Finite Group Databasebeta

← Group #13019572

Character table — Group #13019572

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444444448888888888888888881010101010101010161616161616161640404040404040404040404040404040404040404040
order12222244445101010101010102222442020202020202020202020204444444410101010101010104444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-111-1-111-1-111-1-111
χ11111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ12111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ13111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ14111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1
χ15111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222-2-2-2-2222222222-20000-2-2-2-20000000022-2-2-2-22222-2-200002-200000000000000000000
χ18222222-2-2-2-2222222222-20000-2-2-2-200000000-2-22222-2-222-2-20000-2200000000000000000000
χ19222222-2-2-2-222222222-220000-2-2-2-20000000022-2-2-2-222-2-2220000-2200000000000000000000
χ20222222-2-2-2-222222222-220000-2-2-2-200000000-2-22222-2-2-2-22200002-200000000000000000000
χ212222-2-222-2-2222-2-22-2-200000022-2-2000000002222-2-2-2-20000000000000000000000002i−2i002i−2i
χ222222-2-222-2-2222-2-22-2-200000022-2-2000000002222-2-2-2-2000000000000000000000000−2i2i00−2i2i
χ232222-2-222-2-2222-2-22-2-200000022-2-200000000-2-2-2-222220000000000000000000000002-200-22
χ242222-2-222-2-2222-2-22-2-200000022-2-200000000-2-2-2-22222000000000000000000000000-22002-2
χ252222-2-2-2-222222-2-22-2-2000000-2-2220000000022-2-222-2-200000000000000000000002i−2i002i−2i00
χ262222-2-2-2-222222-2-22-2-2000000-2-2220000000022-2-222-2-20000000000000000000000−2i2i00−2i2i00
χ272222-2-2-2-222222-2-22-2-2000000-2-22200000000-2-222-2-22200000000000000000000002-200-2200
χ282222-2-2-2-222222-2-22-2-2000000-2-22200000000-2-222-2-2220000000000000000000000-22002-200
χ2922-2-22-22-22-22-2-2-2-222200002-22-22-22222-2-2-2-22i−2i2i−2i2i−2i2i−2i0000000000002i−2i0000000000000000
χ3022-2-22-22-22-22-2-2-2-222200002-22-22-22222-2-2-2-2−2i2i−2i2i−2i2i−2i2i000000000000−2i2i0000000000000000
χ3122-2-22-22-22-22-2-2-2-22220000-222-22-2-2-2-2-222222i−2i2i−2i2i−2i2i−2i000000000000−2i2i0000000000000000
χ3222-2-22-22-22-22-2-2-2-22220000-222-22-2-2-2-2-22222−2i2i−2i2i−2i2i−2i2i0000000000002i−2i0000000000000000
χ3322-2-22-2-22-222-2-2-2-2222002-200-22-22000000002i−2i−2i2i−2i2i2i−2i000022-2-2002i−2i000000000000000000
χ3422-2-22-2-22-222-2-2-2-2222002-200-22-2200000000−2i2i2i−2i2i−2i−2i2i000022-2-200−2i2i000000000000000000
χ3522-2-22-2-22-222-2-2-2-222200-2200-22-22000000002i−2i−2i2i−2i2i2i−2i0000-2-22200−2i2i000000000000000000
χ3622-2-22-2-22-222-2-2-2-222200-2200-22-2200000000−2i2i2i−2i2i−2i−2i2i0000-2-222002i−2i000000000000000000
χ3722-2-2-222-2-222-2-2222-2-20000002-2-22000000002i−2i2i−2i−2i2i−2i2i00000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ3822-2-2-222-2-222-2-2222-2-20000002-2-22000000002i−2i2i−2i−2i2i−2i2i000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ3922-2-2-222-2-222-2-2222-2-20000002-2-2200000000−2i2i−2i2i2i−2i2i−2i00000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ4022-2-2-222-2-222-2-2222-2-20000002-2-2200000000−2i2i−2i2i2i−2i2i−2i000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ4122-2-2-22-222-22-2-2222-2-2000000-222-2000000002i−2i−2i2i2i−2i−2i2i0000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000
χ4222-2-2-22-222-22-2-2222-2-2000000-222-2000000002i−2i−2i2i2i−2i−2i2i00000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000
