Finite Group Databasebeta

← Group #13019573

Character table — Group #13019573

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444444448888888888888888881010101010101010161616161616161640404040404040404040404040404040404040404040
order12222244445101010101010102244442020202020202020202020204444444410101010202020202244448888888888888888
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
χ511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ9111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ10111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ11111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ12111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111−i−i−i−iiiiiiiii−i−i−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
χ17222222-2-2-2-222222222002-200-2-2-2-20000000022-2-2-2-222000022-2-22-200000000000000000000
χ18222222-2-2-2-222222222002-200-2-2-2-200000000-2-22222-2-2000022-2-2-2200000000000000000000
χ19222222-2-2-2-22222222200-2200-2-2-2-20000000022-2-2-2-2220000-2-222-2200000000000000000000
χ20222222-2-2-2-22222222200-2200-2-2-2-200000000-2-22222-2-20000-2-2222-200000000000000000000
χ212222-2-222-2-222-2-22-2-2200000022-2-2000000002222-2-2-2-20000000000000000000000002i−2i002i−2i
χ222222-2-222-2-222-2-22-2-2200000022-2-2000000002222-2-2-2-2000000000000000000000000−2i2i00−2i2i
χ232222-2-222-2-222-2-22-2-2200000022-2-200000000-2-2-2-222220000000000000000000000002-200-22
χ242222-2-222-2-222-2-22-2-2200000022-2-200000000-2-2-2-22222000000000000000000000000-22002-2
χ252222-2-2-2-22222-2-22-2-22000000-2-2220000000022-2-222-2-200000000000000000000002i−2i002i−2i00
χ262222-2-2-2-22222-2-22-2-22000000-2-2220000000022-2-222-2-20000000000000000000000−2i2i00−2i2i00
χ272222-2-2-2-22222-2-22-2-22000000-2-22200000000-2-222-2-22200000000000000000000002-200-2200
χ282222-2-2-2-22222-2-22-2-22000000-2-22200000000-2-222-2-2220000000000000000000000-22002-200
χ2922-2-22-22-22-22-2-2-2222-20000002-22-2000000002i−2i2i−2i2i−2i2i−2i0000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000
χ3022-2-22-22-22-22-2-2-2222-20000002-22-2000000002i−2i2i−2i2i−2i2i−2i00000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000
χ3122-2-22-22-22-22-2-2-2222-20000002-22-200000000−2i2i−2i2i−2i2i−2i2i0000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000
χ3222-2-22-22-22-22-2-2-2222-20000002-22-200000000−2i2i−2i2i−2i2i−2i2i00000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000
χ3322-2-22-2-22-222-2-2-2222-2000000-22-22000000002i−2i−2i2i−2i2i2i−2i00000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ3422-2-22-2-22-222-2-2-2222-2000000-22-22000000002i−2i−2i2i−2i2i2i−2i000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ3522-2-22-2-22-222-2-2-2222-2000000-22-2200000000−2i2i2i−2i2i−2i−2i2i00000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ3622-2-22-2-22-222-2-2-2222-2000000-22-2200000000−2i2i2i−2i2i−2i−2i2i000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ3722-2-2-222-2-222-2222-2-2-22-200002-2-22000000002i−2i2i−2i−2i2i−2i2i22-2-20000002i−2i000000000000000000
χ3822-2-2-222-2-222-2222-2-2-22-200002-2-2200000000−2i2i−2i2i2i−2i2i−2i22-2-2000000−2i2i000000000000000000
χ3922-2-2-222-2-222-2222-2-2-2-2200002-2-22000000002i−2i2i−2i−2i2i−2i2i-2-222000000−2i2i000000000000000000
χ4022-2-2-222-2-222-2222-2-2-2-2200002-2-2200000000−2i2i−2i2i2i−2i2i−2i-2-2220000002i−2i000000000000000000
χ4122-2-2-22-222-22-2222-2-2-200002i−2i-222-22i2i2i2i−2i−2i−2i−2i2i−2i−2i2i2i−2i−2i2i0000000000002-20000000000000000
