Finite Group Databasebeta

← Group #13022461

Character table — Group #13022461

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444444448888888888888888881010101010101010161616161616161640404040404040404040404040404040404040404040
order12222244445101010101010104444442020202020202020202020202222444420202020202020202244444444444488888888
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
χ511111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ12111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ13111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-111
χ14111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-111-1-1
χ15111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222-2-2-2-2222222222-200002222-2-2-2-2-2-2-2-22222-2-2-2-200000000002-2000000000000000000
χ18222222-2-2-2-2222222222-200002222-2-2-2-2-2-2-2-2-2-2-2-222220000000000-22000000000000000000
χ19222222-2-2-2-222222222-220000-2-2-2-22222-2-2-2-22222-2-2-2-20000000000-22000000000000000000
χ20222222-2-2-2-222222222-220000-2-2-2-22222-2-2-2-2-2-2-2-2222200000000002-2000000000000000000
χ212222-2-222-2-22-2-2-2-222200002-20000000022-2-22-22-22-22-2000022-2-200002-20000000000000000
χ222222-2-222-2-22-2-2-2-222200002-20000000022-2-2-22-22-22-22000022-2-20000-220000000000000000
χ232222-2-222-2-22-2-2-2-22220000-220000000022-2-22-22-22-22-20000-2-2220000-220000000000000000
χ242222-2-222-2-22-2-2-2-22220000-220000000022-2-2-22-22-22-220000-2-22200002-20000000000000000
χ252222-2-2-2-2222-2-2-2-2222002-20000000000-2-2222-22-2-22-2222-2-200002-200000000000000000000
χ262222-2-2-2-2222-2-2-2-2222002-20000000000-2-222-22-222-22-222-2-20000-2200000000000000000000
χ272222-2-2-2-2222-2-2-2-222200-220000000000-2-2222-22-2-22-22-2-2220000-2200000000000000000000
χ282222-2-2-2-2222-2-2-2-222200-220000000000-2-222-22-222-22-2-2-22200002-200000000000000000000
χ292-2-222-22-22-2222-2-2-2-22000000000000002-22-222-2-22-2-220000000000000000000000002i−2i002i−2i
χ302-2-222-22-22-2222-2-2-2-22000000000000002-22-222-2-22-2-22000000000000000000000000−2i2i00−2i2i
χ312-2-222-22-22-2222-2-2-2-22000000000000002-22-2-2-222-222-20000000000000000000000002-200-22
χ322-2-222-22-22-2222-2-2-2-22000000000000002-22-2-2-222-222-2000000000000000000000000-22002-2
χ332-2-222-2-22-22222-2-2-2-2200000000000000-22-2222-2-2-222-200000000000000000000002i−2i002i−2i00
χ342-2-222-2-22-22222-2-2-2-2200000000000000-22-2222-2-2-222-20000000000000000000000−2i2i00−2i2i00
χ352-2-222-2-22-22222-2-2-2-2200000000000000-22-22-2-2222-2-2200000000000000000000002-200-2200
χ362-2-222-2-22-22222-2-2-2-2200000000000000-22-22-2-2222-2-220000000000000000000000-22002-200
χ372-2-22-222-2-222-2-222-2-22000000000000002-2-222-2-2222-2-2000000000000002i−2i002i−2i0000000000
χ382-2-22-222-2-222-2-222-2-22000000000000002-2-222-2-2222-2-200000000000000−2i2i00−2i2i0000000000
χ392-2-22-222-2-222-2-222-2-22000000000000002-2-22-222-2-2-222000000000000002-200-220000000000
χ402-2-22-222-2-222-2-222-2-22000000000000002-2-22-222-2-2-22200000000000000-22002-20000000000
χ412-2-22-22-222-22-2-222-2-2200000000000000-222-22-2-22-2-22200000000000000002-2002-200000000
χ422-2-22-22-222-22-2-222-2-2200000000000000-222-22-2-22-2-2220000000000000000-2200-2200000000
χ432-2-22-22-222-22-2-222-2-2200000000000000-222-2-222-222-2-200000000000000002i−2i00−2i2i00000000
χ442-2-22-22-222-22-2-222-2-2200000000000000-222-2-222-222-2-20000000000000000−2i2i002i−2i00000000
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
χ474444444444-1-1-1-1-1-1-1-1-4-444-4-411111111-1-1-1-100000000-1-1-1-111110000000000000000000000
χ484444444444-1-1-1-1-1-1-1-1-4-4-4-44411111111-1-1-1-1000000001111-1-1-1-10000000000000000000000
χ49444444-4-4-4-4-1-1-1-1-1-1-1-14-40000-1-1-1-111111111000000005−55−55−55−50000000000000000000000
χ50444444-4-4-4-4-1-1-1-1-1-1-1-14-40000-1-1-1-11111111100000000−55−55−55−550000000000000000000000
χ51444444-4-4-4-4-1-1-1-1-1-1-1-1-4400001111-1-1-1-11111000000005−55−5−55−550000000000000000000000
χ52444444-4-4-4-4-1-1-1-1-1-1-1-1-4400001111-1-1-1-1111100000000−55−555−55−50000000000000000000000
χ534444-4-444-4-4-11111-1-1-100004-455−5−555−5−5-1-111000000005−5−55-1-1110000000000000000000000
χ544444-4-444-4-4-11111-1-1-100004-4−5−555−5−555-1-11100000000−555−5-1-1110000000000000000000000
χ554444-4-444-4-4-11111-1-1-10000-4455−5−555−5−5-1-11100000000−555−511-1-10000000000000000000000
χ564444-4-444-4-4-11111-1-1-10000-44−5−555−5−555-1-111000000005−5−5511-1-10000000000000000000000
χ574444-4-4-4-444-11111-1-1-1004-40055−5−5−5−55511-1-100000000-1-1115−5−550000000000000000000000
χ584444-4-4-4-444-11111-1-1-1004-400−5−55555−5−511-1-100000000-1-111−555−50000000000000000000000
χ594444-4-4-4-444-11111-1-1-100-440055−5−5−5−55511-1-10000000011-1-1−555−50000000000000000000000
χ604444-4-4-4-444-11111-1-1-100-4400−5−55555−5−511-1-10000000011-1-15−5−550000000000000000000000
χ6188-8-8000000800008-8-800000000000000000000000000000000000000000000000000000000
χ6288-8-8000000-225−2525−25-222000000−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ180000000000000000000000000000000000000000000000
χ6388-8-8000000-225−2525−25-2220000002ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ180000000000000000000000000000000000000000000000
χ6488-8-8000000-2−2525−2525-222000000−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ180000000000000000000000000000000000000000000000
χ6588-8-8000000-2−2525−2525-2220000002ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ180000000000000000000000000000000000000000000000
χ668-88-800000080000-88-800000000000000000000000000000000000000000000000000000000
χ678-88-8000000-225−25−25252-220000000000−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18000000000000000000000000000000000000000000
χ688-88-8000000-225−25−25252-2200000000002ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18000000000000000000000000000000000000000000
χ698-88-8000000-2−252525−252-220000000000−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ18000000000000000000000000000000000000000000
χ708-88-8000000-2−252525−252-2200000000002ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18000000000000000000000000000000000000000000
χ718-8-888-88-88-8-2-2-22222-200000000000000-22-2200000000000000000000000000000000000000
χ728-8-888-8-88-88-2-2-22222-2000000000000002-22-200000000000000000000000000000000000000
χ738-8-88-888-8-88-222-2-222-200000000000000-222-200000000000000000000000000000000000000
χ748-8-88-88-888-8-222-2-222-2000000000000002-2-2200000000000000000000000000000000000000

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