Finite Group Databasebeta

← Group #13020318

Character table — Group #13020318

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111122444444444444448810101010101016161616161616161616161616161620202020202020202020202020202020202020202040408080808080
order12222244444451010101010101044224444420202020202020202020202020202444444444444444444444448888
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
χ911111111-1-1-1-11111111111111111-1-1-1111111-1-1-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-111-11-11-1
χ1011111111-1-1-1-11111111111111111-1-1-1111111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-11
χ1111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11i−i−ii
χ1211111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11−iii−i
χ1311111111-1-1-1-111111111-1-11111111-1-1-1-1-1-111-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-11-11
χ1411111111-1-1-1-111111111-1-11111111-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-11-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-11111-11111iiii−i−i−i−i−i−i−i−iiiii11-1−iii−i
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-11111-11111−i−i−i−iiiiiiiii−i−i−i−i11-1i−i−ii
χ17222222-2-222-2-2222222220022-2-2-2-20-2-20000-2-2220000222-2-200000000000000000000000
χ18222222-2-222-2-22222222200-2-222220-2-20000-2-2220000-2-2-22200000000000000000000000
χ19222222-2-2-2-222222222220022-2-2-2-20220000-2-2-2-200002-2-22200000000000000000000000
χ20222222-2-2-2-2222222222200-2-222220220000-2-2-2-20000-222-2-200000000000000000000000
χ212222-2-22-2000022-2-22-2-22002222-2-200000002-2000000-20000000022-2-2000022-2-20000000
χ222222-2-22-2000022-2-22-2-22002222-2-200000002-2000000-200000000-2-2220000-2-2220000000
χ232222-2-22-2000022-2-22-2-2200-2-2-2-22200000002-20000002000000002i2i−2i−2i0000−2i−2i2i2i0000000
χ242222-2-22-2000022-2-22-2-2200-2-2-2-22200000002-2000000200000000−2i−2i2i2i00002i2i−2i−2i0000000
χ252222-2-2-22000022-2-22-2-220022-2-2220000000-22000000-2000022-2-2000022-2-200000000000
χ262222-2-2-22000022-2-22-2-220022-2-2220000000-22000000-20000-2-2220000-2-22200000000000
χ272222-2-2-22000022-2-22-2-2200-2-222-2-20000000-22000000200002i2i−2i−2i0000−2i−2i2i2i00000000000
χ282222-2-2-22000022-2-22-2-2200-2-222-2-20000000-2200000020000−2i−2i2i2i00002i2i−2i−2i00000000000
χ292-2-222-2002i−2i002-2-2-2222-200002i−2i2i−2i0000000002i−2i00000002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000
χ302-2-222-2002i−2i002-2-2-2222-200002i−2i2i−2i0000000002i−2i00000002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000
χ312-2-222-2002i−2i002-2-2-2222-20000−2i2i−2i2i0000000002i−2i0000000-221−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i0000000
χ322-2-222-2002i−2i002-2-2-2222-20000−2i2i−2i2i0000000002i−2i0000000-22−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i0000000
χ332-2-222-200−2i2i002-2-2-2222-200002i−2i2i−2i000000000−2i2i0000000-221+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i0000000
χ342-2-222-200−2i2i002-2-2-2222-200002i−2i2i−2i000000000−2i2i0000000-22−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i0000000
χ352-2-222-200−2i2i002-2-2-2222-20000−2i2i−2i2i000000000−2i2i00000002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000
χ362-2-222-200−2i2i002-2-2-2222-20000−2i2i−2i2i000000000−2i2i00000002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000
χ372-2-22-2200002-22-2222-2-2-200002i−2i−2i2i02-200000000000002i−2i001−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i0000000
χ382-2-22-2200002-22-2222-2-2-200002i−2i−2i2i02-200000000000002i−2i00−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i0000000
χ392-2-22-2200002-22-2222-2-2-20000−2i2i2i−2i02-20000000000000−2i2i001+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i0000000
χ402-2-22-2200002-22-2222-2-2-20000−2i2i2i−2i02-20000000000000−2i2i00−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i0000000
χ412-2-22-220000-222-2222-2-2-200002i−2i−2i2i0-220000000000000−2i2i001−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i1+i−1−i0000000
χ422-2-22-220000-222-2222-2-2-200002i−2i−2i2i0-220000000000000−2i2i00−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i−1−i1+i0000000
χ432-2-22-220000-222-2222-2-2-20000−2i2i2i−2i0-2200000000000002i−2i001+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i1−i−1+i0000000
χ442-2-22-220000-222-2222-2-2-20000−2i2i2i−2i0-2200000000000002i−2i00−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i−1+i1−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
χ4744444444-4-4-4-4-1-1-1-1-1-1-1-144000000-411-1-1-1-1-1-11111110000000000000000000000000000
χ4844444444-4-4-4-4-1-1-1-1-1-1-1-1-4-40000004111111-1-111-1-1-1-10000000000000000000000000000
χ49444444-4-444-4-4-1-1-1-1-1-1-1-10000000001155−5−511-1-155−5−50000000000000000000000000000
χ50444444-4-444-4-4-1-1-1-1-1-1-1-100000000011−5−55511-1-1−5−5550000000000000000000000000000
χ51444444-4-4-4-444-1-1-1-1-1-1-1-1000000000-1-155−5−51111−5−5550000000000000000000000000000
χ52444444-4-4-4-444-1-1-1-1-1-1-1-1000000000-1-1−5−555111155−5−50000000000000000000000000000
χ5344-4-4000000004400-400-42-24-400000002-22-2000000000000000000000000000002-200000
χ5444-4-4000000004400-400-42-2-4400000002-22-200000000000000000000000000000-2200000
χ5544-4-4000000004400-400-4-224-40000000-22-2200000000000000000000000000000-2200000
χ5644-4-4000000004400-400-4-22-440000000-22-22000000000000000000000000000002-200000
χ578888-8-88-80000-2-222-222-2000000000000000-220000000000000000000000000000000000
χ588888-8-8-880000-2-222-222-20000000000000002-20000000000000000000000000000000000
χ5988-8-800000000-2-225−25225−2524-4000000000−1+51−5−1−51+5000000000000000000000000000000000000
χ6088-8-800000000-2-225−25225−252-440000000001−5−1+51+5−1−5000000000000000000000000000000000000
χ6188-8-800000000-2-2−25252−252524-4000000000−1−51+5−1+51−5000000000000000000000000000000000000
χ6288-8-800000000-2-2−25252−25252-440000000001+5−1−51−5−1+5000000000000000000000000000000000000
χ638-88-8000000008-800-8008000000000000000000000000000000000000000000000000000
χ648-88-800000000-2225−252−2525-20000000000000000000−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ140000000000000000000000000000
χ658-88-800000000-2225−252−2525-200000000000000000002ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ140000000000000000000000000000
χ668-88-800000000-22−2525225−25-200000000000000000002ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ180000000000000000000000000000
χ678-88-800000000-22−2525225−25-20000000000000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ180000000000000000000000000000
χ688-8-888-8008i−8i00-2222-2-2-2200000000000000000−2i2i00000000000000000000000000000000
χ698-8-888-800−8i8i00-2222-2-2-22000000000000000002i−2i00000000000000000000000000000000
χ708-8-88-8800008-8-22-2-2-2222000000000-220000000000000000000000000000000000000000
χ718-8-88-880000-88-22-2-2-22220000000002-20000000000000000000000000000000000000000

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