Finite Group Databasebeta

← Group #500672

Character table — Group #500672

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222444444444448888888888888881616161616161616161616161616161616161616
order12222244444488882244444888844888881616161616161616222222444444888816161616
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ51111111111111111-1-1111-1-11111-1-11-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-1
χ61111111111111111-1-1111-1-11111-1-11-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1-1-1
χ71111111111111111-1-1111-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ81111111111111111-1-1111-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ9111111-1-11111111111-1-1-1111-1-11-1-1-111-1-11111-1-1-1-111-1-11-1111-1-1-111-1-111-1-1
χ10111111-1-11111111111-1-1-1111-1-11-1-1-111-1-11111-1-1-1-1-1-111-11-1-1-1111-1-11111-1-1
χ11111111-1-11111111111-1-1-1111-1-11-1-1-111-1-1-1-1-1-1111111-1-11-1-1-11-111-1-111-1-111
χ12111111-1-11111111111-1-1-1111-1-11-1-1-111-1-1-1-1-1-11111-1-111-1111-11-1-111-1-1-1-111
χ13111111-1-111111111-1-1-1-1-1-1-11-1-1111-1-1-1111111-1-1-1-111-1-1-1111-11-1-1-1-111-1-111
χ14111111-1-111111111-1-1-1-1-1-1-11-1-1111-1-1-1111111-1-1-1-1-1-1111-1-1-11-11111-1-1-1-111
χ15111111-1-111111111-1-1-1-1-1-1-11-1-1111-1-1-111-1-1-1-1111111-1-1-11-1-1-111111-1-111-1-1
χ16111111-1-111111111-1-1-1-1-1-1-11-1-1111-1-1-111-1-1-1-11111-1-1111-1111-1-1-1-1-11111-1-1
χ17222222222222-2-2-2-22222222-2-2-2-222-2-2-2-2-20000000000000000000000000000
χ18222222222222-2-2-2-2-2-2222-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ19222222-2-22222-2-2-2-222-2-2-222-222-2-2-22-2-2220000000000000000000000000000
χ20222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222-222222-2-20000000000000000000000000000
χ212222-2-22222-2-2000022-22-2-2-200002-20000022−2−222−2−200000000000000002−22−2
χ222222-2-22222-2-2000022-22-2-2-200002-200000−2−222−2−2220000000000000000−22−22
χ232222-2-22222-2-20000-2-2-22-2220000-220000022−2−222−2−20000000000000000−22−22
χ242222-2-22222-2-20000-2-2-22-2220000-2200000−2−222−2−22200000000000000002−22−2
χ252222-2-222-2-222222200-2-2200-222-200-200000000000000002200-2-20000000000
χ262222-2-222-2-222222200-2-2200-222-200-20000000000000000-2-200220000000000
χ272222-2-222-2-222-2-2-2-200-2-22002-2-220020000000000002-22-20000000000000000
χ282222-2-222-2-222-2-2-2-200-2-22002-2-22002000000000000-22-220000000000000000
χ292222-2-2-2-222-2-20000222-22-2-20000-220000022−2−2−2−22200000000000000002−2−22
χ302222-2-2-2-222-2-20000222-22-2-20000-2200000−2−22222−2−20000000000000000−222−2
χ312222-2-2-2-222-2-20000-2-22-222200002-20000022−2−2−2−2220000000000000000−222−2
χ322222-2-2-2-222-2-20000-2-22-222200002-200000−2−22222−2−200000000000000002−2−22
χ332222-2-2-2-2-2-22222220022-200-2-2-2-200200000000000000002-200-220000000000
χ342222-2-2-2-2-2-22222220022-200-2-2-2-20020000000000000000-22002-20000000000
χ352222-2-2-2-2-2-222-2-2-2-20022-200222200-20000000000002-2-220000000000000000
χ362222-2-2-2-2-2-222-2-2-2-20022-200222200-2000000000000-222-20000000000000000
χ372-2-222-2002-22-222-2-22-20002-2200-20002-200000000000000002i−2i00002i−2i000000
χ382-2-222-2002-22-222-2-22-20002-2200-20002-20000000000000000−2i2i0000−2i2i000000
χ392-2-222-2002-22-222-2-2-22000-22200-2000-2200000000000000002i−2i0000−2i2i000000
χ402-2-222-2002-22-222-2-2-22000-22200-2000-220000000000000000−2i2i00002i−2i000000
χ412-2-222-2002-22-2-2-2222-20002-2-2002000-22000000000000000000002-2002-20000
χ422-2-222-2002-22-2-2-2222-20002-2-2002000-2200000000000000000000-2200-220000
χ432-2-222-2002-22-2-2-222-22000-22-20020002-2000000000000000000002-200-220000
χ442-2-222-2002-22-2-2-222-22000-22-20020002-200000000000000000000-22002-20000
χ4544444444-4-4-4-40000004-4-400000000000000000000000000000000000000000
χ46444444-4-4-4-4-4-4000000-44400000000000000000000000000000000000000000
χ4744-4-4004-4000022−2222−220000000022−2200000000ζ+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
χ4844-4-4004-4000022−2222−220000000022−2200000000−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
χ4944-4-4004-40000−2222−222200000000−222200000000ζ−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
χ5044-4-4004-40000−2222−222200000000−222200000000−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
χ5144-4-400-44000022−2222−2200000000−222200000000ζ+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
χ5244-4-400-44000022−2222−2200000000−222200000000−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
χ5344-4-400-440000−2222−22220000000022−2200000000ζ−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
χ5444-4-400-440000−2222−22220000000022−2200000000−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
χ554-4-444-400-44-44000000000000000000004-40000000000000000000000000000
χ564-4-444-400-44-4400000000000000000000-440000000000000000000000000000
χ574-4-44-44004-4-4400004-4000-44000000000000000000000000000000000000000
χ584-4-44-44004-4-440000-440004-4000000000000000000000000000000000000000
χ594-4-44-4400-444-444-4-40000000-400400000000000000000000000000000000000
χ604-4-44-4400-444-4-4-4440000000400-400000000000000000000000000000000000
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.