χ4222-2-2-22-222-22-2222-2-2-200002i−2i-222-22i2i2i2i−2i−2i−2i−2i−2i2i2i−2i−2i2i2i−2i000000000000-220000000000000000
χ4322-2-2-22-222-22-2222-2-2-20000−2i2i-222-2−2i−2i−2i−2i2i2i2i2i2i−2i−2i2i2i−2i−2i2i000000000000-220000000000000000
χ4422-2-2-22-222-22-2222-2-2-20000−2i2i-222-2−2i−2i−2i−2i2i2i2i2i−2i2i2i−2i−2i2i2i−2i0000000000002-20000000000000000
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
χ49444444-4-4-4-4-1-1-1-1-1-1-1-1004-400111155−5−555−5−5000000005−55−5-1-1110000000000000000000000
χ50444444-4-4-4-4-1-1-1-1-1-1-1-1004-4001111−5−555−5−55500000000−55−55-1-1110000000000000000000000
χ51444444-4-4-4-4-1-1-1-1-1-1-1-100-4400111155−5−555−5−500000000−55−5511-1-10000000000000000000000
χ52444444-4-4-4-4-1-1-1-1-1-1-1-100-44001111−5−555−5−555000000005−55−511-1-10000000000000000000000
χ5344-4-4-444-4-44-11-1-1-11114-40000-111-1i5i5−i5−i5−i5−i5i5i500000000-1-111i5−i5i5−i50000000000000000000000
χ5444-4-4-444-4-44-11-1-1-11114-40000-111-1−i5−i5i5i5i5i5−i5−i500000000-1-111−i5i5−i5i50000000000000000000000
χ5544-4-4-444-4-44-11-1-1-1111-440000-111-1i5i5−i5−i5−i5−i5i5i50000000011-1-1−i5i5−i5i50000000000000000000000
χ5644-4-4-444-4-44-11-1-1-1111-440000-111-1−i5−i5i5i5i5i5−i5−i50000000011-1-1i5−i5i5−i50000000000000000000000
χ5744-4-4-44-444-4-11-1-1-111100004i−4i1-1-11−i−i−i−iiiii000000005−5−55i5−i5−i5i50000000000000000000000
χ5844-4-4-44-444-4-11-1-1-111100004i−4i1-1-11−i−i−i−iiiii00000000−555−5−i5i5i5−i50000000000000000000000
χ5944-4-4-44-444-4-11-1-1-11110000−4i4i1-1-11iiii−i−i−i−i000000005−5−55−i5i5i5−i50000000000000000000000
χ6044-4-4-44-444-4-11-1-1-11110000−4i4i1-1-11iiii−i−i−i−i00000000−555−5i5−i5−i5i50000000000000000000000
χ618888-8-888-8-8-2-222-222-2000000-2-2220000000000000000000000000000000000000000000000
χ628888-8-8-8-888-2-222-222-200000022-2-20000000000000000000000000000000000000000000000
χ6388-8-88-88-88-8-2222-2-2-22000000-22-220000000000000000000000000000000000000000000000
χ6488-8-88-8-88-88-2222-2-2-220000002-22-20000000000000000000000000000000000000000000000
χ658-88-80000008-800-800800000000000000000000000000000000000000000000000000000000
χ668-88-8000000-2225−25225−25-200000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ362ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000000000000000000
χ678-88-8000000-2225−25225−25-20000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000000000000000000
χ688-88-8000000-22−25252−2525-20000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000000000000000000
χ698-88-8000000-22−25252−2525-200000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ282ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000000000000000000
χ708-8-880000008800-800-800000000000000000000000000000000000000000000000000000000
χ718-8-88000000-2-225−252−252520000000000−2ζ22+2ζ382ζ22−2ζ38−2ζ6+2ζ142ζ6−2ζ142ζ22−2ζ38−2ζ22+2ζ382ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000000000
χ728-8-88000000-2-225−252−2525200000000002ζ22−2ζ38−2ζ22+2ζ382ζ6−2ζ14−2ζ6+2ζ14−2ζ22+2ζ382ζ22−2ζ38−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000000000
χ738-8-88000000-2-2−2525225−25200000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ22+2ζ382ζ22−2ζ38−2ζ6+2ζ142ζ6−2ζ142ζ22−2ζ38−2ζ22+2ζ3800000000000000000000000000000000000000
χ748-8-88000000-2-2−2525225−2520000000000−2ζ6+2ζ142ζ6−2ζ142ζ22−2ζ38−2ζ22+2ζ382ζ6−2ζ14−2ζ6+2ζ14−2ζ22+2ζ382ζ22−2ζ3800000000000000000000000000000000000000

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