Finite Group Databasebeta

← Group #13022554

Character table — Group #13022554

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444444448888888888888888881010101010101010161616161616161640404040404040404040404040404040404040404040
order12222244445101010101010102244442020202020202020202020202222444410101010202020204444444444444488888888
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
χ17222222-2-2-2-222222222002-200-2-2-2-2000000002222-2-2-2-2000022-2-22-200000000000000000000
χ18222222-2-2-2-222222222002-200-2-2-2-200000000-2-2-2-22222000022-2-2-2200000000000000000000
χ19222222-2-2-2-22222222200-2200-2-2-2-2000000002222-2-2-2-20000-2-222-2200000000000000000000
χ20222222-2-2-2-22222222200-2200-2-2-2-200000000-2-2-2-222220000-2-2222-200000000000000000000
χ212222-2-222-2-222-2-22-2-2200000022-2-20000000022-2-22-22-200000000000000002i−2i002i−2i00000000
χ222222-2-222-2-222-2-22-2-2200000022-2-20000000022-2-22-22-20000000000000000−2i2i00−2i2i00000000
χ232222-2-222-2-222-2-22-2-2200000022-2-200000000-2-222-22-2200000000000000002-200-2200000000
χ242222-2-222-2-222-2-22-2-2200000022-2-200000000-2-222-22-220000000000000000-22002-200000000
χ252222-2-2-2-22222-2-22-2-22000000-2-2220000000022-2-2-22-22000000000000002i−2i002i−2i0000000000
χ262222-2-2-2-22222-2-22-2-22000000-2-2220000000022-2-2-22-2200000000000000−2i2i00−2i2i0000000000
χ272222-2-2-2-22222-2-22-2-22000000-2-22200000000-2-2222-22-2000000000000002-200-220000000000
χ282222-2-2-2-22222-2-22-2-22000000-2-22200000000-2-2222-22-200000000000000-22002-20000000000
χ292-2-222-22-22-22-2222-2-2-200002i−2i2-22-22i2i2i2i−2i−2i−2i−2i2-22-2-2-2220000000000002i−2i0000000000000000
χ302-2-222-22-22-22-2222-2-2-200002i−2i2-22-22i2i2i2i−2i−2i−2i−2i-22-2222-2-2000000000000−2i2i0000000000000000
χ312-2-222-22-22-22-2222-2-2-20000−2i2i2-22-2−2i−2i−2i−2i2i2i2i2i2-22-2-2-222000000000000−2i2i0000000000000000
χ322-2-222-22-22-22-2222-2-2-20000−2i2i2-22-2−2i−2i−2i−2i2i2i2i2i-22-2222-2-20000000000002i−2i0000000000000000
χ332-2-222-2-22-222-2222-2-2-22-20000-22-22000000002-22-222-2-222-2-20000002-2000000000000000000
χ342-2-222-2-22-222-2222-2-2-22-20000-22-2200000000-22-22-2-22222-2-2000000-22000000000000000000
χ352-2-222-2-22-222-2222-2-2-2-220000-22-22000000002-22-222-2-2-2-222000000-22000000000000000000
χ362-2-222-2-22-222-2222-2-2-2-220000-22-2200000000-22-22-2-222-2-2220000002-2000000000000000000
χ372-2-22-222-2-222-2-2-2222-20000002-2-22000000002-2-22-222-200000000000000000000002-2002-200
χ382-2-22-222-2-222-2-2-2222-20000002-2-22000000002-2-22-222-20000000000000000000000-2200-2200
χ392-2-22-222-2-222-2-2-2222-20000002-2-2200000000-222-22-2-2200000000000000000000002i−2i00−2i2i00
χ402-2-22-222-2-222-2-2-2222-20000002-2-2200000000-222-22-2-220000000000000000000000−2i2i002i−2i00
χ412-2-22-22-222-22-2-2-2222-2000000-222-2000000002-2-222-2-220000000000000000000000002-2002-2
χ422-2-22-22-222-22-2-2-2222-2000000-222-2000000002-2-222-2-22000000000000000000000000-2200-22
χ432-2-22-22-222-22-2-2-2222-2000000-222-200000000-222-2-222-20000000000000000000000002i−2i00−2i2i
χ442-2-22-22-222-22-2-2-2222-2000000-222-200000000-222-2-222-2000000000000000000000000−2i2i002i−2i
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
χ534-4-444-44-44-4-11-1-1-111100004i−4i-11-11−i−i−i−iiiii000000005−5−55i5−i5i5−i50000000000000000000000
χ544-4-444-44-44-4-11-1-1-111100004i−4i-11-11−i−i−i−iiiii00000000−555−5−i5i5−i5i50000000000000000000000
χ554-4-444-44-44-4-11-1-1-11110000−4i4i-11-11iiii−i−i−i−i000000005−5−55−i5i5−i5i50000000000000000000000
χ564-4-444-44-44-4-11-1-1-11110000−4i4i-11-11iiii−i−i−i−i00000000−555−5i5−i5i5−i50000000000000000000000
χ574-4-444-4-44-44-11-1-1-11114-400001-11-1i5i5−i5−i5−i5−i5i5i500000000-1-111i5−i5−i5i50000000000000000000000
χ584-4-444-4-44-44-11-1-1-11114-400001-11-1−i5−i5i5i5i5i5−i5−i500000000-1-111−i5i5i5−i50000000000000000000000
χ594-4-444-4-44-44-11-1-1-1111-4400001-11-1i5i5−i5−i5−i5−i5i5i50000000011-1-1−i5i5i5−i50000000000000000000000
χ604-4-444-4-44-44-11-1-1-1111-4400001-11-1−i5−i5i5i5i5i5−i5−i50000000011-1-1i5−i5−i5i50000000000000000000000
χ618888-8-888-8-8-2-222-222-2000000-2-2220000000000000000000000000000000000000000000000
χ628888-8-8-8-888-2-222-222-200000022-2-20000000000000000000000000000000000000000000000
χ6388-8-80000008800-800-800000000000000000000000000000000000000000000000000000000
χ6488-8-8000000-2-225−25225−25200000000002ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ1900000000000000000000000000000000000000
χ6588-8-8000000-2-225−25225−2520000000000−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ1900000000000000000000000000000000000000
χ6688-8-8000000-2-2−25252−252520000000000−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ700000000000000000000000000000000000000
χ6788-8-8000000-2-2−25252−2525200000000002ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ700000000000000000000000000000000000000
χ688-88-80000008-800-800800000000000000000000000000000000000000000000000000000000
χ698-88-8000000-2225−252−2525-20000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000000000
χ708-88-8000000-2225−252−2525-200000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000000000
χ718-88-8000000-22−2525225−25-200000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ1800000000000000000000000000000000000000
χ728-88-8000000-22−2525225−25-20000000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ1800000000000000000000000000000000000000
χ738-8-88-888-8-88-2222-2-2-22000000-222-20000000000000000000000000000000000000000000000
χ748-8-88-88-888-8-2222-2-2-220000002-2-220000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.