Finite Group Databasebeta

← Group #13027070

Character table — Group #13027070

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444444448888888888888888881010101010101010161616161616161640404040404040404040404040404040404040404040
order124422244451010102020202044448810102020202020202020202088888888202020204040404044888816161616161616161616161616161616
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
χ511111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ611111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ711111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ811111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ9111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ10111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ11111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii
χ12111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i
χ13111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-111-1-111
χ14111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-111-1-1
χ15111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111−i−iiiii−i−iii−i−i−i−iii
χ1722222-2-22-2-222-2-222-2-20000002-22-2000000002222-2-2-2-200000000000000002-2002-200000000
χ1822222-2-22-2-222-2-222-2-20000002-22-2000000002222-2-2-2-20000000000000000-2200-2200000000
χ1922222-2-22-2-222-2-222-2-20000002-22-200000000-2-2-2-2222200000000000000002i−2i00−2i2i00000000
χ2022222-2-22-2-222-2-222-2-20000002-22-200000000-2-2-2-222220000000000000000−2i2i002i−2i00000000
χ212222-22-2-22-222-2-222-2-200002i−2i-22-220000000022-2-2-2-22200002i2i−2i−2i2i−2i00000000000000000000
χ222222-22-2-22-222-2-222-2-200002i−2i-22-2200000000-2-22222-2-200002i2i−2i−2i−2i2i00000000000000000000
χ232222-22-2-22-222-2-222-2-20000−2i2i-22-220000000022-2-2-2-2220000−2i−2i2i2i−2i2i00000000000000000000
χ242222-22-2-22-222-2-222-2-20000−2i2i-22-2200000000-2-22222-2-20000−2i−2i2i2i2i−2i00000000000000000000
χ252222-2-22-2-2222222222000000-2-2-2-20000000022-2-222-2-200000000000000000000002i−2i002i−2i00
χ262222-2-22-2-2222222222000000-2-2-2-20000000022-2-222-2-20000000000000000000000−2i2i00−2i2i00
χ272222-2-22-2-2222222222000000-2-2-2-200000000-2-222-2-22200000000000000000000002-200-2200
χ282222-2-22-2-2222222222000000-2-2-2-200000000-2-222-2-2220000000000000000000000-22002-200
χ2922-2-2222-2-2-22222-2-2-2-200000022-2-2000000002i−2i2i−2i2i−2i2i−2i00000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ3022-2-2222-2-2-22222-2-2-2-200000022-2-2000000002i−2i2i−2i2i−2i2i−2i000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ3122-2-2222-2-2-22222-2-2-2-200000022-2-200000000−2i2i−2i2i−2i2i−2i2i00000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ3222-2-2222-2-2-22222-2-2-2-200000022-2-200000000−2i2i−2i2i−2i2i−2i2i000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ3322-2-22-2-2-22222-2-2-2-222002i−2i002-2-22000000002i−2i2i−2i−2i2i−2i2i2i2i−2i−2i000000002-20000000000000000
