Finite Group Databasebeta

← Group #13027129

Character table — Group #13027129

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444444444444555588888888888888881010101010101616161616161616202020204040404040404040404040404040404040404040
order124422244444445101010202020208888248810102020202020202020202088888810102020404040408888448816161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i
χ61111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiii
χ81111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iiiiiii−i−i−i−i
χ91111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1
χ101111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-111
χ111111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-111
χ121111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1
χ131111111111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111−i−iiiii−i−iii−i−i−i−iii
χ1722222-2-22-2-200002-2-2222-2-22222002i−2i2-22-200000000-2-222-2-200002i2i−2i−2i00002i−2i000000000000000000
χ1822222-2-22-2-200002-2-2222-2-2222200−2i2i2-22-200000000-2-222-2-20000−2i−2i2i2i0000−2i2i000000000000000000
χ1922222-2-22-2-200002-2-2222-2-2-2-2-2-2002i−2i2-22-20000000022-2-22200002i2i−2i−2i0000−2i2i000000000000000000
χ2022222-2-22-2-200002-2-2222-2-2-2-2-2-200−2i2i2-22-20000000022-2-2220000−2i−2i2i2i00002i−2i000000000000000000
χ212222-22-2-2-2200002-2-2222-2-222220000-22-2200000000-2-2-2-2220000000000000000000000002-2002-200
χ222222-22-2-2-2200002-2-2222-2-222220000-22-2200000000-2-2-2-222000000000000000000000000-2200-2200
χ232222-22-2-2-2200002-2-2222-2-2-2-2-2-20000-22-22000000002222-2-20000000000000000000000002i−2i00−2i2i00
χ242222-22-2-2-2200002-2-2222-2-2-2-2-2-20000-22-22000000002222-2-2000000000000000000000000−2i2i002i−2i00
χ252222-2-22-22-200002222222222220000-2-2-2-20000000022-2-2-2-2000000000000000000002i−2i2i−2i00000000
χ262222-2-22-22-200002222222222220000-2-2-2-20000000022-2-2-2-200000000000000000000−2i2i−2i2i00000000
χ272222-2-22-22-2000022222222-2-2-2-20000-2-2-2-200000000-2-22222000000000000000000002-2-2200000000
χ282222-2-22-22-2000022222222-2-2-2-20000-2-2-2-200000000-2-2222200000000000000000000-222-200000000
χ2922-2-2222-2-2-200002222-2-2-2-22i2i−2i−2i000022-2-2000000002i−2i2i−2i2i−2i00000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37
χ3022-2-2222-2-2-200002222-2-2-2-22i2i−2i−2i000022-2-2000000002i−2i2i−2i2i−2i000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37
χ3122-2-2222-2-2-200002222-2-2-2-2−2i−2i2i2i000022-2-200000000−2i2i−2i2i−2i2i00000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39
χ3222-2-2222-2-2-200002222-2-2-2-2−2i−2i2i2i000022-2-200000000−2i2i−2i2i−2i2i000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39
χ3322-2-22-2-2-22200002-2-22-2-2222i2i−2i−2i00002-2-2200000000−2i2i2i−2i−2i2i0000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ3422-2-22-2-2-22200002-2-22-2-2222i2i−2i−2i00002-2-2200000000−2i2i2i−2i−2i2i00000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ3522-2-22-2-2-22200002-2-22-2-222−2i−2i2i2i00002-2-22000000002i−2i−2i2i2i−2i0000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ3622-2-22-2-2-22200002-2-22-2-222−2i−2i2i2i00002-2-22000000002i−2i−2i2i2i−2i00000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ3722-2-2-22-222-222-2-22-2-22-2-2222i2i−2i−2i0000-222-22222-2-2-2-2−2i2i−2i2i2i−2i000000002i2i−2i−2i00000000000000000000
