Finite Group Databasebeta

← Group #13017779

Character table — Group #13017779

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122444444448888888888888888810101010101016161616161616161620202040404040404040404040404040404040408080
order12224422445101010444441010101020202020202020202244442020202020202020202244444488888888888844
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
χ511111111111111-1-1-11-111111111-1-1-1-111111111-1-11-1-1-1-1111-11-1-1-11111-1-1-1-11111-1-1
χ611111111111111-1-1-11-111111111-1-1-1-111111111-1-11-1-1-1-1111-11-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111-1-1-11-111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1-11-1111ii−i−i−i−iiiii−i−i−ii
χ811111111111111-1-1-11-111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1-11-1111−i−iiiii−i−i−i−iiii−i
χ9111111-1-111111111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111111-1-11-1-111-111111111-1-1-1-1-1-1
χ10111111-1-111111111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111111-1-11-1-111-1-1-1-1-1-1-1-1-1111111
χ11111111-1-111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-111-1-11ii−i−iii−i−i−i−iii−ii
χ12111111-1-111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-111-1-11−i−iii−i−iiiii−i−ii−i
χ13111111-1-1111111-1-11-11-1-1-1-111111111111111-1-1111-1-1-1-1-1-111-1-1-111111-1-1-1-1-1-1-1-111
χ14111111-1-1111111-1-11-11-1-1-1-111111111111111-1-1111-1-1-1-1-1-111-1-1-11-1-1-1-111111111-1-1
χ15111111-1-1111111-1-11-11-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1111-1ii−i−i−i−iii−i−iiii−i
χ16111111-1-1111111-1-11-11-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1111-1−i−iiiii−i−iii−i−i−ii
χ1722222222-2-22222000-20222222-2-20000222-2-22-2-200-2000022-20-200000000000000000
χ1822222222-2-22222000-20222222-2-20000-2-2-222-2-2-200-20000-2-220200000000000000000
χ19222222-2-2-2-2222200020-2-2-2-222-2-20000222-2-222200-20000-2-2-20200000000000000000
χ20222222-2-2-2-2222200020-2-2-2-222-2-20000-2-2-222-22200-200002220-200000000000000000
χ212222-2-2002-222222-20000000-2-2-2-2000022-2-2-2-20000222-2-2002002-2000000000000000
χ222222-2-2002-222222-20000000-2-2-2-20000-2-222220000222-2-200-200-22000000000000000
χ232222-2-2002-22222-220000000-2-2-2-2000022-2-2-2-200002-2-22200200-22000000000000000
χ242222-2-2002-22222-220000000-2-2-2-20000-2-2222200002-2-22200-2002-2000000000000000
χ252222-2-200-2222220020-20000-2-222222222-222-200-2-2-2000000-2-2000200000000000000
χ262222-2-200-2222220020-20000-2-2222222-2-22-2-2200-2-2-200000022000-200000000000000
χ272222-2-200-22222200-2020000-2-222-2-2-2-222-222-20022-2000000-22000-200000000000000
χ282222-2-200-22222200-2020000-2-222-2-2-2-2-2-22-2-220022-20000002-2000200000000000000
χ2922-2-22-22-20022-2-20000022-2-22-20000002-2200-20000000002-20000002−22−200002−22−200
χ3022-2-22-22-20022-2-20000022-2-22-20000002-2200-20000000002-2000000−22−220000−22−2200
χ3122-2-22-22-20022-2-20000022-2-22-2000000-22-2002000000000-22000000i2−i2−i2i20000i2−i2−i2i200
χ3222-2-22-22-20022-2-20000022-2-22-2000000-22-2002000000000-22000000−i2i2i2−i20000−i2i2i2−i200
χ3322-2-22-2-220022-2-200000-2-2222-20000002-2200-2000000000-220000002−22−20000−22−2200
χ3422-2-22-2-220022-2-200000-2-2222-20000002-2200-2000000000-22000000−22−2200002−22−200
χ3522-2-22-2-220022-2-200000-2-2222-2000000-22-20020000000002-2000000i2−i2−i2i20000−i2i2i2−i200
χ3622-2-22-2-220022-2-200000-2-2222-2000000-22-20020000000002-2000000−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
χ384444444444-1-1-1-1-4-4-44-4-1-1-1-1-1-1-1-11111000000-1-111-111110000000000000000000000
χ3944444444-4-4-1-1-1-1000-40-1-1-1-1-1-11155−5−5000000115−515−55−50000000000000000000000
χ4044444444-4-4-1-1-1-1000-40-1-1-1-1-1-111−5−55500000011−551−55−550000000000000000000000
χ41444444-4-444-1-1-1-144-4-4-41111-1-1-1-111110000001111-1-1-1-1-10000000000000000000000
χ42444444-4-444-1-1-1-1-4-44-441111-1-1-1-1-1-1-1-100000011-1-1-111110000000000000000000000
χ43444444-4-4-4-4-1-1-1-1000401111-1-11155−5−5000000-1-15−51−55−550000000000000000000000
χ44444444-4-4-4-4-1-1-1-1000401111-1-111−5−555000000-1-1−5515−55−50000000000000000000000
χ454444-4-4004-4-1-1-1-14-40005−55−5111155−5−50000005−5−55-1-1-1110000000000000000000000
χ464444-4-4004-4-1-1-1-14-4000−55−551111−5−555000000−555−5-1-1-1110000000000000000000000
χ474444-4-4004-4-1-1-1-1-440005−55−51111−5−5550000005−55−5-111-1-10000000000000000000000
χ484444-4-4004-4-1-1-1-1-44000−55−55111155−5−5000000−55−55-111-1-10000000000000000000000
χ494444-4-400-44-1-1-1-10040-45−55−511-1-1-1-1-1-1000000−551115−5−550000000000000000000000
χ504444-4-400-44-1-1-1-10040-4−55−5511-1-1-1-1-1-10000005−5111−555−50000000000000000000000
χ514444-4-400-44-1-1-1-100-4045−55−511-1-11111000000−55-1-11−555−50000000000000000000000
χ524444-4-400-44-1-1-1-100-404−55−5511-1-111110000005−5-1-115−5−550000000000000000000000
χ5344-4-4-44000044-4-4000000000-440000004-4-40040000000000000000000000000000000
χ5444-4-4-44000044-4-4000000000-44000000-44400-40000000000000000000000000000000
χ554-44-40000004-4-44000000000000000000004i−4i0000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000
χ564-44-40000004-4-44000000000000000000004i−4i00000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000
χ574-44-40000004-4-4400000000000000000000−4i4i0000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000
χ584-44-40000004-4-4400000000000000000000−4i4i00000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000
χ5988-8-88-88-800-2-22200000-2-222-220000000000000000000000000000000000000000000
χ6088-8-88-8-8800-2-2220000022-2-2-220000000000000000000000000000000000000000000
χ6188-8-8-880000-2-2220000025−25−25252-20000000000000000000000000000000000000000000
χ6288-8-8-880000-2-22200000−252525−252-20000000000000000000000000000000000000000000
χ638-8-880000008-88-8000000000000000000000000000000000000000000000000000000
χ648-8-88000000-22-220000000000025−25−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ380000000000000000000000000000000000000
χ658-8-88000000-22-220000000000025−252ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ380000000000000000000000000000000000000
χ668-8-88000000-22-2200000000000−25252ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ380000000000000000000000000000000000000
χ678-8-88000000-22-2200000000000−2525−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ380000000000000000000000000000000000000
χ6816-1616-16000000-444-4000000000000000000000000000000000000000000000000000000

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