Finite Group Databasebeta

← Group #13020321

Character table — Group #13020321

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111122444444444444448810101010101016161616161616161616161616161620202020202020202020202020202020202020202040408080808080
order12222222444451010101010101044224444210101010101020202020202020202224444444444444444444448888
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
χ9111111-1-111-1-11111111111111111-1-1-1-1-1-1-111-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-111-11-11-1
χ10111111-1-111-1-11111111111111111-1-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-11
χ11111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-11111iiii−i−i−i−i−i−i−i−iiiii-1-11i−i−ii
χ12111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11−iii−i
χ13111111-1-111-1-111111111-1-11111111-1-1111111-1-1-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-11-11
χ14111111-1-111-1-111111111-1-11111111-1-1111111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-11-1
χ15111111-1-111-1-111111111-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1−iii−i
χ16111111-1-111-1-111111111-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1i−i−ii
χ1722222222-2-2-2-2222222220022-2-2-2-20220000-2-2-2-20000222-2-200000000000000000000000
χ1822222222-2-2-2-22222222200-2-222220220000-2-2-2-20000-2-2-22200000000000000000000000
χ19222222-2-2-2-222222222220022-2-2-2-20-2-20000-2-22200002-2-22200000000000000000000000
χ20222222-2-2-2-2222222222200-2-222220-2-20000-2-2220000-222-2-200000000000000000000000
χ212222-2-2002-20022-2-222-2-2002222-2-200000002-2000000-20000000022-2-2000022-2-20000000
χ222222-2-2002-20022-2-222-2-2002222-2-200000002-2000000-200000000-2-2220000-2-2220000000
χ232222-2-2002-20022-2-222-2-200-2-2-2-22200000002-20000002000000002i2i−2i−2i0000−2i−2i2i2i0000000
χ242222-2-2002-20022-2-222-2-200-2-2-2-22200000002-2000000200000000−2i−2i2i2i00002i2i−2i−2i0000000
χ252222-2-200-220022-2-222-2-20022-2-2220000000-22000000-2000022-2-2000022-2-200000000000
χ262222-2-200-220022-2-222-2-20022-2-2220000000-22000000-20000-2-2220000-2-22200000000000
χ272222-2-200-220022-2-222-2-200-2-222-2-20000000-22000000200002i2i−2i−2i0000−2i−2i2i2i00000000000
χ282222-2-200-220022-2-222-2-200-2-222-2-20000000-2200000020000−2i−2i2i2i00002i2i−2i−2i00000000000
χ2922-2-22-22-2000022-2-2-2-22200002i−2i2i−2i02-20000000000000002i−2i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i0000000
χ3022-2-22-22-2000022-2-2-2-22200002i−2i2i−2i02-20000000000000002i−2i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i0000000
χ3122-2-22-22-2000022-2-2-2-2220000−2i2i−2i2i02-2000000000000000−2i2i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i0000000
χ3222-2-22-22-2000022-2-2-2-2220000−2i2i−2i2i02-2000000000000000−2i2i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000000
χ3322-2-22-2-22000022-2-2-2-22200002i−2i2i−2i0-22000000000000000−2i2i1+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i0000000
χ3422-2-22-2-22000022-2-2-2-22200002i−2i2i−2i0-22000000000000000−2i2i−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i0000000
χ3522-2-22-2-22000022-2-2-2-2220000−2i2i−2i2i0-220000000000000002i−2i1−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i0000000
χ3622-2-22-2-22000022-2-2-2-2220000−2i2i−2i2i0-220000000000000002i−2i−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i0000000
χ3722-2-2-2200002i−2i2222-2-2-2-200002i−2i−2i2i0000000002i−2i000002-2001−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000
χ3822-2-2-2200002i−2i2222-2-2-2-200002i−2i−2i2i0000000002i−2i000002-200−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000
χ3922-2-2-2200002i−2i2222-2-2-2-20000−2i2i2i−2i0000000002i−2i00000-22001+i−1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000
χ4022-2-2-2200002i−2i2222-2-2-2-20000−2i2i2i−2i0000000002i−2i00000-2200−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000
χ4122-2-2-220000−2i2i2222-2-2-2-200002i−2i−2i2i000000000−2i2i00000-22001−i−1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000
χ4222-2-2-220000−2i2i2222-2-2-2-200002i−2i−2i2i000000000−2i2i00000-2200−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000
χ4322-2-2-220000−2i2i2222-2-2-2-20000−2i2i2i−2i000000000−2i2i000002-2001+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000
χ4422-2-2-220000−2i2i2222-2-2-2-20000−2i2i2i−2i000000000−2i2i000002-200−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000
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
χ534-4-44000000004-4004-4002-24-40000000000000002-22-20000000000000000000002-200000
χ544-4-44000000004-4004-4002-2-440000000000000002-22-2000000000000000000000-2200000
χ554-4-44000000004-4004-400-224-4000000000000000-22-22000000000000000000000-2200000
χ564-4-44000000004-4004-400-22-44000000000000000-22-220000000000000000000002-200000
χ578888-8-8008-800-2-222-2-222000000000000000-220000000000000000000000000000000000
χ588888-8-800-8800-2-222-2-2220000000000000002-20000000000000000000000000000000000
χ5988-8-88-88-80000-2-22222-2-2000000000-220000000000000000000000000000000000000000
χ6088-8-88-8-880000-2-22222-2-20000000002-20000000000000000000000000000000000000000
χ6188-8-8-8800008i−8i-2-2-2-2222200000000000000000−2i2i00000000000000000000000000000000
χ6288-8-8-880000−8i8i-2-2-2-22222000000000000000002i−2i00000000000000000000000000000000
χ638-88-8000000008-800-8800000000000000000000000000000000000000000000000000000
χ648-88-800000000-2225−252-225−25000000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18000000000000000000000000000000000000
χ658-88-800000000-2225−252-225−2500000000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ18000000000000000000000000000000000000
χ668-88-800000000-22−25252-2−252500000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000000000000000
χ678-88-800000000-22−25252-2−2525000000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000000000000000
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 20 (ζ20 = 1); i = ζ5.