Finite Group Databasebeta

← Group #464052

Character table — Group #464052

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222222244448888888888888888881616161616161616161616161616161616161616
order12224444222222444444888822444444888888888822244444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1111111-1111111-111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-111-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-111111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-111111-1-1111111-1-1-1-1
χ911111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-111-1-111-1-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-11-1-1111-11-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11-111-1-1-11-111-1-111-1-111
χ1211111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-111111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-1-1-111-11-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111-1-1-1-1111-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-11111-1-1-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1111-1-11-11-1-111-1-1-1-111
χ17222222222-2-2-2-222-2-2-2-2222222-22-200000000-2-222-2-200000000000000000000
χ18222222222-2-2-2-222-2-2-2-222222-22-2200000000-2-2-2-22200000000000000000000
χ19222222222-2-2-2-222-2-2-2-22-2-2-2-22-22-20000000022-2-22200000000000000000000
χ20222222222-2-2-2-222-2-2-2-22-2-2-2-2-22-22000000002222-2-200000000000000000000
χ212222-2-2-2-2222222-2-2-2-2-2-200002-2-2200002i2i−2i−2i00000000000000002i−2i00000000
χ222222-2-2-2-2222222-2-2-2-2-2-200002-2-220000−2i−2i2i2i0000000000000000−2i2i00000000
χ232222-2-2-2-2222222-2-2-2-2-2-20000-222-200002i2i−2i−2i0000000000000000−2i2i00000000
χ242222-2-2-2-2222222-2-2-2-2-2-20000-222-20000−2i−2i2i2i00000000000000002i−2i00000000
χ252222-2-2-2-22-2-2-2-22-22222-2000022-2-222-2-200000000002000000-2000000000000
χ262222-2-2-2-22-2-2-2-22-22222-2000022-2-2-2-2220000000000-20000002000000000000
χ272222-2-2-2-22-2-2-2-22-22222-20000-2-22222-2-20000000000-20000002000000000000
χ282222-2-2-2-22-2-2-2-22-22222-20000-2-222-2-22200000000002000000-2000000000000
χ292222-2-2-2-2-222-2-2-2222-2-2222-2-20000000000002-200000002-22-20000000000000
χ302222-2-2-2-2-222-2-2-2222-2-2222-2-20000000000002-20000000-22-220000000000000
χ312222-2-2-2-2-222-2-2-2222-2-22-2-222000000000000-2200000002-2-220000000000000
χ322222-2-2-2-2-222-2-2-2222-2-22-2-222000000000000-220000000-222-20000000000000
χ332222-2-2-2-2-2-2-222-22-2-222222-2-2000000000000-22000002200000-2-20000000000
χ342222-2-2-2-2-2-2-222-22-2-222222-2-2000000000000-2200000-2-200000220000000000
χ352222-2-2-2-2-2-2-222-22-2-2222-2-2220000000000002-2000002-200000-220000000000
χ362222-2-2-2-2-2-2-222-22-2-2222-2-2220000000000002-200000-22000002-20000000000
χ372-2-2222-2-222-22-2-222-22-2-20000000000000000002i−2i2i−2i000000000000002i−2i2-200
χ382-2-2222-2-222-22-2-222-22-2-20000000000000000002i−2i2i−2i00000000000000−2i2i-2200
χ392-2-2222-2-222-22-2-222-22-2-2000000000000000000−2i2i−2i2i000000000000002i−2i-2200
χ402-2-2222-2-222-22-2-222-22-2-2000000000000000000−2i2i−2i2i00000000000000−2i2i2-200
χ412-2-2222-2-22-22-22-22-22-22-20000000000000000002i−2i−2i2i0000000000002i−2i00002-2
χ422-2-2222-2-22-22-22-22-22-22-20000000000000000002i−2i−2i2i000000000000−2i2i0000-22
χ432-2-2222-2-22-22-22-22-22-22-2000000000000000000−2i2i2i−2i0000000000002i−2i0000-22
χ442-2-2222-2-22-22-22-22-22-22-2000000000000000000−2i2i2i−2i000000000000−2i2i00002-2
χ4544444444-444-4-4-4-4-4-444-4000000000000000000000000000000000000000000
χ4644444444-4-4-444-4-444-4-4-4000000000000000000000000000000000000000000
χ4744-4-44i−4i4i−4i00000000000022−222i2−2i200002-22i−2i2ζ−2ζ2ζ3−2ζ300000000000000000000000000
χ4844-4-44i−4i4i−4i00000000000022−222i2−2i20000-22−2i2i−2ζ2ζ−2ζ32ζ300000000000000000000000000
χ4944-4-44i−4i4i−4i000000000000−2222−2i22i200002-22i−2i−2ζ2ζ−2ζ32ζ300000000000000000000000000
χ5044-4-44i−4i4i−4i000000000000−2222−2i22i20000-22−2i2i2ζ−2ζ2ζ3−2ζ300000000000000000000000000
χ5144-4-4−4i4i−4i4i00000000000022−22−2i22i200002-2−2i2i−2ζ32ζ3−2ζ2ζ00000000000000000000000000
χ5244-4-4−4i4i−4i4i00000000000022−22−2i22i20000-222i−2i2ζ3−2ζ32ζ−2ζ00000000000000000000000000
χ5344-4-4−4i4i−4i4i000000000000−22222i2−2i200002-2−2i2i2ζ3−2ζ32ζ−2ζ00000000000000000000000000
χ5444-4-4−4i4i−4i4i000000000000−22222i2−2i20000-222i−2i−2ζ32ζ3−2ζ2ζ00000000000000000000000000
χ554-4-4444-4-4-44-4-444-4-444-44000000000000000000000000000000000000000000
χ564-4-4444-4-4-4-444-44-44-4-444000000000000000000000000000000000000000000
χ574-4-44-4-44444-44-4-4-4-44-444000000000000000000000000000000000000000000
χ584-4-44-4-4444-44-44-4-44-44-44000000000000000000000000000000000000000000
χ594-4-44-4-444-44-4-44444-4-44-4000000000000000000000000000000000000000000
χ604-4-44-4-444-4-444-444-444-4-4000000000000000000000000000000000000000000
χ618-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000
χ628-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.