χ3822-2-2-22-222-222-2-22-2-22-2-222−2i−2i2i2i0000-222-22222-2-2-2-22i−2i2i−2i−2i2i00000000−2i−2i2i2i00000000000000000000
χ3922-2-2-22-222-2-2-2222-2-22-2-2222i2i−2i−2i0000-222-2-2-2-2-22222−2i2i−2i2i2i−2i00000000−2i−2i2i2i00000000000000000000
χ4022-2-2-22-222-2-2-2222-2-22-2-222−2i−2i2i2i0000-222-2-2-2-2-222222i−2i2i−2i−2i2i000000002i2i−2i−2i00000000000000000000
χ4122-2-2-2-222-2200002222-2-2-2-22i2i−2i−2i2-200-2-222000000002i−2i−2i2i−2i2i22-2-200000000002i−2i0000000000000000
χ4222-2-2-2-222-2200002222-2-2-2-22i2i−2i−2i-2200-2-222000000002i−2i−2i2i−2i2i-2-2220000000000−2i2i0000000000000000
χ4322-2-2-2-222-2200002222-2-2-2-2−2i−2i2i2i2-200-2-22200000000−2i2i2i−2i2i−2i22-2-20000000000−2i2i0000000000000000
χ4422-2-2-2-222-2200002222-2-2-2-2−2i−2i2i2i-2200-2-22200000000−2i2i2i−2i2i−2i-2-22200000000002i−2i0000000000000000
χ4544444444444444-1-1-1-1-1-1-1-100004444-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1000000000000000000000000
χ4644444444444444-1-1-1-1-1-1-1-10000-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100000011111111000000000000000000000000
χ474444444444-4-4-4-4-1-1-1-1-1-1-1-1000044-4-4-1-1-1-111111111000000-1-1-1-11111000000000000000000000000
χ484444444444-4-4-4-4-1-1-1-1-1-1-1-10000-4-444-1-1-1-1111111110000001111-1-1-1-1000000000000000000000000
χ4944444-4-44-4-40000-111-1-1-1110000004i−4i-11-11i5i5−i5−i5i5i5−i5−i50000005−55−5−i−iii000000000000000000000000
χ5044444-4-44-4-40000-111-1-1-1110000004i−4i-11-11−i5−i5i5i5−i5−i5i5i5000000−55−55−i−iii000000000000000000000000
χ5144444-4-44-4-40000-111-1-1-111000000−4i4i-11-11i5i5−i5−i5i5i5−i5−i5000000−55−55ii−i−i000000000000000000000000
χ5244444-4-44-4-40000-111-1-1-111000000−4i4i-11-11−i5−i5i5i5−i5−i5i5i50000005−55−5ii−i−i000000000000000000000000
χ5344-4-4-44-444-444-4-4-111-111-1-1000000001-1-11-1-1-1-111110000005−5−555−55−5000000000000000000000000
χ5444-4-4-44-444-444-4-4-111-111-1-1000000001-1-11-1-1-1-11111000000−555−5−55−55000000000000000000000000
χ5544-4-4-44-444-4-4-444-111-111-1-1000000001-1-111111-1-1-1-10000005−5−55−55−55000000000000000000000000
χ5644-4-4-44-444-4-4-444-111-111-1-1000000001-1-111111-1-1-1-1000000−555−55−55−5000000000000000000000000
χ5744-4-4-4-444-440000-1-1-1-1111100004-40011-1-1i5i5−i5−i5−i5−i5i5i5000000-1-111i5−i5−i5i5000000000000000000000000
χ5844-4-4-4-444-440000-1-1-1-1111100004-40011-1-1−i5−i5i5i5i5i5−i5−i5000000-1-111−i5i5i5−i5000000000000000000000000
χ5944-4-4-4-444-440000-1-1-1-111110000-440011-1-1i5i5−i5−i5−i5−i5i5i500000011-1-1−i5i5i5−i5000000000000000000000000
χ6044-4-4-4-444-440000-1-1-1-111110000-440011-1-1−i5−i5i5i5i5i5−i5−i500000011-1-1i5−i5−i5i5000000000000000000000000
χ614-44i−4i0000002-22i−2i400-44i−4i00−4ζ13−4ζ21−4ζ29−4ζ374ζ13+4ζ21+4ζ29+4ζ37−4ζ7−4ζ23−4ζ31−4ζ394ζ7+4ζ23+4ζ31+4ζ39000000002-22-22i−2i2i−2i00000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000000000