χ3422-2-22-2-2-22222-2-2-2-222002i−2i002-2-2200000000−2i2i−2i2i2i−2i2i−2i2i2i−2i−2i00000000-220000000000000000
χ3522-2-22-2-2-22222-2-2-2-22200−2i2i002-2-22000000002i−2i2i−2i−2i2i−2i2i−2i−2i2i2i00000000-220000000000000000
χ3622-2-22-2-2-22222-2-2-2-22200−2i2i002-2-2200000000−2i2i−2i2i2i−2i2i−2i−2i−2i2i2i000000002-20000000000000000
χ3722-2-2-22-22-2222-2-2-2-222000000-222-2000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37
χ3822-2-2-22-22-2222-2-2-2-222000000-222-2000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37
χ3922-2-2-22-22-2222-2-2-2-222000000-222-200000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39
χ4022-2-2-22-22-2222-2-2-2-222000000-222-200000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39
χ4122-2-2-2-2222-22222-2-2-2-22i−2i0000-2-2222i2i2i2i−2i−2i−2i−2i2i−2i−2i2i2i−2i−2i2i00000000002-2000000000000000000
χ4222-2-2-2-2222-22222-2-2-2-22i−2i0000-2-2222i2i2i2i−2i−2i−2i−2i−2i2i2i−2i−2i2i2i−2i0000000000-22000000000000000000
χ4322-2-2-2-2222-22222-2-2-2-2−2i2i0000-2-222−2i−2i−2i−2i2i2i2i2i2i−2i−2i2i2i−2i−2i2i0000000000-22000000000000000000
χ4422-2-2-2-2222-22222-2-2-2-2−2i2i0000-2-222−2i−2i−2i−2i2i2i2i2i−2i2i2i−2i−2i2i2i−2i00000000002-2000000000000000000
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
χ464444444444-1-1-1-1-1-1-1-144-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100000000111111110000000000000000000000
χ474444444444-1-1-1-1-1-1-1-1-4-444-4-4-1-1-1-11111111100000000-1-1-1-111110000000000000000000000
χ484444444444-1-1-1-1-1-1-1-1-4-4-4-444-1-1-1-111111111000000001111-1-1-1-10000000000000000000000
χ494444-44-4-44-4-1-111-1-11100004i−4i1-11-155−5−555−5−500000000i5−i5i5−i5−i−iii0000000000000000000000
χ504444-44-4-44-4-1-111-1-11100004i−4i1-11-1−5−555−5−55500000000−i5i5−i5i5−i−iii0000000000000000000000
χ514444-44-4-44-4-1-111-1-1110000−4i4i1-11-155−5−555−5−500000000−i5i5−i5i5ii−i−i0000000000000000000000
χ524444-44-4-44-4-1-111-1-1110000−4i4i1-11-1−5−555−5−55500000000i5−i5i5−i5ii−i−i0000000000000000000000
χ5344-4-44-4-4-444-1-11111-1-1004i−4i00-111-1i5i5−i5−i5−i5−i5i5i500000000−i−iii5−55−50000000000000000000000
χ5444-4-44-4-4-444-1-11111-1-1004i−4i00-111-1−i5−i5i5i5i5i5−i5−i500000000−i−iii−55−550000000000000000000000
χ5544-4-44-4-4-444-1-11111-1-100−4i4i00-111-1i5i5−i5−i5−i5−i5i5i500000000ii−i−i−55−550000000000000000000000
χ5644-4-44-4-4-444-1-11111-1-100−4i4i00-111-1−i5−i5i5i5i5i5−i5−i500000000ii−i−i5−55−50000000000000000000000
χ5744-4-4-4-4444-4-1-1-1-111114i−4i000011-1-1−i−i−i−iiiii000000005−5−55−i5i5i5−i50000000000000000000000
χ5844-4-4-4-4444-4-1-1-1-111114i−4i000011-1-1−i−i−i−iiiii00000000−555−5i5−i5−i5i50000000000000000000000
