Finite Group Databasebeta

← Group #13017781

Character table — Group #13017781

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122444444448888888888888888810101010101016161616161616161620202040404040404040404040404040404040408080
order12224444445101010444442020202020202020202020202244442020202020202020204444444488888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−ii−i
χ41111111111111111111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−ii
χ511111111111111-1-1-11-1111111-1-1-1-111111111111-1-1-1-1-1-1111-11-1-1-11111-1-1-1-11111-1-1
χ611111111111111-1-1-11-1111111-1-1-1-111111111111-1-1-1-1-1-1111-11-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111-1-1-11-1111111-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11-1111ii−i−i−i−iiiii−i−i−ii
χ811111111111111-1-1-11-1111111-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11-1111−i−iiiii−i−i−i−iiii−i
χ9111111-1-111111111-1-1-111-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-11-1-111-111111111-1-1-1-1-1-1
χ10111111-1-111111111-1-1-111-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1111111
χ11111111-1-111111111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-11111-1-111-111-1-11ii−i−iii−i−i−i−iii−ii
χ12111111-1-111111111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-11111-1-111-111-1-11−i−iii−i−iiiii−i−ii−i
χ13111111-1-1111111-1-11-1111-1-1-1-11111111111111-1-1-1-1-1-111-1-111-1-1-111111-1-1-1-1-1-1-1-111
χ14111111-1-1111111-1-11-1111-1-1-1-11111111111111-1-1-1-1-1-111-1-111-1-1-11-1-1-1-111111111-1-1
χ15111111-1-1111111-1-11-1111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-1111-1ii−i−i−i−iii−i−iiii−i
χ16111111-1-1111111-1-11-1111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-1111-1−i−iiiii−i−iii−i−i−ii
χ1722222222-2-22222000-202222220000-2-2222-2-22-2-2-200000022-20-200000000000000000
χ1822222222-2-22222000-202222220000-2-2-2-2-222-2-2-2-2000000-2-220200000000000000000
χ19222222-2-2-2-222220002022-2-2-2-20000-2-2222-2-22-222000000-2-2-20200000000000000000
χ20222222-2-2-2-222220002022-2-2-2-20000-2-2-2-2-222-2-2220000002220-200000000000000000
χ212222-2-2002-222220020-2-2-20000-2-2-2-22222-222-2-20000002200-2-2000200000000000000
χ222222-2-2002-222220020-2-2-20000-2-2-2-222-2-22-2-22-2000000220022000-200000000000000
χ232222-2-2002-2222200-202-2-2000022222222-222-2-2000000-2-200-22000-200000000000000
χ242222-2-2002-2222200-202-2-20000222222-2-22-2-22-2000000-2-2002-2000200000000000000
χ252222-2-200-2222222-2000-2-200000000-2-222-2-2-2-220022-2-200002002-2000000000000000
χ262222-2-200-2222222-2000-2-200000000-2-2-2-2222220022-2-20000-200-22000000000000000
χ272222-2-200-222222-22000-2-200000000-2-222-2-2-2-2200-2-2220000200-22000000000000000
χ282222-2-200-222222-22000-2-200000000-2-2-2-22222200-2-2220000-2002-2000000000000000
χ2922-2-22-22-20022-2-2000002-222-2-20000002-2200-20000000002-20000002−22−200002−22−200
χ3022-2-22-22-20022-2-2000002-222-2-20000002-2200-20000000002-2000000−22−220000−22−2200
χ3122-2-22-22-20022-2-2000002-222-2-2000000-22-2002000000000-22000000i2−i2−i2i20000i2−i2−i2i200
χ3222-2-22-22-20022-2-2000002-222-2-2000000-22-2002000000000-22000000−i2i2i2−i20000−i2i2i2−i200
χ3322-2-22-2-220022-2-2000002-2-2-2220000002-2200-2000000000-220000002−22−20000−22−2200
χ3422-2-22-2-220022-2-2000002-2-2-2220000002-2200-2000000000-22000000−22−2200002−22−200
