Finite Group Databasebeta

← Group #13022536

Character table — Group #13022536

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444444448888888888888888881010101010101010161616161616161640404040404040404040404040404040404040404040
order12222244445101010101010102244882020202040404040404040402222444410101010202020202244444488888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i-1-1ii−i−iiiii−i−i−i−i
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iii-1-1−i−iii−i−i−i−iiiii
χ511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111ii−i−i11−i−iiiii−i−i−i−iii
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111−i−iii11ii−i−i−i−iiiii−i−i
χ9111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1111111-1-11111-1-1-1-1-1-1-1-1
χ10111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111
χ11111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1ii−i−i11ii−i−i−i−i−i−iiiii
χ12111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−iii11−i−iiiiiii−i−i−i−i
χ13111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111
χ14111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1
χ15111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i-1-1−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−i−iii-1-1ii−i−iii−i−i−i−iii
χ17222222-2-2-2-222222222000000-2-2-2-2000000002222-2-2-2-20000000000000000000000002i−2i002i−2i
χ18222222-2-2-2-222222222000000-2-2-2-2000000002222-2-2-2-2000000000000000000000000−2i2i00−2i2i
χ19222222-2-2-2-222222222000000-2-2-2-200000000-2-2-2-222220000000000000000000000002-200-22
χ20222222-2-2-2-222222222000000-2-2-2-200000000-2-2-2-22222000000000000000000000000-22002-2
χ212222-2-222-2-222-2-2-2-22200000022-2-20000000022-2-22-22-200000000000000000000002i−2i002i−2i00
χ222222-2-222-2-222-2-2-2-22200000022-2-20000000022-2-22-22-20000000000000000000000−2i2i00−2i2i00
χ232222-2-222-2-222-2-2-2-22200000022-2-200000000-2-222-22-2200000000000000000000002-200-2200
χ242222-2-222-2-222-2-2-2-22200000022-2-200000000-2-222-22-220000000000000000000000-22002-200
χ252222-2-2-2-22222-2-2-2-222002-200-2-2220000000022-2-2-22-22000022-2-2002-2000000000000000000
χ262222-2-2-2-22222-2-2-2-222002-200-2-22200000000-2-2222-22-2000022-2-200-22000000000000000000
χ272222-2-2-2-22222-2-2-2-22200-2200-2-2220000000022-2-2-22-220000-2-22200-22000000000000000000
χ282222-2-2-2-22222-2-2-2-22200-2200-2-22200000000-2-2222-22-20000-2-222002-2000000000000000000
χ292-22-22-22-22-22-222-2-22-200002i−2i2-22-22i2i2i2i−2i−2i−2i−2i2-22-22-2-2200000000000000002i−2i000000000000
χ302-22-22-22-22-22-222-2-22-200002i−2i2-22-22i2i2i2i−2i−2i−2i−2i-22-22-222-20000000000000000−2i2i000000000000
χ312-22-22-22-22-22-222-2-22-20000−2i2i2-22-2−2i−2i−2i−2i2i2i2i2i2-22-22-2-220000000000000000−2i2i000000000000
χ322-22-22-22-22-22-222-2-22-20000−2i2i2-22-2−2i−2i−2i−2i2i2i2i2i-22-22-222-200000000000000002i−2i000000000000
χ332-22-22-2-22-222-222-2-22-2000000-22-22000000002-22-2-222-20000000000002i−2i2i−2i00000000000000
χ342-22-22-2-22-222-222-2-22-2000000-22-22000000002-22-2-222-2000000000000−2i2i−2i2i00000000000000
χ352-22-22-2-22-222-222-2-22-2000000-22-2200000000-22-222-2-220000000000002-2-2200000000000000
χ362-22-22-2-22-222-222-2-22-2000000-22-2200000000-22-222-2-22000000000000-222-200000000000000
χ372-22-2-222-2-222-2-2-2222-20000002-2-22000000002-2-2222-2-20000000000000000002i−2i2i−2i00000000
χ382-22-2-222-2-222-2-2-2222-20000002-2-22000000002-2-2222-2-2000000000000000000−2i2i−2i2i00000000
χ392-22-2-222-2-222-2-2-2222-20000002-2-2200000000-222-2-2-2220000000000000000002-2-2200000000
χ402-22-2-222-2-222-2-2-2222-20000002-2-2200000000-222-2-2-222000000000000000000-222-200000000
χ412-22-2-22-222-22-2-2-2222-22-20000-222-2000000002-2-22-2-22222-2-200002-200000000000000000000
χ422-22-2-22-222-22-2-2-2222-22-20000-222-200000000-222-222-2-222-2-20000-2200000000000000000000
χ432-22-2-22-222-22-2-2-2222-2-220000-222-2000000002-2-22-2-222-2-2220000-2200000000000000000000
χ442-22-2-22-222-22-2-2-2222-2-220000-222-200000000-222-222-2-2-2-22200002-200000000000000000000
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
χ494444-4-4-4-444-1-11111-1-1004-40011-1-155−5−555−5−5000000005−55−5-1-1110000000000000000000000
χ504444-4-4-4-444-1-11111-1-1004-40011-1-1−5−555−5−55500000000−55−55-1-1110000000000000000000000
