Finite Group Databasebeta

← Group #500299

Character table — Group #500299

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222444444444448888888888888881616161616161616161616161616161616161616
order12222244444488882244444888844888881616161616161616244444444444888816161616
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111-1-1-1-1
χ51111111111111111111-1-1-1-11111-1-11-1-1-1-111111111111-1-1-1-11-1-1-1-11111-1-1-1-1
χ61111111111111111111-1-1-1-11111-1-11-1-1-1-111111111-1-1-11111-11111-1-1-1-1-1-1-1-1
χ71111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-111-1-1-1-11111
χ81111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111111111
χ91111111-1-11111111-1-1-11111-1-111-1-1-111-1-11111-1-1-1-111-1-1-111-111-1-111-1-111-1-1
χ101111111-1-11111111-1-1-11111-1-111-1-1-111-1-11111-1-1-1-1-1-1111-1-11-1-111-1-11111-1-1
χ111111111-1-11111111-1-1-11111-1-111-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-111
χ121111111-1-11111111-1-1-11111-1-111-1-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-111
χ131111111-1-11111111-1-1-1-1-1-1-1-1-11111-1-1-1111111-1-1-1-111-111-1-1-1-1-11111-1-1-1-111
χ141111111-1-11111111-1-1-1-1-1-1-1-1-11111-1-1-1111111-1-1-1-1-1-11-1-111111-1-1-1-111-1-111
χ151111111-1-11111111-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-1111111-11111-1-1-1-1-1-1-11111-1-1
χ161111111-1-11111111-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-11111-1-11-1-1-1-11111111-1-111-1-1
χ17222222222222-2-2-2-22222222-2-2-2-222-2-2-2-2-20000000000000000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ192222222-2-2222-2-2-2-2-2-2-2222222-2-2-2-22-2-2220000000000000000000000000000
χ202222222-2-2222-2-2-2-2-2-2-2-2-2-2-222-2-222222-2-20000000000000000000000000000
χ212222-2-2222-2-2200002-2-222-2-20000-220000022−2−222−2−200000000000000002−22−2
χ222222-2-2222-2-2200002-2-222-2-20000-2200000−2−222−2−2220000000000000000−22−22
χ232222-2-2222-2-2200002-2-2-2-22200002-20000022−2−222−2−20000000000000000−22−22
χ242222-2-2222-2-2200002-2-2-2-22200002-200000−2−222−2−22200000000000000002−22−2
χ252222-2-22-2-2-2-220000-22222-2-200002-20000022−2−2−2−22200000000000000002−2−22
χ262222-2-22-2-2-2-220000-22222-2-200002-200000−2−22222−2−20000000000000000−222−2
χ272222-2-22-2-2-2-220000-222-2-2220000-220000022−2−2−2−2220000000000000000−222−2
χ282222-2-22-2-2-2-220000-222-2-2220000-2200000−2−22222−2−200000000000000002−2−22
χ292222-2-2-22222-22222-22-2000022-2-200-20000000000002-220000-2000000000000
χ302222-2-2-22222-22222-22-2000022-2-200-2000000000000-22-200002000000000000
χ312222-2-2-22222-2-2-2-2-2-22-20000-2-2220020000000000000002-20002-20000000000
χ322222-2-2-22222-2-2-2-2-2-22-20000-2-222002000000000000000-22000-220000000000
χ332222-2-2-2-2-222-222222-220000-2-2-2-20020000000000002-2-200002000000000000
χ342222-2-2-2-2-222-222222-220000-2-2-2-2002000000000000-2220000-2000000000000
χ352222-2-2-2-2-222-2-2-2-2-22-220000222200-20000000000000002-2000-220000000000
χ362222-2-2-2-2-222-2-2-2-2-22-220000222200-2000000000000000-220002-20000000000
χ3722-2-22-2-2002-2222-2-20002i−2i2i−2i002-20002i−2i0000000000000002i−2i000002-2000000
χ3822-2-22-2-2002-2222-2-20002i−2i2i−2i002-20002i−2i000000000000000−2i2i00000-22000000
χ3922-2-22-2-2002-2222-2-2000−2i2i−2i2i002-2000−2i2i0000000000000002i−2i00000-22000000
χ4022-2-22-2-2002-2222-2-2000−2i2i−2i2i002-2000−2i2i000000000000000−2i2i000002-2000000
χ4122-2-22-2-2002-22-2-2220002i−2i2i−2i00-22000−2i2i000000000000000000002i−2i002-20000
χ4222-2-22-2-2002-22-2-2220002i−2i2i−2i00-22000−2i2i00000000000000000000−2i2i00-220000
χ4322-2-22-2-2002-22-2-222000−2i2i−2i2i00-220002i−2i000000000000000000002i−2i00-220000
χ4422-2-22-2-2002-22-2-222000−2i2i−2i2i00-220002i−2i00000000000000000000−2i2i002-20000
χ45444444-444-4-4-40000-4-440000000000000000000000000000000000000000000
χ46444444-4-4-4-4-4-4000044-40000000000000000000000000000000000000000000
χ4744-4-44-4400-44-4000000000000000000004-40000000000000000000000000000
χ4844-4-44-4400-44-400000000000000000000-440000000000000000000000000000
χ4944-4-4-444004-4-444-4-4000000000-4400000000000000000000000000000000000
χ5044-4-4-444004-4-4-4-4440000000004-400000000000000000000000000000000000
χ5144-4-4-44-400-44400000004i−4i−4i4i000000000000000000000000000000000000000
χ5244-4-4-44-400-4440000000−4i4i4i−4i000000000000000000000000000000000000000
χ534-4-440004i−4i00022−2222−2200000002i2−2i2000000000ζ+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
χ544-4-440004i−4i00022−2222−2200000002i2−2i2000000000−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
χ554-4-440004i−4i000−2222−22220000000−2i22i2000000000ζ−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
χ564-4-440004i−4i000−2222−22220000000−2i22i2000000000−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
χ574-4-44000−4i4i00022−2222−220000000−2i22i2000000000ζ+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
χ584-4-44000−4i4i00022−2222−220000000−2i22i2000000000−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
χ594-4-44000−4i4i000−2222−222200000002i2−2i2000000000ζ−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
χ604-4-44000−4i4i000−2222−222200000002i2−2i2000000000−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
χ618-88-80000000042−42−42420000000000000000000000000000000000000000000000
χ628-88-800000000−424242−420000000000000000000000000000000000000000000000

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