Finite Group Databasebeta

← Group #129792

Character table — Group #129792

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222444444444448888888888888881616161616161616161616161616161616161616
order12222222444488882224444888824888881616161616161616244444444444888816161616
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111-1-11-1-111111-1-11-1-1-1-111111111111-1-11-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111-1-11-1-111111-1-11-1-1-1-111111111-1-1-111-1111111-1-1-1-1-1-1-1-1
χ711111111111111111-1-11-1-111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1-1-11111
χ811111111111111111-1-11-1-111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111111111
χ9111111-1-11111-1-1-1-1-111-111-111-1-1-1-1111-1-1iiii−i−i−i−i1-1-1-1-1111ii−i−iii−i−iii−i−i
χ10111111-1-11111-1-1-1-1-111-111-111-1-1-1-1111-1-1iiii−i−i−i−i-11111-1-1-1−i−iii−i−iiiii−i−i
χ11111111-1-11111-1-1-1-1-111-111-111-1-1-1-1111-1-1−i−i−i−iiiii1-1-1-1-1111−i−iii−i−iii−i−iii
χ12111111-1-11111-1-1-1-1-111-111-111-1-1-1-1111-1-1−i−i−i−iiiii-11111-1-1-1ii−i−iii−i−i−i−iii
χ13111111-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111iiii−i−i−i−i1-1-1111-1-1−i−iiiii−i−i−i−iii
χ14111111-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111iiii−i−i−i−i-111-1-1-111ii−i−i−i−iii−i−iii
χ15111111-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111−i−i−i−iiiii1-1-1111-1-1ii−i−i−i−iiiii−i−i
χ16111111-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111−i−i−i−iiiii-111-1-1-111−i−iiiii−i−iii−i−i
χ17222222222222-2-2-2-22222222-2-2-2-222-2-2-2-2-20000000000000000000000000000
χ18222222222222-2-2-2-22-2-22-2-22-2-2-2-2-2-2-222220000000000000000000000000000
χ19222222-2-222222222-222-222-2-2-222-2-2-2-2-2220000000000000000000000000000
χ20222222-2-222222222-2-2-2-2-2-2-2-2-22222-222-2-20000000000000000000000000000
χ212222-2-22222-2-20000-222-2-2-2200002-20000022−2−222−2−200000000000000002−22−2
χ222222-2-22222-2-20000-222-2-2-2200002-200000−2−222−2−2220000000000000000−22−22
χ232222-2-22222-2-20000-2-2-2-22220000-220000022−2−222−2−20000000000000000−22−22
χ242222-2-22222-2-20000-2-2-2-22220000-2200000−2−222−2−22200000000000000002−22−2
χ252222-2-222-2-2222222-200200-222-2-200-200000000000022-200-200000000000000
χ262222-2-222-2-2222222-200200-222-2-200-2000000000000-2-2200200000000000000
χ272222-2-222-2-222-2-2-2-2-200200-2-2-2220020000000000000002-202-2000000000000
χ282222-2-222-2-222-2-2-2-2-200200-2-2-222002000000000000000-220-22000000000000
χ292222-2-2-2-222-2-200002222-2-2-20000-2200000i2i2−i2−i2−i2−i2i2i20000000000000000i2−i2−i2i2
χ302222-2-2-2-222-2-200002222-2-2-20000-2200000−i2−i2i2i2i2i2−i2−i20000000000000000−i2i2i2−i2
χ312222-2-2-2-222-2-200002-2-2222-200002-200000i2i2−i2−i2−i2−i2i2i20000000000000000−i2i2i2−i2
χ322222-2-2-2-222-2-200002-2-2222-200002-200000−i2−i2i2i2i2i2−i2−i20000000000000000i2−i2−i2i2
χ332222-2-2-2-2-2-2222222200-2002-2-2-2-20020000000000000002-20-22000000000000
χ342222-2-2-2-2-2-2222222200-2002-2-2-2-2002000000000000000-2202-2000000000000
χ352222-2-2-2-2-2-222-2-2-2-2200-2002222200-20000000000002-2200-200000000000000
χ362222-2-2-2-2-2-222-2-2-2-2200-2002222200-2000000000000-22-200200000000000000
χ372-2-222-2002-22-22i2i−2i−2i02-202-20002i−2i000002i−2i00000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ382-2-222-2002-22-22i2i−2i−2i02-202-20002i−2i000002i−2i0000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ392-2-222-2002-22-22i2i−2i−2i0-220-220002i−2i00000−2i2i00000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000
χ402-2-222-2002-22-22i2i−2i−2i0-220-220002i−2i00000−2i2i0000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000
χ412-2-222-2002-22-2−2i−2i2i2i02-202-2000−2i2i00000−2i2i00000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ422-2-222-2002-22-2−2i−2i2i2i02-202-2000−2i2i00000−2i2i0000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ432-2-222-2002-22-2−2i−2i2i2i0-220-22000−2i2i000002i−2i00000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000
χ442-2-222-2002-22-2−2i−2i2i2i0-220-22000−2i2i000002i−2i0000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000
χ4544444444-4-4-4-40000400-400-4000000000000000000000000000000000000000
χ46444444-4-4-4-4-4-40000-4004004000000000000000000000000000000000000000
χ4744-4-4004-4000022−2222−22000000022−22000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000000000000000
χ4844-4-4004-4000022−2222−22000000022−22000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000000000000000
χ4944-4-4004-40000−2222−22220000000−2222000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000000000000000
χ5044-4-4004-40000−2222−22220000000−2222000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000000000000000
χ5144-4-400-44000022−2222−220000000−2222000000000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000000000000000
χ5244-4-400-44000022−2222−220000000−2222000000000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000000000000000
χ5344-4-400-440000−2222−2222000000022−22000000000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000000000
χ5444-4-400-440000−2222−2222000000022−22000000000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000000000
χ554-4-444-400-44-440000000000000000004-4000000000000000000000000000000
χ564-4-444-400-44-44000000000000000000-44000000000000000000000000000000
χ574-4-44-44004-4-44000004-40-440000000000000000000000000000000000000000
χ584-4-44-44004-4-4400000-4404-40000000000000000000000000000000000000000
χ594-4-44-4400-444-44i4i−4i−4i000000000−4i4i00000000000000000000000000000000000
χ604-4-44-4400-444-4−4i−4i4i4i0000000004i−4i00000000000000000000000000000000000
χ618-88-8000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000
χ628-88-800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.