χ5944-4-4-4-4444-4-1-1-1-11111−4i4i000011-1-1iiii−i−i−i−i000000005−5−55i5−i5−i5i50000000000000000000000
χ6044-4-4-4-4444-4-1-1-1-11111−4i4i000011-1-1iiii−i−i−i−i00000000−555−5−i5i5i5−i50000000000000000000000
χ6188888-8-88-8-8-2-222-2-222000000-22-220000000000000000000000000000000000000000000000
χ628888-8-88-8-88-2-2-2-2-2-2-2-200000022220000000000000000000000000000000000000000000000
χ6388-8-8888-8-8-8-2-2-2-22222000000-2-2220000000000000000000000000000000000000000000000
χ6488-8-8-88-88-88-2-22222-2-20000002-2-220000000000000000000000000000000000000000000000
χ658-88i−8i0000008-8008i−8i0000000000000000000000000000000000000000000000000000000000
χ668-88i−8i000000-2225−25−2i2i2i5−2i50000000000−ζ4−ζ6+ζ12+ζ14−ζ22−ζ28+ζ36+ζ38ζ4+ζ6−ζ12−ζ14+ζ22+ζ28−ζ36−ζ38−ζ4−ζ6−ζ12+ζ14+ζ22+ζ28+ζ36−ζ38ζ4+ζ6+ζ12−ζ14−ζ22−ζ28−ζ36+ζ38−ζ4+ζ6+ζ12−ζ14+ζ22−ζ28+ζ36−ζ38ζ4−ζ6−ζ12+ζ14−ζ22+ζ28−ζ36+ζ38−ζ4+ζ6−ζ12−ζ14−ζ22+ζ28+ζ36+ζ38ζ4−ζ6+ζ12+ζ14+ζ22−ζ28−ζ36−ζ3800000000000000000000000000000000000000
χ678-88i−8i000000-2225−25−2i2i2i5−2i50000000000ζ4+ζ6−ζ12−ζ14+ζ22+ζ28−ζ36−ζ38−ζ4−ζ6+ζ12+ζ14−ζ22−ζ28+ζ36+ζ38ζ4+ζ6+ζ12−ζ14−ζ22−ζ28−ζ36+ζ38−ζ4−ζ6−ζ12+ζ14+ζ22+ζ28+ζ36−ζ38ζ4−ζ6−ζ12+ζ14−ζ22+ζ28−ζ36+ζ38−ζ4+ζ6+ζ12−ζ14+ζ22−ζ28+ζ36−ζ38ζ4−ζ6+ζ12+ζ14+ζ22−ζ28−ζ36−ζ38−ζ4+ζ6−ζ12−ζ14−ζ22+ζ28+ζ36+ζ3800000000000000000000000000000000000000
χ688-88i−8i000000-22−2525−2i2i−2i52i50000000000−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+ζ38−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
χ698-88i−8i000000-22−2525−2i2i−2i52i50000000000ζ4+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−ζ38ζ4−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
χ708-8−8i8i0000008-800−8i8i0000000000000000000000000000000000000000000000000000000000
χ718-8−8i8i000000-2225−252i−2i−2i52i50000000000−ζ4+ζ6+ζ12−ζ14+ζ22−ζ28+ζ36−ζ38ζ4−ζ6−ζ12+ζ14−ζ22+ζ28−ζ36+ζ38−ζ4+ζ6−ζ12−ζ14−ζ22+ζ28+ζ36+ζ38ζ4−ζ6+ζ12+ζ14+ζ22−ζ28−ζ36−ζ38−ζ4−ζ6+ζ12+ζ14−ζ22−ζ28+ζ36+ζ38ζ4+ζ6−ζ12−ζ14+ζ22+ζ28−ζ36−ζ38−ζ4−ζ6−ζ12+ζ14+ζ22+ζ28+ζ36−ζ38ζ4+ζ6+ζ12−ζ14−ζ22−ζ28−ζ36+ζ3800000000000000000000000000000000000000
χ728-8−8i8i000000-2225−252i−2i−2i52i50000000000ζ4−ζ6−ζ12+ζ14−ζ22+ζ28−ζ36+ζ38−ζ4+ζ6+ζ12−ζ14+ζ22−ζ28+ζ36−ζ38ζ4−ζ6+ζ12+ζ14+ζ22−ζ28−ζ36−ζ38−ζ4+ζ6−ζ12−ζ14−ζ22+ζ28+ζ36+ζ38ζ4+ζ6−ζ12−ζ14+ζ22+ζ28−ζ36−ζ38−ζ4−ζ6+ζ12+ζ14−ζ22−ζ28+ζ36+ζ38ζ4+ζ6+ζ12−ζ14−ζ22−ζ28−ζ36+ζ38−ζ4−ζ6−ζ12+ζ14+ζ22+ζ28+ζ36−ζ3800000000000000000000000000000000000000
χ738-8−8i8i000000-22−25252i−2i2i5−2i50000000000−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−ζ38−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
χ748-8−8i8i000000-22−25252i−2i2i5−2i50000000000ζ4−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+ζ38ζ4+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

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