χ4322-2-2-22-222-22-2-2222-2-2000000-222-200000000−2i2i2i−2i−2i2i2i−2i0000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000
χ4422-2-2-22-222-22-2-2222-2-2000000-222-200000000−2i2i2i−2i−2i2i2i−2i00000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000
χ454444444444-1-1-1-1-1-1-1-1444444-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-10000000000000000000000
χ464444444444-1-1-1-1-1-1-1-144-4-4-4-4-1-1-1-11111111100000000-1-1-1-111110000000000000000000000
χ474444444444-1-1-1-1-1-1-1-1-4-444-4-4-1-1-1-111111111000000001111-1-1-1-10000000000000000000000
χ484444444444-1-1-1-1-1-1-1-1-4-4-4-444-1-1-1-1-1-1-1-1-1-1-1-100000000111111110000000000000000000000
χ49444444-4-4-4-4-1-1-1-1-1-1-1-14-40000111155−5−555−5−500000000-1-1115−55−50000000000000000000000
χ50444444-4-4-4-4-1-1-1-1-1-1-1-14-400001111−5−555−5−55500000000-1-111−55−550000000000000000000000
χ51444444-4-4-4-4-1-1-1-1-1-1-1-1-440000111155−5−555−5−50000000011-1-1−55−550000000000000000000000
χ52444444-4-4-4-4-1-1-1-1-1-1-1-1-4400001111−5−555−5−5550000000011-1-15−55−50000000000000000000000
χ5344-4-44-44-44-4-11111-1-1-100004-4-11-11-1-1-1-11111000000005−55−55−5−550000000000000000000000
χ5444-4-44-44-44-4-11111-1-1-100004-4-11-11-1-1-1-1111100000000−55−55−555−50000000000000000000000
χ5544-4-44-44-44-4-11111-1-1-10000-44-11-111111-1-1-1-1000000005−55−5−555−50000000000000000000000
χ5644-4-44-44-44-4-11111-1-1-10000-44-11-111111-1-1-1-100000000−55−555−5−550000000000000000000000
χ5744-4-44-4-44-44-11111-1-1-1004-4001-11-155−5−5−5−555000000005−5−55-1-1110000000000000000000000
χ5844-4-44-4-44-44-11111-1-1-1004-4001-11-1−5−55555−5−500000000−555−5-1-1110000000000000000000000
χ5944-4-44-4-44-44-11111-1-1-100-44001-11-155−5−5−5−55500000000−555−511-1-10000000000000000000000
χ6044-4-44-4-44-44-11111-1-1-100-44001-11-1−5−55555−5−5000000005−5−5511-1-10000000000000000000000
χ618888-8-888-8-8-2-2-222-222000000-2-2220000000000000000000000000000000000000000000000
χ628888-8-8-8-888-2-2-222-22200000022-2-20000000000000000000000000000000000000000000000
χ6388-8-8-888-8-88-222-2-2-222000000-222-20000000000000000000000000000000000000000000000
χ6488-8-8-88-888-8-222-2-2-2220000002-2-220000000000000000000000000000000000000000000000
χ658-88-800000088-800-80000000000000000000000000000000000000000000000000000000000
χ668-88-8000000-2-2225−25225−2500000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ362ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000000000000000000
χ678-88-8000000-2-2225−25225−250000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000000000000000000
χ688-88-8000000-2-22−25252−25250000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000000000000000000
χ698-88-8000000-2-22−25252−252500000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ282ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000000000000000000
χ708-8-880000008-8800-80000000000000000000000000000000000000000000000000000000000
χ718-8-88000000-22-225−252−25250000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000000000000000000
χ728-8-88000000-22-225−252−252500000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000000000000000000
χ738-8-88000000-22-2−2525225−2500000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000000000000000000
χ748-8-88000000-22-2−2525225−250000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000000000000000000

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