i−i111i−i−i−iii−i−iii-1i−i
χ16111111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111-1−i−iii111−iiii−i−iii−i−i-1−ii
χ17222222-2-2-20022222222000-2-2-2-2000000002222000000000-200-22222000-200-2000000000
χ18222222-2-2-20022222222000-2-2-2-2000000002222000000000-200-2-2-2-2-20002002000000000
χ19222222-2-2-20022222222000-2-2-2-200000000-2-2-2-200000000020022i2i−2i−2i000−2i002i000000000
χ20222222-2-2-20022222222000-2-2-2-200000000-2-2-2-20000000002002−2i−2i2i2i0002i00−2i000000000
χ212222-2-222-22222-2-2-2-222-2002-2-220000000022-2-20000022-2-2-2-2-2200002000000000000000
χ222222-2-222-22222-2-2-2-222-2002-2-2200000000-2-2220000022-2-2222-20000-2000000000000000
χ232222-2-222-2-2-222-2-2-2-2222002-2-220000000022-2-200000-2-222-22220000-2000000000000000
χ242222-2-222-2-2-222-2-2-2-2222002-2-2200000000-2-22200000-2-2222-2-2-200002000000000000000
χ252222-2-2-2-220022-2-2-2-222000-222-20000000022-2-2000000000200-2000000002i−2i02i−2i0000000
χ262222-2-2-2-220022-2-2-2-222000-222-20000000022-2-2000000000200-200000000−2i2i0−2i2i0000000
χ272222-2-2-2-220022-2-2-2-222000-222-200000000-2-222000000000-2002000000002-20-220000000
χ282222-2-2-2-220022-2-2-2-222000-222-200000000-2-222000000000-200200000000-2202-20000000
χ292-2-222-2000002-222-2-22-20i2−i20000i2i2i2i2−i2−i2−i2−i22i−2i2i−2i0000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3902−20000001−i−1+i1+i−1−i000
χ302-2-222-2000002-222-2-22-20i2−i20000i2i2i2i2−i2−i2−i2−i22i−2i2i−2i00000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3902−2000000−1+i1−i−1−i1+i000
χ312-2-222-2000002-222-2-22-20i2−i20000i2i2i2i2−i2−i2−i2−i2−2i2i−2i2i0000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370−220000001+i−1−i1−i−1+i000
χ322-2-222-2000002-222-2-22-20i2−i20000i2i2i2i2−i2−i2−i2−i2−2i2i−2i2i00000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370−22000000−1−i1+i−1+i1−i000
χ332-2-222-2000002-222-2-22-20−i2i20000−i2−i2−i2−i2i2i2i2i22i−2i2i−2i0000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390−22000000−1+i1−i−1−i1+i000
χ342-2-222-2000002-222-2-22-20−i2i20000−i2−i2−i2−i2i2i2i2i22i−2i2i−2i00000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390−220000001−i−1+i1+i−1−i000
χ352-2-222-2000002-222-2-22-20−i2i20000−i2−i2−i2−i2i2i2i2i2−2i2i−2i2i0000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3702−2000000−1−i1+i−1+i1−i000
χ362-2-222-2000002-222-2-22-20−i2i20000−i2−i2−i2−i2i2i2i2i2−2i2i−2i2i00000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3702−20000001+i−1−i1−i−1+i000
χ3744444444444-1-1-1-1-1-1-1-1444-1-1-1-1-1-1-1-1-1-1-1-100004-1-1-1-1-1-1-1-1000000000000000000000000
χ3844444444444-1-1-1-1-1-1-1-14-4-4-1-1-1-1111111110000-41111-1-1-1-1000000000000000000000000
χ39444444444-4-4-1-1-1-1-1-1-1-1-444-1-1-1-1-1-1-1-1-1-1-1-10000-411111111000000000000000000000000
χ40444444444-4-4-1-1-1-1-1-1-1-1-4-4-4-1-1-1-11111111100004-1-1-1-11111000000000000000000000000
χ414444-4-444-444-1-11111-1-1-400-111-155−5−555−5−50000055−5−5-1-111000000000000000000000000
χ424444-4-444-444-1-11111-1-1-400-111-1−5−555−5−55500000−5−555-1-111000000000000000000000000
χ434444-4-444-4-4-4-1-11111-1-1400-111-155−5−555−5−500000−5−55511-1-1000000000000000000000000
χ444444-4-444-4-4-4-1-11111-1-1400-111-1−5−555−5−5550000055−5−511-1-1000000000000000000000000
χ4544-4-4004-404-44-40000-44000400-4000000000000000004-400000000000000000000000000
χ4644-4-4004-404-4-115−55−51-1000-15−51−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ3800000−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38-115−5000000000000000000000000
χ4744-4-4004-404-4-115−55−51-1000-15−51ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ3800000ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38-115−5000000000000000000000000
χ4844-4-4004-404-4-11−55−551-1000-1−551ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ3800000ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38-11−55000000000000000000000000
χ4944-4-4004-404-4-11−55−551-1000-1−551−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ3800000−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38-11−55000000000000000000000000
χ5044-4-4004-40-444-40000-44000400-400000000000000000-4400000000000000000000000000
χ5144-4-4004-40-44-115−55−51-1000-15−51−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ3800000ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ381-1−55000000000000000000000000
χ5244-4-4004-40-44-115−55−51-1000-15−51ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ3800000−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ381-1−55000000000000000000000000
χ5344-4-4004-40-44-11−55−551-1000-1−551ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ3800000−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ381-15−5000000000000000000000000
χ5444-4-4004-40-44-11−55−551-1000-1−551−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ3800000ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ381-15−5000000000000000000000000
χ5544-4-400-440004-40000-44000-400400000000000000000000004i−4i000000000000000000000
χ5644-4-400-440004-40000-44000-40040000000000000000000000−4i4i000000000000000000000
χ574-4-44-44000004-4-4-4444-40000000000000004i−4i−4i4i000000000000000000000000000000000
χ584-4-44-44000004-4-4-4444-4000000000000000−4i4i4i−4i000000000000000000000000000000000
χ59888888-8-8-800-2-2-2-2-2-2-2-20002222000000000000000000000000000000000000000000000
χ608888-8-8-8-8800-2-22222-2-20002-2-22000000000000000000000000000000000000000000000
χ6188-8-800-88000-2225−2525−252-20002−2525-2000000000000000000000000000000000000000000000
χ6288-8-800-88000-22−2525−25252-2000225−25-2000000000000000000000000000000000000000000000
χ638-88-80000000880000-8-80000000000000000000000000000000000000000000000000000
χ648-88-80000000-2-225−25−2525220000000ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ390000000000000000000000000000000000000
χ658-88-80000000-2-225−25−2525220000000−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ390000000000000000000000000000000000000
χ668-88-80000000-2-2−252525−25220000000−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ390000000000000000000000000000000000000
χ678-88-80000000-2-2−252525−25220000000ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ390000000000000000000000000000000000000
χ688-8-888-800000-22-2-222-2204i2−4i20000−i2−i2−i2−i2i2i2i2i20000000000000000000000000000000000000
χ698-8-888-800000-22-2-222-220−4i24i20000i2i2i2i2−i2−i2−i2−i20000000000000000000000000000000000000
χ708-8-88-8800000-2222-2-2-220000000i10i10−i10−i10−i10−i10i10i100000000000000000000000000000000000000
χ718-8-88-8800000-2222-2-2-220000000−i10−i10i10i10i10i10−i10−i100000000000000000000000000000000000000

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