Finite Group Databasebeta

← Group #13020306

Character table — Group #13020306

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111122444444444444448810101010101016161616161616161616161616161620202020202020202020202020202020202020202040408080808080
order12222222444451010101010101044444444210101010101020202020202020202244488888888888888884428888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1ii−i−i
χ41111111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1−i−iii
χ511111111111111111111-1-1111111-111-1-1-1-11111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1
χ611111111111111111111-1-1111111-111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i111−i−iii
χ811111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii111ii−i−i
χ9111111-1-111-1-11111111111111111-1-1-1-1-1-1-111-1-11111-1-11-1-11111-1-1-1-11111-1-1-1-111-11-11-1
χ10111111-1-111-1-11111111111111111-1-1-1-1-1-1-111-1-11111-1-11-1-1-1-1-1-11111-1-1-1-1111111-1-11-11
χ11111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-111iiii−i−i−i−i−i−i−i−iiiii-1-11i−i−ii
χ12111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-111−i−i−i−iiiiiiiii−i−i−i−i-1-11−iii−i
χ13111111-1-111-1-111111111-1-11111111-1-1111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-11-11-11
χ14111111-1-111-1-111111111-1-11111111-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-11111-1-111-11-1
χ15111111-1-111-1-111111111-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-111-111iiii−i−i−i−i−i−i−i−iiiii11-1−iii−i
χ16111111-1-111-1-111111111-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-111-111−i−i−i−iiiiiiiii−i−i−i−i11-1i−i−ii
χ1722222222-2-2-2-222222222002222-2-20220000-2-2-2-2000022-2-2-200000000000000000000000
χ1822222222-2-2-2-22222222200-2-2-2-2220220000-2-2-2-20000-2-222200000000000000000000000
χ19222222-2-2-2-22222222222002222-2-20-2-20000-2-2220000-2-2-22200000000000000000000000
χ20222222-2-2-2-2222222222200-2-2-2-2220-2-20000-2-2220000222-2-200000000000000000000000
χ212222-2-2002-20022-2-222-2-2002-22-22200000002-200000000-200000022-2-2000022-2-20000000
χ222222-2-2002-20022-2-222-2-2002-22-22200000002-200000000-2000000-2-2220000-2-2220000000
χ232222-2-2002-20022-2-222-2-200-22-22-2-200000002-20000000020000002i2i−2i−2i0000−2i−2i2i2i0000000
χ242222-2-2002-20022-2-222-2-200-22-22-2-200000002-2000000002000000−2i−2i2i2i00002i2i−2i−2i0000000
χ252222-2-200-220022-2-222-2-2002-22-2-2-20000000-22000000002002i2i−2i−2i00002i2i−2i−2i00000000000
χ262222-2-200-220022-2-222-2-2002-22-2-2-20000000-2200000000200−2i−2i2i2i0000−2i−2i2i2i00000000000
χ272222-2-200-220022-2-222-2-200-22-22220000000-2200000000-20022-2-20000-2-22200000000000
χ282222-2-200-220022-2-222-2-200-22-22220000000-2200000000-200-2-222000022-2-200000000000
χ292-22-22-200002i−2i2222-2-2-2-2002-2-22000000000002i−2i00000002i−2i2−22−2i2−i2i2−i22−22−2i2−i2i2−i20000000
χ302-22-22-200002i−2i2222-2-2-2-2002-2-22000000000002i−2i00000002i−2i−22−22−i2i2−i2i2−22−22−i2i2−i2i20000000
χ312-22-22-200002i−2i2222-2-2-2-200-222-2000000000002i−2i0000000−2i2ii2−i2i2−i2−22−22−i2i2−i2i22−22−20000000
χ322-22-22-200002i−2i2222-2-2-2-200-222-2000000000002i−2i0000000−2i2i−i2i2−i2i22−22−2i2−i2i2−i2−22−220000000
χ332-22-22-20000−2i2i2222-2-2-2-2002-2-2200000000000−2i2i0000000−2i2i2−22−2−i2i2−i2i22−22−2−i2i2−i2i20000000
χ342-22-22-20000−2i2i2222-2-2-2-2002-2-2200000000000−2i2i0000000−2i2i−22−22i2−i2i2−i2−22−22i2−i2i2−i20000000
χ352-22-22-20000−2i2i2222-2-2-2-200-222-200000000000−2i2i00000002i−2ii2−i2i2−i22−22−2−i2i2−i2i2−22−220000000
