Finite Group Databasebeta

← Group #500643

Character table — Group #500643

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222444444488888888888888888888888881616161616161616161616163232
order122222444444888844488884444444481616161616161616161616161616161624444444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-111-1-1
χ31111111111111111111111111-1-111-1-111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1
χ41111111111111111111111111-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111
χ511111111111111111111111-1-111-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ611111111111111111111111-1-111-1-1111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1
χ9111111-1-111111111-1-1-11-1-111-1111-111-11111-1-1-1-11111-1-1-1-1-111-111-1-1-1-11-11-1
χ10111111-1-111111111-1-1-11-1-111-1111-111-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111-1-11
χ11111111-1-111111111-1-1-11-1-111-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11-1-111111-1-11
χ12111111-1-111111111-1-1-11-1-111-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-11-11-1
χ13111111-1-111111111-1-1-11-1-11-1111-1111-11111-1-1-1-1-1-1-1-11111-111-1-1-111-1-1-11-11
χ14111111-1-111111111-1-1-11-1-11-1111-1111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-111-1
χ15111111-1-111111111-1-1-11-1-11-11-1-1-11-1-1-11111-1-1-1-1-1-1-1-111111-1-1111-1-111-111-1
χ16111111-1-111111111-1-1-11-1-11-11-1-1-11-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-11-11
χ17222222222222-2-2-2-2222-2-2-2-222002200-200000000000000000000000000-2-200
χ18222222222222-2-2-2-2222-2-2-2-2-2-200-2-200-2000000000000000000000000002200
χ19222222-2-22222-2-2-2-2-2-2-2-222-22-2002-200200000000000000000000000000-2200
χ20222222-2-22222-2-2-2-2-2-2-2-222-2-2200-22002000000000000000000000000002-200
χ212222-2-2222-2-220000-22-200002200-2-200022−2−222−2−222−2−222−2−200000000000000
χ222222-2-2222-2-220000-22-200002200-2-2000−2−222−2−222−2−222−2−22200000000000000
χ232222-2-2222-2-220000-22-20000-2-2002200022−2−222−2−2−2−222−2−22200000000000000
χ242222-2-2222-2-220000-22-20000-2-20022000−2−222−2−22222−2−222−2−200000000000000
χ252222-2-222-222-22222-2-22-222-2002200-2-2-20000000000000000200-20000000000
χ262222-2-222-222-22222-2-22-222-200-2-20022-20000000000000000-20020000000000
χ272222-2-222-222-2-2-2-2-2-2-222-2-22000000002000000000000000000002-22-2000000
χ282222-2-222-222-2-2-2-2-2-2-222-2-2200000000200000000000000000000-22-22000000
χ292222-2-2-2-22-2-2200002-2200002-200-2200022−2−2−2−22222−2−2−2−22200000000000000
χ302222-2-2-2-22-2-2200002-2200002-200-22000−2−22222−2−2−2−22222−2−200000000000000
χ312222-2-2-2-22-2-2200002-220000-22002-200022−2−2−2−222−2−22222−2−200000000000000
χ322222-2-2-2-22-2-2200002-220000-22002-2000−2−22222−2−222−2−2−2−22200000000000000
χ332222-2-2-2-2-222-2222222-2-2-2-2-2002200-2-220000000000000000-20020000000000
χ342222-2-2-2-2-222-2222222-2-2-2-2-200-2-2002220000000000000000200-20000000000
χ352222-2-2-2-2-222-2-2-2-2-222-2222200000000-2000000000000000000002-2-22000000
χ362222-2-2-2-2-222-2-2-2-2-222-2222200000000-200000000000000000000-222-2000000
χ372-2-222-20022-2-222-2-2000-2002002i−2i002i−2i000002i−2i2i−2i00000000000000002-20000
χ382-2-222-20022-2-222-2-2000-2002002i−2i002i−2i00000−2i2i−2i2i0000000000000000-220000
χ392-2-222-20022-2-222-2-2000-200200−2i2i00−2i2i000002i−2i2i−2i0000000000000000-220000
χ402-2-222-20022-2-222-2-2000-200200−2i2i00−2i2i00000−2i2i−2i2i00000000000000002-20000
χ412-2-22-2200-22-2222-2-2000200-2002i−2i00−2i2i02-22-200000000000002i−2i00000000000
χ422-2-22-2200-22-2222-2-2000200-2002i−2i00−2i2i0-22-220000000000000−2i2i00000000000
χ432-2-22-2200-22-2222-2-2000200-200−2i2i002i−2i02-22-20000000000000−2i2i00000000000
χ442-2-22-2200-22-2222-2-2000200-200−2i2i002i−2i0-22-2200000000000002i−2i00000000000
χ4544444444-4-4-4-400004-4-40000000000000000000000000000000000000000000
χ46444444-4-4-4-4-4-40000-4440000000000000000000000000000000000000000000
χ4744-4-4004-4000022−2222−22000022−22000000000000000000ζ+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+ζ700000000000000
χ4844-4-4004-4000022−2222−22000022−22000000000000000000−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−ζ700000000000000
χ4944-4-4004-40000−2222−22220000−2222000000000000000000ζ−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−ζ700000000000000
χ5044-4-4004-40000−2222−22220000−2222000000000000000000−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+ζ700000000000000
χ5144-4-400-44000022−2222−220000−2222000000000000000000ζ+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−ζ700000000000000
χ5244-4-400-44000022−2222−220000−2222000000000000000000−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+ζ700000000000000
χ5344-4-400-440000−2222−2222000022−22000000000000000000ζ−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+ζ700000000000000
χ5444-4-400-440000−2222−2222000022−22000000000000000000−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−ζ700000000000000
χ554-4-444-40044-4-4-4-444000400-4000000000000000000000000000000000000000
χ564-4-444-400-4-4440000000000000000000022−22−222200000000000000000000000000
χ574-4-444-400-4-44400000000000000000000−222222−2200000000000000000000000000
χ584-4-44-44004-44-40000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ594-4-44-44004-44-4000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ604-4-44-4400-44-44-4-444000-4004000000000000000000000000000000000000000
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.