χ514444-4-4-4-444-1-11111-1-100-440011-1-155−5−555−5−500000000−55−5511-1-10000000000000000000000
χ524444-4-4-4-444-1-11111-1-100-440011-1-1−5−555−5−555000000005−55−511-1-10000000000000000000000
χ534-44-44-44-44-4-11-1-111-1100004i−4i-11-11−i−i−i−iiiii000000005−5−55i5−i5i5−i50000000000000000000000
χ544-44-44-44-44-4-11-1-111-1100004i−4i-11-11−i−i−i−iiiii00000000−555−5−i5i5−i5i50000000000000000000000
χ554-44-44-44-44-4-11-1-111-110000−4i4i-11-11iiii−i−i−i−i000000005−5−55−i5i5−i5i50000000000000000000000
χ564-44-44-44-44-4-11-1-111-110000−4i4i-11-11iiii−i−i−i−i00000000−555−5i5−i5i5−i50000000000000000000000
χ574-44-4-44-444-4-1111-1-1-114-400001-1-11i5i5−i5−i5−i5−i5i5i500000000-1-111i5−i5−i5i50000000000000000000000
χ584-44-4-44-444-4-1111-1-1-114-400001-1-11−i5−i5i5i5i5i5−i5−i500000000-1-111−i5i5i5−i50000000000000000000000
χ594-44-4-44-444-4-1111-1-1-11-4400001-1-11i5i5−i5−i5−i5−i5i5i50000000011-1-1−i5i5i5−i50000000000000000000000
χ604-44-4-44-444-4-1111-1-1-11-4400001-1-11−i5−i5i5i5i5i5−i5−i50000000011-1-1i5−i5−i5i50000000000000000000000
χ61888888-8-8-8-8-2-2-2-2-2-2-2-200000022220000000000000000000000000000000000000000000000
χ628888-8-888-8-8-2-22222-2-2000000-2-2220000000000000000000000000000000000000000000000
χ6388-8-80000008-80000-8800000000000000000000000000000000000000000000000000000000
χ6488-8-8000000-2225−2525−252-20000000000−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ3900000000000000000000000000000000000000
χ6588-8-8000000-2225−2525−252-20000000000ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ3900000000000000000000000000000000000000
χ6688-8-8000000-22−2525−25252-20000000000ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ3900000000000000000000000000000000000000
χ6788-8-8000000-22−2525−25252-20000000000−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ3900000000000000000000000000000000000000
χ688-88-88-8-88-88-22-2-222-220000002-22-20000000000000000000000000000000000000000000000
χ698-88-8-888-8-88-2222-2-2-22000000-222-20000000000000000000000000000000000000000000000
χ708-8-88000000880000-8-800000000000000000000000000000000000000000000000000000000
χ718-8-88000000-2-225−25−2525220000000000ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ39−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ39−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ39ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ39−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ39ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ39ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ39−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ3900000000000000000000000000000000000000
χ728-8-88000000-2-225−25−2525220000000000−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ39ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ39ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ39−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ39ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ39−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ39−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ39ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ3900000000000000000000000000000000000000
χ738-8-88000000-2-2−252525−25220000000000−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ39ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ39−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ39ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ39ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ39−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ39ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ39−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ3900000000000000000000000000000000000000
χ748-8-88000000-2-2−252525−25220000000000ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ39−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ39ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ39−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ39−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ39ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ39−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ39ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ3900000000000000000000000000000000000000

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