Finite Group Databasebeta

← Group #13017687

Character table — Group #13017687

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111222244444444444888888888888888881010101016161616161616162020202020202020404040404040404040404080808080
order12222244444510101010101010244441010101020202020202020204444202020202020202022224444244888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ511111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111111111-1-1-1-1
χ611111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111iiii−i−i−i−i−i−iii
χ811111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111−i−i−i−iiiiiii−i−i
χ9111111111-1-111111111-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-111-1-1-111-1-111-1-11-11-1
χ10111111111-1-111111111-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-111-1-111-11-11
χ11111111111-1-111111111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111ii−i−i−i−iiii−i−ii
χ12111111111-1-111111111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111−i−iiiii−i−i−iii−i
χ13111111111-1-111111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-11111-1-111-1-1-11-11
χ14111111111-1-111111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-111-1-111-1-1111-11-1
χ15111111111-1-111111111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-1ii−i−i−i−iii−iii−i
χ16111111111-1-111111111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-1−i−iiiii−i−ii−i−ii
χ17222222-2-2-22222222222-20000-2-2-2-2-2-2-2-22222222200000000000022-2-2-200000000000000
χ18222222-2-2-22222222222-20000-2-2-2-2-2-2-2-22222-2-2-2-2000000000000-2-222200000000000000
χ19222222-2-2-2-2-222222222200002222-2-2-2-2-2-2-2-22222000000000000-2-2-2-2200000000000000
χ20222222-2-2-2-2-222222222200002222-2-2-2-2-2-2-2-2-2-2-2-20000000000002222-200000000000000
χ212222-2-222-20022-2-2-2-22202-200000022-2-200002-22-222-2-2000022-2-2002-2000000000000000
χ222222-2-222-20022-2-2-2-22202-200000022-2-20000-22-2222-2-20000-2-22200-22000000000000000
χ232222-2-222-20022-2-2-2-2220-2200000022-2-200002-22-2-2-2220000-2-222002-2000000000000000
χ242222-2-222-20022-2-2-2-2220-2200000022-2-20000-22-22-2-222000022-2-200-22000000000000000
χ252222-2-2-2-220022-2-2-2-2220002-20000-2-22200002-22-2000022-2-2000000-2202-2000000000000
χ262222-2-2-2-220022-2-2-2-2220002-20000-2-2220000-22-22000022-2-20000002-20-22000000000000
χ272222-2-2-2-220022-2-2-2-222000-220000-2-22200002-22-20000-2-222000000-220-22000000000000
χ282222-2-2-2-220022-2-2-2-222000-220000-2-2220000-22-220000-2-2220000002-202-2000000000000
χ292-22-22-20002i−2i2-222-2-22-200000000000002i2i−2i−2i2-2-220000000000002i−2i00000i2−i22−2i2−i22−20000
χ302-22-22-20002i−2i2-222-2-22-200000000000002i2i−2i−2i2-2-220000000000002i−2i00000−i2i2−22−i2i2−220000
χ312-22-22-20002i−2i2-222-2-22-200000000000002i2i−2i−2i-222-2000000000000−2i2i000002−2−i2i2−22i2−i20000
χ322-22-22-20002i−2i2-222-2-22-200000000000002i2i−2i−2i-222-2000000000000−2i2i00000−22i2−i22−2−i2i20000
χ332-22-22-2000−2i2i2-222-2-22-20000000000000−2i−2i2i2i2-2-22000000000000−2i2i00000i2−i2−22i2−i2−220000
χ342-22-22-2000−2i2i2-222-2-22-20000000000000−2i−2i2i2i2-2-22000000000000−2i2i00000−i2i22−2−i2i22−20000
χ352-22-22-2000−2i2i2-222-2-22-20000000000000−2i−2i2i2i-222-20000000000002i−2i000002−2i2−i2−22−i2i20000
χ362-22-22-2000−2i2i2-222-2-22-20000000000000−2i−2i2i2i-222-20000000000002i−2i00000−22−i2i22−2i2−i20000
χ3744444444444-1-1-1-1-1-1-1-144444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-100000000000000000000000
