Finite Group Databasebeta

← Group #465211

Character table — Group #465211

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222222244448888888888888888881616161616161616161616161616161616161616
order12224444222222444444888822444444888888888822444444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-11-1-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1111111-1111-111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111
χ5111111111111111111111111-1-1-1-11111111111-1-1-1-1-1111-11-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-11-11111111111-1-1-1-1
χ911111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1111-1-1-11111-1-1-1-1-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11-1-1-1111-1-111-1-111-1-111
χ1211111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-1-1-11-1-111-1-11111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111-1-111-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-11111-1-1-1-111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1111-111-1-1-1-111-1-1-1-111
χ17222222222-2-2-22-2-2-2-222-22222000022-2-222-2-2-2-2000000000000000000000000
χ18222222222-2-2-22-2-2-2-222-222220000-2-222-2-222-2-2000000000000000000000000
χ19222222222-2-2-22-2-2-2-222-2-2-2-2-2000022-2-2-2-22222000000000000000000000000
χ20222222222-2-2-22-2-2-2-222-2-2-2-2-20000-2-22222-2-222000000000000000000000000
χ212222-2-2-2-2222222-2-2-2-2-2-2000022-2-200002i−2i2i−2i000000000000000000002i−2i0000
χ222222-2-2-2-2222222-2-2-2-2-2-2000022-2-20000−2i2i−2i2i00000000000000000000−2i2i0000
χ232222-2-2-2-2222222-2-2-2-2-2-20000-2-22200002i−2i2i−2i00000000000000000000−2i2i0000
χ242222-2-2-2-2222222-2-2-2-2-2-20000-2-2220000−2i2i−2i2i000000000000000000002i−2i0000
χ252222-2-2-2-22-2-2-22-2222-2-220000000000002i−2i−2i2i002i2i−2i−2i2000-2000000000000000
χ262222-2-2-2-22-2-2-22-2222-2-220000000000002i−2i−2i2i00−2i−2i2i2i-20002000000000000000
χ272222-2-2-2-22-2-2-22-2222-2-22000000000000−2i2i2i−2i002i2i−2i−2i-20002000000000000000
χ282222-2-2-2-22-2-2-22-2222-2-22000000000000−2i2i2i−2i00−2i−2i2i2i2000-2000000000000000
χ292222-2-2-2-2-222-2-2-222-222-222-2-20000000000002-2000000000000002i−2i2i−2i000000
χ302222-2-2-2-2-222-2-2-222-222-222-2-20000000000002-200000000000000−2i2i−2i2i000000
χ312222-2-2-2-2-222-2-2-222-222-2-2-222000000000000-22000000000000002i−2i−2i2i000000
χ322222-2-2-2-2-222-2-2-222-222-2-2-222000000000000-2200000000000000−2i2i2i−2i000000
χ332222-2-2-2-2-2-2-22-22-2-2222222-2-2000000000000-220000022-20-200000000000000
χ342222-2-2-2-2-2-2-22-22-2-2222222-2-2000000000000-2200000-2-220200000000000000
χ352222-2-2-2-2-2-2-22-22-2-22222-2-2220000000000002-2000002-220-200000000000000
χ362222-2-2-2-2-2-2-22-22-2-22222-2-2220000000000002-200000-22-20200000000000000
χ372-2-22-2-222-22-222-22-222-2-2000000002-22-20000000000000000002i−2i000000002i−2i
χ382-2-22-2-222-22-222-22-222-2-2000000002-22-2000000000000000000−2i2i00000000−2i2i
χ392-2-22-2-222-22-222-22-222-2-200000000-22-220000000000000000002i−2i00000000−2i2i
χ402-2-22-2-222-22-222-22-222-2-200000000-22-22000000000000000000−2i2i000000002i−2i
χ412-2-22-2-222-2-22-222-22-22-22000000002-2-2200000000000000002-2000000002-200
χ422-2-22-2-222-2-22-222-22-22-22000000002-2-220000000000000000-2200000000-2200
χ432-2-22-2-222-2-22-222-22-22-2200000000-222-200000000000000002-200000000-2200
χ442-2-22-2-222-2-22-222-22-22-2200000000-222-20000000000000000-22000000002-200
χ4544444444-444-4-4-4-4-44-4-44000000000000000000000000000000000000000000
χ4644444444-4-4-44-4444-4-4-4-4000000000000000000000000000000000000000000
χ4744-4-44i−4i4i−4i0000000000002i2−2i222−222-22i−2i00000000002ζ−2ζ2ζ3−2ζ300000000000000000000
χ4844-4-44i−4i4i−4i0000000000002i2−2i222−22-22−2i2i0000000000−2ζ2ζ−2ζ32ζ300000000000000000000
χ4944-4-44i−4i4i−4i000000000000−2i22i2−22222-22i−2i0000000000−2ζ2ζ−2ζ32ζ300000000000000000000
χ5044-4-44i−4i4i−4i000000000000−2i22i2−2222-22−2i2i00000000002ζ−2ζ2ζ3−2ζ300000000000000000000
χ5144-4-4−4i4i−4i4i0000000000002i2−2i2−22222-2−2i2i00000000002ζ3−2ζ32ζ−2ζ00000000000000000000
χ5244-4-4−4i4i−4i4i0000000000002i2−2i2−2222-222i−2i0000000000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ5344-4-4−4i4i−4i4i000000000000−2i22i222−222-2−2i2i0000000000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ5444-4-4−4i4i−4i4i000000000000−2i22i222−22-222i−2i00000000002ζ3−2ζ32ζ−2ζ00000000000000000000
χ554-4-4444-4-444-4-4-444-4-44-44000000000000000000000000000000000000000000
χ564-4-4444-4-44-444-4-4-4444-4-4000000000000000000000000000000000000000000
χ574-4-4444-4-4-44-444-4-44-4-444000000000000000000000000000000000000000000
χ584-4-4444-4-4-4-44-4444-44-44-4000000000000000000000000000000000000000000
χ594-4-44-4-44444-4-4-44-444-44-4000000000000000000000000000000000000000000
χ604-4-44-4-4444-444-4-44-4-4-444000000000000000000000000000000000000000000
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.