Finite Group Databasebeta

← Group #13015113

Character table — Group #13015113

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111114444444444444488888888888810101010101010101616161616161616161620202020404040404040404040404040404040408080
order12222222444444510101010101010202020202020202020202020444444442210101010101010104444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ91111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111111-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11-1
χ101111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111111-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1111-1
χ111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-11-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-111-11
χ121111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-11-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111-1-1-11
χ131111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii-11
χ141111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i-11
χ151111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111ii−i−i−i−iii−i−iiiii−i−i1-1
χ161111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111−i−iiiii−i−iii−i−i−i−iii1-1
χ1722222222-2-222-2-222222222-2-2-2-22222-2-2-2-22222-2-2-2-2000000000022-2-2000000000000000000
χ1822222222-2-222-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-222220000000000-2-222000000000000000000
χ1922222222-2-2-2-22222222222-2-2-2-2-2-2-2-222222222-2-2-2-20000000000-2-222000000000000000000
χ2022222222-2-2-2-22222222222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000022-2-2000000000000000000
χ2122-222-2-2-2002-200222-2-22-2-2000022-2-2000000002i2i−2i−2i0000000000002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ2222-222-2-2-2002-200222-2-22-2-2000022-2-2000000002i2i−2i−2i0000000000002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ2322-222-2-2-2002-200222-2-22-2-2000022-2-200000000−2i−2i2i2i000000000000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ2422-222-2-2-2002-200222-2-22-2-2000022-2-200000000−2i−2i2i2i000000000000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ2522-222-2-2-200-2200222-2-22-2-20000-2-222000000002i2i−2i−2i000000000000−2i2i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ2622-222-2-2-200-2200222-2-22-2-20000-2-222000000002i2i−2i−2i000000000000−2i2i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ2722-222-2-2-200-2200222-2-22-2-20000-2-22200000000−2i−2i2i2i0000000000002i−2i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ2822-222-2-2-200-2200222-2-22-2-20000-2-22200000000−2i−2i2i2i0000000000002i−2i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ292-222-22-2-22-2000022-22-2-22-222-2-2000000002i2i−2i−2i2i−2i2i−2i000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900
χ302-222-22-2-22-2000022-22-2-22-222-2-2000000002i2i−2i−2i2i−2i2i−2i0000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900
χ312-222-22-2-22-2000022-22-2-22-222-2-200000000−2i−2i2i2i−2i2i−2i2i000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700
χ322-222-22-2-22-2000022-22-2-22-222-2-200000000−2i−2i2i2i−2i2i−2i2i0000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700
χ332-222-22-2-2-22000022-22-2-22-2-2-222000000002i2i−2i−2i−2i2i−2i2i0000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000
χ342-222-22-2-2-22000022-22-2-22-2-2-222000000002i2i−2i−2i−2i2i−2i2i00000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000
χ352-222-22-2-2-22000022-22-2-22-2-2-22200000000−2i−2i2i2i2i−2i2i−2i0000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000
χ362-222-22-2-2-22000022-22-2-22-2-2-22200000000−2i−2i2i2i2i−2i2i−2i00000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000
χ3744444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000044-1-1-1-1-1-1-1-10000000000000000000000
χ3844444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-4-4111111110000000000000000000000
χ394444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-111111111000000004-4-1-1-1-111110000000000000000000000
χ404444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-11111111100000000-441111-1-1-1-10000000000000000000000
χ4144444444-4-444-4-4-1-1-1-1-1-1-1-11111-1-1-1-11111000000000055−5−555−5−50000000000000000000000
χ4244444444-4-444-4-4-1-1-1-1-1-1-1-11111-1-1-1-111110000000000−5−555−5−5550000000000000000000000
χ4344444444-4-4-4-444-1-1-1-1-1-1-1-111111111-1-1-1-1000000000055−5−5−5−5550000000000000000000000
χ4444444444-4-4-4-444-1-1-1-1-1-1-1-111111111-1-1-1-10000000000−5−55555−5−50000000000000000000000
χ45444-4-4-4-4400004-44-4-4-4-44440000000044-4-40000000000000000000000000000000000000000
χ46444-4-4-4-4400004-4-11111-1-1-15−55−55−55−5-1-1110000000000−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ360000000000000000000000
χ47444-4-4-4-4400004-4-11111-1-1-15−55−55−55−5-1-1110000000000ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ360000000000000000000000
χ48444-4-4-4-4400004-4-11111-1-1-1−55−55−55−55-1-1110000000000−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ360000000000000000000000
χ49444-4-4-4-4400004-4-11111-1-1-1−55−55−55−55-1-1110000000000ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ360000000000000000000000
χ50444-4-4-4-440000-444-4-4-4-444400000000-4-4440000000000000000000000000000000000000000
χ51444-4-4-4-440000-44-11111-1-1-15−55−5−55−5511-1-10000000000−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ360000000000000000000000
χ52444-4-4-4-440000-44-11111-1-1-15−55−5−55−5511-1-10000000000ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ360000000000000000000000
χ53444-4-4-4-440000-44-11111-1-1-1−55−555−55−511-1-10000000000−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ360000000000000000000000
χ54444-4-4-4-440000-44-11111-1-1-1−55−555−55−511-1-10000000000ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ360000000000000000000000
χ5544-4-4-444-40000004-4-4444-4-40000000000004i−4i4i−4i000000000000000000000000000000000000
χ5644-4-4-444-40000004-4-4444-4-4000000000000−4i4i−4i4i000000000000000000000000000000000000
χ574-44-44-44-40000004-44-44-44-40000000000000000000000000000004i−4i00000000000000000000
χ584-44-44-44-40000004-44-44-44-4000000000000000000000000000000−4i4i00000000000000000000
χ594-4-44-4-44400000044-4-44-4-4400000000000000004-4-4400000000000000000000000000000000
χ604-4-44-4-44400000044-4-44-4-440000000000000000-444-400000000000000000000000000000000
χ614-4-4-444-440000004-444-4-4-440000000000004-4-44000000000000000000000000000000000000
χ624-4-4-444-440000004-444-4-4-44000000000000-444-4000000000000000000000000000000000000
χ6388-888-8-8-8008-800-2-2-222-2220000-2-22200000000000000000000000000000000000000000000
χ6488-888-8-8-800-8800-2-2-222-222000022-2-200000000000000000000000000000000000000000000
χ6588-8-8-888-8000000-222-2-2-222000025−25−252500000000000000000000000000000000000000000000
χ6688-8-8-888-8000000-222-2-2-2220000−252525−2500000000000000000000000000000000000000000000
χ678-888-88-8-88-80000-2-22-222-22-2-222000000000000000000000000000000000000000000000000
χ688-888-88-8-8-880000-2-22-222-2222-2-2000000000000000000000000000000000000000000000000
χ698-88-88-88-8000000-22-22-22-2225−25−2525000000000000000000000000000000000000000000000000
χ708-88-88-88-8000000-22-22-22-22−252525−25000000000000000000000000000000000000000000000000
χ718-8-88-8-888000000-2-222-222-20000000025−2525−250000000000000000000000000000000000000000
χ728-8-88-8-888000000-2-222-222-200000000−2525−25250000000000000000000000000000000000000000
χ738-8-8-888-88000000-22-2-2222-20000000025−25−25250000000000000000000000000000000000000000
χ748-8-8-888-88000000-22-2-2222-200000000−252525−250000000000000000000000000000000000000000

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