Finite Group Databasebeta

← Group #13019570

Character table — Group #13019570

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444444448888888888888888881010101010101010161616161616161640404040404040404040404040404040404040404040
order12222244445101010101010104444442020202020202020202020204444444420202020202020204444448888888888888888
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
χ511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ9111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-1
χ10111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111
χ11111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111iiii−i−i−i−i−i−i−i−iiiii
χ12111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111−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
χ17222222-2-2-2-222222222002-20000000000-2-2-2-222-2-2-2-222000022-2-2002-2000000000000000000
χ18222222-2-2-2-222222222002-20000000000-2-2-2-2-2-22222-2-2000022-2-200-22000000000000000000
χ19222222-2-2-2-22222222200-220000000000-2-2-2-222-2-2-2-2220000-2-22200-22000000000000000000
χ20222222-2-2-2-22222222200-220000000000-2-2-2-2-2-22222-2-20000-2-222002-2000000000000000000
χ212222-2-222-2-222-2-2-2-2220000000000000022-2-22222-2-2-2-20000000000000000000000002i−2i002i−2i
χ222222-2-222-2-222-2-2-2-2220000000000000022-2-22222-2-2-2-2000000000000000000000000−2i2i00−2i2i
χ232222-2-222-2-222-2-2-2-2220000000000000022-2-2-2-2-2-222220000000000000000000000002-200-22
χ242222-2-222-2-222-2-2-2-2220000000000000022-2-2-2-2-2-22222000000000000000000000000-22002-2
χ252222-2-2-2-22222-2-2-2-22200000000000000-2-22222-2-222-2-200000000000000000000002i−2i002i−2i00
χ262222-2-2-2-22222-2-2-2-22200000000000000-2-22222-2-222-2-20000000000000000000000−2i2i00−2i2i00
χ272222-2-2-2-22222-2-2-2-22200000000000000-2-222-2-222-2-22200000000000000000000002-200-2200
χ282222-2-2-2-22222-2-2-2-22200000000000000-2-222-2-222-2-2220000000000000000000000-22002-200
χ292-22-22-22-22-22-2-2-222-22000000000000002-22-22i−2i2i−2i2i−2i2i−2i0000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000
χ302-22-22-22-22-22-2-2-222-22000000000000002-22-22i−2i2i−2i2i−2i2i−2i00000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000
χ312-22-22-22-22-22-2-2-222-22000000000000002-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000
χ322-22-22-22-22-22-2-2-222-22000000000000002-22-2−2i2i−2i2i−2i2i−2i2i00000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000
χ332-22-22-2-22-222-2-2-222-2200000000000000-22-222i−2i−2i2i−2i2i2i−2i00000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ342-22-22-2-22-222-2-2-222-2200000000000000-22-222i−2i−2i2i−2i2i2i−2i000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ352-22-22-2-22-222-2-2-222-2200000000000000-22-22−2i2i2i−2i2i−2i−2i2i00000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ362-22-22-2-22-222-2-2-222-2200000000000000-22-22−2i2i2i−2i2i−2i−2i2i000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ372-22-2-222-2-222-222-2-2-222i−2i0000000000002-2-222i−2i2i−2i−2i2i−2i2i2i2i−2i−2i00002-200000000000000000000
χ382-22-2-222-2-222-222-2-2-222i−2i0000000000002-2-22−2i2i−2i2i2i−2i2i−2i2i2i−2i−2i0000-2200000000000000000000
χ392-22-2-222-2-222-222-2-2-22−2i2i0000000000002-2-222i−2i2i−2i−2i2i−2i2i−2i−2i2i2i0000-2200000000000000000000
χ402-22-2-222-2-222-222-2-2-22−2i2i0000000000002-2-22−2i2i−2i2i2i−2i2i−2i−2i−2i2i2i00002-200000000000000000000
χ412-22-2-22-222-22-222-2-2-2200002i−2i2i2i2i2i−2i−2i−2i−2i-222-22i−2i−2i2i2i−2i−2i2i0000000000002-20000000000000000
χ422-22-2-22-222-22-222-2-2-2200002i−2i2i2i2i2i−2i−2i−2i−2i-222-2−2i2i2i−2i−2i2i2i−2i000000000000-220000000000000000
