Finite Group Databasebeta

← Group #500461

Character table — Group #500461

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222444444488888888888888888888888881616161616161616161616163232
order122222444444888844488882244444481616161616161616161616161616161622244444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-111-1-1
χ3111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ611111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-111
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
χ91111111-1-11111111-1-1-1-1-1111-11-11111-11111-1-1-1-11111-1-1-1-1-111-111-1-1-1-11-11-1
χ101111111-1-11111111-1-1-1-1-1111-11-11111-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111-1-11
χ111111111-1-11111111-1-1-1-1-1111-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11-1-111111-1-11
χ121111111-1-11111111-1-1-1-1-1111-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-11-11-1
χ131111111-1-11111111-1-1-1-1-111-11-111111-11111-1-1-1-1-1-1-1-11111-111-1-1-111-1-1-11-11
χ141111111-1-11111111-1-1-1-1-111-11-111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-111-1
χ151111111-1-11111111-1-1-1-1-111-11-11-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1111-1-111-111-1
χ161111111-1-11111111-1-1-1-1-111-11-11-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-11-11
χ17222222222222-2-2-2-2222-2-2-2-222220000-200000000000000000000000000-2-200
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-20000-2000000000000000000000000002200
χ192222222-2-2222-2-2-2-2-2-2-222-2-22-22-20000200000000000000000000000000-2200
χ202222222-2-2222-2-2-2-2-2-2-222-2-2-22-2200002000000000000000000000000002-200
χ212222-2-2222-2-2200002-2-200002-2-220000022−2−222−2−222−2−222−2−200000000000000
χ222222-2-2222-2-2200002-2-200002-2-2200000−2−222−2−222−2−222−2−22200000000000000
χ232222-2-2222-2-2200002-2-20000-222-20000022−2−222−2−2−2−222−2−22200000000000000
χ242222-2-2222-2-2200002-2-20000-222-200000−2−222−2−22222−2−222−2−200000000000000
χ252222-2-22-2-2-2-220000-222000022-2-20000022−2−2−2−22222−2−2−2−22200000000000000
χ262222-2-22-2-2-2-220000-222000022-2-200000−2−22222−2−2−2−22222−2−200000000000000
χ272222-2-22-2-2-2-220000-2220000-2-2220000022−2−2−2−222−2−22222−2−200000000000000
χ282222-2-22-2-2-2-220000-2220000-2-22200000−2−22222−2−222−2−2−2−22200000000000000
χ292222-2-2-22222-22222-22-222-2-2000022-2-2-20000000000000000-20020000000000
χ302222-2-2-22222-22222-22-222-2-20000-2-222-20000000000000000200-20000000000
χ312222-2-2-22222-2-2-2-2-2-22-2-2-222000000002000000000000000000002-22-2000000
χ322222-2-2-22222-2-2-2-2-2-22-2-2-22200000000200000000000000000000-22-22000000
χ332222-2-2-2-2-222-222222-22-2-2-2-2000022-2-220000000000000000200-20000000000
χ342222-2-2-2-2-222-222222-22-2-2-2-20000-2-22220000000000000000-20020000000000
χ352222-2-2-2-2-222-2-2-2-2-22-22222200000000-2000000000000000000002-2-22000000
χ362222-2-2-2-2-222-2-2-2-2-22-22222200000000-200000000000000000000-222-2000000
χ3722-2-22-2200-22-222-2-200000-2200002i−2i2i−2i000002-22-200000000000000002i−2i0000
χ3822-2-22-2200-22-222-2-200000-2200002i−2i2i−2i00000-22-220000000000000000−2i2i0000
χ3922-2-22-2200-22-222-2-200000-220000−2i2i−2i2i000002-22-20000000000000000−2i2i0000
χ4022-2-22-2200-22-222-2-200000-220000−2i2i−2i2i00000-22-2200000000000000002i−2i0000
χ4122-2-2-22-200-22222-2-2000002-200002i−2i−2i2i02i−2i2i−2i00000000000002-200000000000
χ4222-2-2-22-200-22222-2-2000002-200002i−2i−2i2i0−2i2i−2i2i0000000000000-2200000000000
χ4322-2-2-22-200-22222-2-2000002-20000−2i2i2i−2i02i−2i2i−2i0000000000000-2200000000000
χ4422-2-2-22-200-22222-2-2000002-20000−2i2i2i−2i0−2i2i−2i2i00000000000002-200000000000
χ45444444-444-4-4-40000-4-440000000000000000000000000000000000000000000
χ46444444-4-4-4-4-4-4000044-40000000000000000000000000000000000000000000
χ4744-4-44-4400-44-4-4-444000004-4000000000000000000000000000000000000000
χ4844-4-44-4-4004-44000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ4944-4-44-4-4004-4400000000000000000000−2i22i22i2−2i200000000000000000000000000
χ5044-4-4-444004-4-400000000000000000000000022−22−22220000000000000000000000
χ5144-4-4-444004-4-4000000000000000000000000−222222−220000000000000000000000
χ5244-4-4-44-400-444-4-44400000-44000000000000000000000000000000000000000
χ534-44-40004i−4i00022−2222−220002i2−2i20000000000000000000ζ+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
χ544-44-40004i−4i00022−2222−220002i2−2i20000000000000000000−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
χ554-44-40004i−4i000−2222−2222000−2i22i20000000000000000000ζ−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
χ564-44-40004i−4i000−2222−2222000−2i22i20000000000000000000−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
χ574-44-4000−4i4i00022−2222−22000−2i22i20000000000000000000ζ+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
χ584-44-4000−4i4i00022−2222−22000−2i22i20000000000000000000−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
χ594-44-4000−4i4i000−2222−22220002i2−2i20000000000000000000ζ−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
χ604-44-4000−4i4i000−2222−22220002i2−2i20000000000000000000−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
χ618-8-880000000042−42−42420000000000000000000000000000000000000000000000
χ628-8-8800000000−424242−420000000000000000000000000000000000000000000000

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