χ3844444444444-1-1-1-1-1-1-1-14-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100001111111100000000000000000000000
χ39444444444-4-4-1-1-1-1-1-1-1-1-444-4-41111-1-1-1-111110000-1-1-1-1111100000000000000000000000
χ40444444444-4-4-1-1-1-1-1-1-1-1-4-4-4441111-1-1-1-1111100001111-1-1-1-100000000000000000000000
χ41444444-4-4-444-1-1-1-1-1-1-1-1-4000011111111-1-1-1-100005−55−55−55−500000000000000000000000
χ42444444-4-4-444-1-1-1-1-1-1-1-1-4000011111111-1-1-1-10000−55−55−55−5500000000000000000000000
χ43444444-4-4-4-4-4-1-1-1-1-1-1-1-140000-1-1-1-11111111100005−55−5−55−5500000000000000000000000
χ44444444-4-4-4-4-4-1-1-1-1-1-1-1-140000-1-1-1-1111111110000−55−555−55−500000000000000000000000
χ454444-4-444-400-1-11111-1-104-40055−5−5-1-1115−55−50000-1-1115−5−5500000000000000000000000
χ464444-4-444-400-1-11111-1-104-400−5−555-1-111−55−550000-1-111−555−500000000000000000000000
χ474444-4-444-400-1-11111-1-10-440055−5−5-1-1115−55−5000011-1-1−555−500000000000000000000000
χ484444-4-444-400-1-11111-1-10-4400−5−555-1-111−55−55000011-1-15−5−5500000000000000000000000
χ494444-4-4-4-4400-1-11111-1-10004-455−5−511-1-1−55−550000−555−5-1-11100000000000000000000000
χ504444-4-4-4-4400-1-11111-1-10004-4−5−55511-1-15−55−500005−5−55-1-11100000000000000000000000
χ514444-4-4-4-4400-1-11111-1-1000-4455−5−511-1-1−55−5500005−5−5511-1-100000000000000000000000
χ524444-4-4-4-4400-1-11111-1-1000-44−5−55511-1-15−55−50000−555−511-1-100000000000000000000000
χ534-44-4-44000004-4-4-4444-40000000000000000044-4-40000000000000000000000000000000
χ544-44-4-44000004-4-4-4444-400000000000000000-4-4440000000000000000000000000000000
χ554-4-44004-40004-40000-440000000004-4000000000000000000004-40000000000000000000
χ564-4-44004-40004-40000-440000000004-400000000000000000000-440000000000000000000
χ574-4-4400-440004-40000-44000000000-440000000000000000004-4000000000000000000000
χ584-4-4400-440004-40000-44000000000-44000000000000000000-44000000000000000000000
χ5988-8-80000000880000-8-80000000000000000000000000000000000000000000000000000
χ6088-8-80000000-2-225−2525−252200000−2ζ4+2ζ12−2ζ28+2ζ362ζ4−2ζ12+2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ360000000000000000000000000000000000000000000
χ6188-8-80000000-2-225−2525−2522000002ζ4−2ζ12+2ζ28−2ζ36−2ζ4+2ζ12−2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ360000000000000000000000000000000000000000000
χ6288-8-80000000-2-2−2525−25252200000−2ζ4−2ζ12+2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ362ζ4−2ζ12+2ζ28−2ζ36−2ζ4+2ζ12−2ζ28+2ζ360000000000000000000000000000000000000000000
χ6388-8-80000000-2-2−2525−252522000002ζ4+2ζ12−2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ36−2ζ4+2ζ12−2ζ28+2ζ362ζ4−2ζ12+2ζ28−2ζ360000000000000000000000000000000000000000000
χ648-88-88-80008i−8i-22-2-222-220000000000000−2i−2i2i2i00000000000000000000000000000000000
χ658-88-88-8000−8i8i-22-2-222-2200000000000002i2i−2i−2i00000000000000000000000000000000000
χ668-88-8-8800000-2222-2-2-2200000000000002i5−2i5−2i52i500000000000000000000000000000000000
χ678-88-8-8800000-2222-2-2-220000000000000−2i52i52i5−2i500000000000000000000000000000000000
χ688-8-88008-8000-2225−25−25252-2000000000-2225−25000000000000000000000000000000000000000
χ698-8-88008-8000-22−252525−252-2000000000-22−2525000000000000000000000000000000000000000
χ708-8-8800-88000-2225−25−25252-20000000002-2−2525000000000000000000000000000000000000000
χ718-8-8800-88000-22−252525−252-20000000002-225−25000000000000000000000000000000000000000

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