χ432-22-2-22-222-22-222-2-2-220000−2i2i−2i−2i−2i−2i2i2i2i2i-222-22i−2i−2i2i2i−2i−2i2i000000000000-220000000000000000
χ442-22-2-22-222-22-222-2-2-220000−2i2i−2i−2i−2i−2i2i2i2i2i-222-2−2i2i2i−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
χ464444444444-1-1-1-1-1-1-1-144-4-4-4-411111111-1-1-1-100000000-1-1-1-111110000000000000000000000
χ474444444444-1-1-1-1-1-1-1-1-4-444-4-411111111-1-1-1-1000000001111-1-1-1-10000000000000000000000
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
χ49444444-4-4-4-4-1-1-1-1-1-1-1-1004-40055−5−555−5−51111000000005−55−5-1-1110000000000000000000000
χ50444444-4-4-4-4-1-1-1-1-1-1-1-1004-400−5−555−5−555111100000000−55−55-1-1110000000000000000000000
χ51444444-4-4-4-4-1-1-1-1-1-1-1-100-440055−5−555−5−5111100000000−55−5511-1-10000000000000000000000
χ52444444-4-4-4-4-1-1-1-1-1-1-1-100-4400−5−555−5−5551111000000005−55−511-1-10000000000000000000000
χ534-44-4-444-4-44-11-1-1111-14i−4i0000i5i5−i5−i5−i5−i5i5i5-111-100000000−i−iii5−55−50000000000000000000000
χ544-44-4-444-4-44-11-1-1111-14i−4i0000−i5−i5i5i5i5i5−i5−i5-111-100000000−i−iii−55−550000000000000000000000
χ554-44-4-444-4-44-11-1-1111-1−4i4i0000i5i5−i5−i5−i5−i5i5i5-111-100000000ii−i−i−55−550000000000000000000000
χ564-44-4-444-4-44-11-1-1111-1−4i4i0000−i5−i5i5i5i5i5−i5−i5-111-100000000ii−i−i5−55−50000000000000000000000
χ574-44-4-44-444-4-11-1-1111-100004i−4i−i−i−i−iiiii1-1-1100000000i5−i5−i5i55−5−550000000000000000000000
χ584-44-4-44-444-4-11-1-1111-100004i−4i−i−i−i−iiiii1-1-1100000000−i5i5i5−i5−555−50000000000000000000000
χ594-44-4-44-444-4-11-1-1111-10000−4i4iiiii−i−i−i−i1-1-1100000000i5−i5−i5i5−555−50000000000000000000000
χ604-44-4-44-444-4-11-1-1111-10000−4i4iiiii−i−i−i−i1-1-1100000000−i5i5i5−i55−5−550000000000000000000000
χ618888-8-888-8-8-2-22222-2-200000000000000-2-22200000000000000000000000000000000000000
χ628888-8-8-8-888-2-22222-2-20000000000000022-2-200000000000000000000000000000000000000
χ6388-8-80000008-800008-800000000000000000000000000000000000000000000000000000000
χ6488-8-8000000-2225−2525−25-220000002ζ6−2ζ14−2ζ6+2ζ14−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ14−2ζ22+2ζ382ζ22−2ζ38000000000000000000000000000000000000000000
χ6588-8-8000000-2225−2525−25-22000000−2ζ6+2ζ142ζ6−2ζ142ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ142ζ22−2ζ38−2ζ22+2ζ38000000000000000000000000000000000000000000
χ6688-8-8000000-22−2525−2525-22000000−2ζ22+2ζ382ζ22−2ζ38−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ38−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000000000000000000000
χ6788-8-8000000-22−2525−2525-220000002ζ22−2ζ38−2ζ22+2ζ382ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ382ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000000000000000000000
χ688-88-88-88-88-8-2222-2-22-200000000000000-22-2200000000000000000000000000000000000000
χ698-88-88-8-88-88-2222-2-22-2000000000000002-22-200000000000000000000000000000000000000
χ708-8-88000000880000-8-800000000000000000000000000000000000000000000000000000000
χ718-8-88000000-2-225−25−252522000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28000000000000000000000000000000000000000000
χ728-8-88000000-2-225−25−2525220000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28000000000000000000000000000000000000000000
χ738-8-88000000-2-2−252525−25220000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36000000000000000000000000000000000000000000
χ748-8-88000000-2-2−252525−2522000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36000000000000000000000000000000000000000000

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