χ624-44i−4i0000002-22i−2i400-44i−4i004ζ13+4ζ21+4ζ29+4ζ37−4ζ13−4ζ21−4ζ29−4ζ374ζ7+4ζ23+4ζ31+4ζ39−4ζ7−4ζ23−4ζ31−4ζ39000000002-22-22i−2i2i−2i000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000000000
χ634-44i−4i000000-22−2i2i400-44i−4i00−4ζ13−4ζ21−4ζ29−4ζ374ζ13+4ζ21+4ζ29+4ζ37−4ζ7−4ζ23−4ζ31−4ζ394ζ7+4ζ23+4ζ31+4ζ3900000000-22-22−2i2i−2i2i000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000000000
χ644-44i−4i000000-22−2i2i400-44i−4i004ζ13+4ζ21+4ζ29+4ζ37−4ζ13−4ζ21−4ζ29−4ζ374ζ7+4ζ23+4ζ31+4ζ39−4ζ7−4ζ23−4ζ31−4ζ3900000000-22-22−2i2i−2i2i00000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000000000
χ654-4−4i4i0000002-2−2i2i400-4−4i4i00−4ζ7−4ζ23−4ζ31−4ζ394ζ7+4ζ23+4ζ31+4ζ39−4ζ13−4ζ21−4ζ29−4ζ374ζ13+4ζ21+4ζ29+4ζ37000000002-22-2−2i2i−2i2i00000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000000000
χ664-4−4i4i0000002-2−2i2i400-4−4i4i004ζ7+4ζ23+4ζ31+4ζ39−4ζ7−4ζ23−4ζ31−4ζ394ζ13+4ζ21+4ζ29+4ζ37−4ζ13−4ζ21−4ζ29−4ζ37000000002-22-2−2i2i−2i2i000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000000000
χ674-4−4i4i000000-222i−2i400-4−4i4i00−4ζ7−4ζ23−4ζ31−4ζ394ζ7+4ζ23+4ζ31+4ζ39−4ζ13−4ζ21−4ζ29−4ζ374ζ13+4ζ21+4ζ29+4ζ3700000000-22-222i−2i2i−2i000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000000000
χ684-4−4i4i000000-222i−2i400-4−4i4i004ζ7+4ζ23+4ζ31+4ζ39−4ζ7−4ζ23−4ζ31−4ζ394ζ13+4ζ21+4ζ29+4ζ37−4ζ13−4ζ21−4ζ29−4ζ3700000000-22-222i−2i2i−2i00000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000000000
χ698888-88-8-8-880000-222-2-2-222000000002-22-20000000000000000000000000000000000000000000000
χ708888-8-88-88-80000-2-2-2-2-2-2-2-20000000022220000000000000000000000000000000000000000000000
χ7188-8-8888-8-8-80000-2-2-2-2222200000000-2-2220000000000000000000000000000000000000000000000
χ7288-8-88-8-8-8880000-222-222-2-200000000-222-20000000000000000000000000000000000000000000000
χ738-88i−8i0000004-44i−4i-225−252−2i2i2i5−2i5000000000000−1+i51−i5−1−i51+i5−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ3800000000000000000000000000000000000000
χ748-88i−8i0000004-44i−4i-2−25252−2i2i−2i52i5000000000000−1−i51+i5−1+i51−i5ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ3800000000000000000000000000000000000000
χ758-88i−8i000000-44−4i4i-225−252−2i2i2i5−2i50000000000001−i5−1+i51+i5−1−i5ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ3800000000000000000000000000000000000000
χ768-88i−8i000000-44−4i4i-2−25252−2i2i−2i52i50000000000001+i5−1−i51−i5−1+i5−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ3800000000000000000000000000000000000000
χ778-8−8i8i0000004-4−4i4i-225−2522i−2i−2i52i5000000000000−1−i51+i5−1+i51−i5−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ3800000000000000000000000000000000000000
χ788-8−8i8i0000004-4−4i4i-2−252522i−2i2i5−2i5000000000000−1+i51−i5−1−i51+i5ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ3800000000000000000000000000000000000000
χ798-8−8i8i000000-444i−4i-225−2522i−2i−2i52i50000000000001+i5−1−i51−i5−1+i5ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ3800000000000000000000000000000000000000
χ808-8−8i8i000000-444i−4i-2−252522i−2i2i5−2i50000000000001−i5−1+i51+i5−1−i5−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ3800000000000000000000000000000000000000

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