χ362-22-22-20000−2i2i2222-2-2-2-200-222-200000000000−2i2i00000002i−2i−i2i2−i2i2−22−22i2−i2i2−i22−22−20000000
χ372-22-2-222-2000022-2-2-2-2220022-2-20002-20000000000002-2000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000
χ382-22-2-222-2000022-2-2-2-2220022-2-20002-20000000000002-2000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000
χ392-22-2-222-2000022-2-2-2-22200-2-2220002-2000000000000-220002−2−222−2−22−222−2−222−20000000
χ402-22-2-222-2000022-2-2-2-22200-2-2220002-2000000000000-22000−222−2−222−22−2−222−2−220000000
χ412-22-2-22-22000022-2-2-2-2220022-2-2000-22000000000000-22000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000
χ422-22-2-22-22000022-2-2-2-2220022-2-2000-22000000000000-22000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000
χ432-22-2-22-22000022-2-2-2-22200-2-222000-220000000000002-20002−2−22−222−2−222−22−2−220000000
χ442-22-2-22-22000022-2-2-2-22200-2-222000-220000000000002-2000−222−22−2−222−2−22−222−20000000
χ45444444444444-1-1-1-1-1-1-1-1440000004-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000
χ46444444444444-1-1-1-1-1-1-1-1-4-4000000-4-1-11111-1-1-1-111110000000000000000000000000000
χ4744444444-4-4-4-4-1-1-1-1-1-1-1-1000000000-1-155−5−5111155−5−50000000000000000000000000000
χ4844444444-4-4-4-4-1-1-1-1-1-1-1-1000000000-1-1−5−5551111−5−5550000000000000000000000000000
χ49444444-4-444-4-4-1-1-1-1-1-1-1-144000000-4111111-1-111-1-1-1-10000000000000000000000000000
χ50444444-4-444-4-4-1-1-1-1-1-1-1-1-4-4000000411-1-1-1-1-1-11111110000000000000000000000000000
χ51444444-4-4-4-444-1-1-1-1-1-1-1-10000000001155−5−511-1-1−5−5550000000000000000000000000000
χ52444444-4-4-4-444-1-1-1-1-1-1-1-100000000011−5−55511-1-155−5−50000000000000000000000000000
χ534-4-44000000004-4004-4002-200004-4000000000002-22-20000000000000000000002-200000
χ544-4-44000000004-4004-4002-20000-44000000000002-22-2000000000000000000000-2200000
χ554-4-44000000004-4004-400-2200004-400000000000-22-22000000000000000000000-2200000
χ564-4-44000000004-4004-400-220000-4400000000000-22-220000000000000000000002-200000
χ578888-8-8008-800-2-222-2-222000000000000000-220000000000000000000000000000000000
χ588888-8-800-8800-2-222-2-2220000000000000002-20000000000000000000000000000000000
χ5988-8-8000000008-800-8800000000000000000000000000000000000000000000000000000
χ6088-8-800000000-2225−252-225−25000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36000000000000000000000000000000000000
χ6188-8-800000000-2225−252-225−2500000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36000000000000000000000000000000000000
χ6288-8-800000000-22−25252-2−252500000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28000000000000000000000000000000000000
χ6388-8-800000000-22−25252-2−2525000000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28000000000000000000000000000000000000
χ648-88-88-800008i−8i-2-2-2-2222200000000000000000−2i2i00000000000000000000000000000000
χ658-88-88-80000−8i8i-2-2-2-22222000000000000000002i−2i00000000000000000000000000000000
χ668-88-8-888-80000-2-22222-2-2000000000-220000000000000000000000000000000000000000
χ678-88-8-88-880000-2-22222-2-20000000002-20000000000000000000000000000000000000000
χ688-8-8800000000-2225−25-22−25254-400000000000000000−1−51+5−1+51−50000000000000000000000000000
χ698-8-8800000000-2225−25-22−2525-44000000000000000001+5−1−51−5−1+50000000000000000000000000000
χ708-8-8800000000-22−2525-2225−254-400000000000000000−1+51−5−1−51+50000000000000000000000000000
χ718-8-8800000000-22−2525-2225−25-44000000000000000001−5−1+51+5−1−50000000000000000000000000000

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