χ3522-2-22-2-220022-2-2000002-2-2-222000000-22-20020000000002-2000000i2−i2−i2i20000−i2i2i2−i200
χ3622-2-22-2-220022-2-2000002-2-2-222000000-22-20020000000002-2000000−i2i2i2−i20000i2−i2−i2i200
χ374444444444-1-1-1-144444-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-10000000000000000000000
χ384444444444-1-1-1-1-4-4-44-4-1-1-1-1-1-11111-1-1000000-1-1-11111110000000000000000000000
χ3944444444-4-4-1-1-1-1000-40-1-1-1-1-1-155−5−5110000001115−55−55−50000000000000000000000
χ4044444444-4-4-1-1-1-1000-40-1-1-1-1-1-1−5−55511000000111−55−55−550000000000000000000000
χ41444444-4-444-1-1-1-144-4-4-4-1-111111111-1-1000000-111-1-1-1-1110000000000000000000000
χ42444444-4-444-1-1-1-1-4-44-44-1-11111-1-1-1-1-1-1000000-1111111-1-10000000000000000000000
χ43444444-4-4-4-4-1-1-1-100040-1-1111155−5−5110000001-1-1−55−555−50000000000000000000000
χ44444444-4-4-4-4-1-1-1-100040-1-11111−5−555110000001-1-15−55−5−550000000000000000000000
χ454444-4-4004-4-1-1-1-10040-4115−55−51111-1-100000015−55−5−55-1-10000000000000000000000
χ464444-4-4004-4-1-1-1-10040-411−55−551111-1-10000001−55−555−5-1-10000000000000000000000
χ474444-4-4004-4-1-1-1-100-404115−55−5-1-1-1-1-1-100000015−5−555−5110000000000000000000000
χ484444-4-4004-4-1-1-1-100-40411−55−55-1-1-1-1-1-10000001−555−5−55110000000000000000000000
χ494444-4-400-44-1-1-1-14-4000115−55−5−5−55511000000-1−55-1-1115−50000000000000000000000
χ504444-4-400-44-1-1-1-14-400011−55−5555−5−511000000-15−5-1-111−550000000000000000000000
χ514444-4-400-44-1-1-1-1-44000115−55−555−5−511000000-1−5511-1-1−550000000000000000000000
χ524444-4-400-44-1-1-1-1-4400011−55−55−5−55511000000-15−511-1-15−50000000000000000000000
χ5344-4-4-44000044-4-400000-4400000000004-4-40040000000000000000000000000000000
χ5444-4-4-44000044-4-400000-440000000000-44400-40000000000000000000000000000000
χ554-4-440000004-44-4000000000000000000004i−4i0000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000
χ564-4-440000004-44-4000000000000000000004i−4i00000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000
χ574-4-440000004-44-400000000000000000000−4i4i0000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000
χ584-4-440000004-44-400000000000000000000−4i4i00000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000
χ5988-8-88-88-800-2-22200000-22-2-2220000000000000000000000000000000000000000000
χ6088-8-88-8-8800-2-22200000-2222-2-20000000000000000000000000000000000000000000
χ6188-8-8-880000-2-222000002-225−25−25250000000000000000000000000000000000000000000
χ6288-8-8-880000-2-222000002-2−252525−250000000000000000000000000000000000000000000
χ638-88-80000008-8-88000000000000000000000000000000000000000000000000000000
χ648-88-8000000-222-200000000000−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ3825−250000000000000000000000000000000000000
χ658-88-8000000-222-2000000000002ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38−25250000000000000000000000000000000000000
χ668-88-8000000-222-2000000000002ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ3825−250000000000000000000000000000000000000
χ678-88-8000000-222-200000000000−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ38−25250000000000000000000000000000000000000
χ6816-16-1616000000-44-44000000000000000000000000000000000000000000000000000000

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