Finite Group Databasebeta

← Group #13017780

Character table — Group #13017780

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
χ5111111111111111-1-1-1-111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ6111111111111111-1-1-1-111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−ii
χ8111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiii−i
χ9111111-1-1111111-111-1-11111-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-11-1-111-111111111-1-1-1-1-1-1
χ10111111-1-1111111-111-1-11111-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1111111
χ11111111-1-1111111-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-111-1-11ii−i−iii−i−i−i−iii−ii
χ12111111-1-1111111-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-111-1-11−i−iii−i−iiiii−i−ii−i
χ13111111-1-1111111-1-1-1111111-1-1-1-111111111111-1-1-1-1-1-111-1-11-11-1-111111-1-1-1-1-1-1-1-111
χ14111111-1-1111111-1-1-1111111-1-1-1-111111111111-1-1-1-1-1-111-1-11-11-1-11-1-1-1-111111111-1-1
χ15111111-1-1111111-1-1-1111111-1-1-1-11111-1-1-1-1-1-11-1-1-1-1-1-11111-11-111-1ii−i−i−i−iii−i−iiii−i
χ16111111-1-1111111-1-1-1111111-1-1-1-11111-1-1-1-1-1-11-1-1-1-1-1-11111-11-111-1−i−iiiii−i−iii−i−i−ii
χ1722222222-2-22222-2000022-2-222220000222-2-22-2-2-200000022-2-2000000000000000000
χ1822222222-2-22222-2000022-2-222220000-2-2-222-2-2-2-2000000-2-222000000000000000000
χ19222222-2-2-2-222222000022-2-2-2-2-2-20000222-2-22-222000000-2-2-22000000000000000000
χ20222222-2-2-2-222222000022-2-2-2-2-2-20000-2-2-222-2-222000000222-2000000000000000000
χ212222-2-2002-2222202-200-2-2-2-20000000022-2-2-2-220022-2-200002002-2000000000000000
χ222222-2-2002-2222202-200-2-2-2-200000000-2-2222220022-2-20000-200-22000000000000000
χ232222-2-2002-222220-2200-2-2-2-20000000022-2-2-2-2200-2-2220000200-22000000000000000
χ242222-2-2002-222220-2200-2-2-2-200000000-2-22222200-2-2220000-2002-2000000000000000
χ252222-2-200-2222220002-2-2-2220000-2-2-2-222-222-2-20000002200-20-200200000000000000
χ262222-2-200-2222220002-2-2-2220000-2-2-2-2-2-22-2-22-2000000220020200-200000000000000
χ272222-2-200-222222000-22-2-2220000222222-222-2-2000000-2-200-20200-200000000000000
χ282222-2-200-222222000-22-2-22200002222-2-22-2-22-2000000-2-20020-200200000000000000
χ2922-2-22-22-20022-2-2000002-20022-2-200002-2200-20000000002-20000002−22−200002−22−200
χ3022-2-22-22-20022-2-2000002-20022-2-200002-2200-20000000002-2000000−22−220000−22−2200
χ3122-2-22-22-20022-2-2000002-20022-2-20000-22-2002000000000-22000000i2−i2−i2i20000i2−i2−i2i200
χ3222-2-22-22-20022-2-2000002-20022-2-20000-22-2002000000000-22000000−i2i2i2−i20000−i2i2i2−i200
χ3322-2-22-2-220022-2-2000002-200-2-22200002-2200-2000000000-220000002−22−20000−22−2200
χ3422-2-22-2-220022-2-2000002-200-2-22200002-2200-2000000000-22000000−22−2200002−22−200
χ3522-2-22-2-220022-2-2000002-200-2-2220000-22-20020000000002-2000000i2−i2−i2i20000−i2i2i2−i200
χ3622-2-22-2-220022-2-2000002-200-2-2220000-22-20020000000002-2000000−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
χ384444444444-1-1-1-14-4-4-4-4-1-1-1-1-1-1-1-11111000000-1-1-11111110000000000000000000000
χ3944444444-4-4-1-1-1-1-40000-1-111-1-1-1-155−5−50000001115−55−55−50000000000000000000000
χ4044444444-4-4-1-1-1-1-40000-1-111-1-1-1-1−5−555000000111−55−55−550000000000000000000000
χ41444444-4-444-1-1-1-1-444-4-4-1-1-1-111111111000000-111-1-1-1-1110000000000000000000000
χ42444444-4-444-1-1-1-1-4-4-444-1-1-1-11111-1-1-1-1000000-1111111-1-10000000000000000000000
χ43444444-4-4-4-4-1-1-1-140000-1-111111155−5−50000001-1-1−55−555−50000000000000000000000
χ44444444-4-4-4-4-1-1-1-140000-1-1111111−5−5550000001-1-15−55−5−550000000000000000000000
χ454444-4-4004-4-1-1-1-104-40011115−55−555−5−5000000-15−5-1-111−550000000000000000000000
χ464444-4-4004-4-1-1-1-104-4001111−55−55−5−555000000-1−55-1-1115−50000000000000000000000
χ474444-4-4004-4-1-1-1-10-440011115−55−5−5−555000000-15−511-1-15−50000000000000000000000
χ484444-4-4004-4-1-1-1-10-44001111−55−5555−5−5000000-1−5511-1-1−550000000000000000000000
χ494444-4-400-44-1-1-1-10004-411-1-15−55−511110000001−55−555−5-1-10000000000000000000000
χ504444-4-400-44-1-1-1-10004-411-1-1−55−55111100000015−55−5−55-1-10000000000000000000000
χ514444-4-400-44-1-1-1-1000-4411-1-15−55−5-1-1-1-10000001−555−5−55110000000000000000000000
χ524444-4-400-44-1-1-1-1000-4411-1-1−55−55-1-1-1-100000015−5−555−5110000000000000000000000
χ5344-4-4-44000044-4-400000-4400000000004-4-40040000000000000000000000000000000
χ5444-4-4-44000044-4-400000-440000000000-44400-40000000000000000000000000000000
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
χ5988-8-88-88-800-2-22200000-2200-2-22200000000000000000000000000000000000000000
χ6088-8-88-8-8800-2-22200000-220022-2-200000000000000000000000000000000000000000
χ6188-8-8-880000-2-222000002-20025−25−252500000000000000000000000000000000000000000
χ6288-8-8-880000-2-222000002-200−252525−2500000000000000000000000000000000000000000
χ638-8-880000008-88-8000000000000000000000000000000000000000000000000000000
χ648-8-88000000-22-22000000025−250000−2ζ4+2ζ12−2ζ28+2ζ362ζ4−2ζ12+2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ360000000000000000000000000000000000000
χ658-8-88000000-22-22000000025−2500002ζ4−2ζ12+2ζ28−2ζ36−2ζ4+2ζ12−2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ360000000000000000000000000000000000000
χ668-8-88000000-22-220000000−25250000−2ζ4−2ζ12+2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ362ζ4−2ζ12+2ζ28−2ζ36−2ζ4+2ζ12−2ζ28+2ζ360000000000000000000000000000000000000
χ678-8-88000000-22-220000000−252500002ζ4+2ζ12−2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ36−2ζ4+2ζ12−2ζ28+2ζ362ζ4−2ζ12+2ζ28−2ζ360000000000000000000000000000000000000
χ6816-1616-16000000-444-4000000000000000000000000000000000000000000000000000000

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