Finite Group Databasebeta

← Group #473990

Character table — Group #473990

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222222244448888888888888888881616161616161616161616161616161616161616
order12224444222222444444888822444444888888888844888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-11111-1-111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ911111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111
χ1111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-111-1-1-1-111
χ17222222222-2-2-2-222-2-2-2-2222222-200002-2-2-222-2-2000000000000000000000000
χ18222222222-2-2-2-222-2-2-2-222222-220000-22-2-2-2-222000000000000000000000000
χ19222222222-2-2-2-222-2-2-2-22-2-2-2-22-200002-222-2-222000000000000000000000000
χ20222222222-2-2-2-222-2-2-2-22-2-2-2-2-220000-222222-2-2000000000000000000000000
χ212222-2-2-2-2222222-2-2-2-2-2-200002-222-2-2-2200000000002-2000000000000000000
χ222222-2-2-2-2222222-2-2-2-2-2-200002-2-2-222-220000000000-22000000000000000000
χ232222-2-2-2-2222222-2-2-2-2-2-20000-2222-2-22-20000000000-22000000000000000000
χ242222-2-2-2-2222222-2-2-2-2-2-20000-22-2-2222-200000000002-2000000000000000000
χ252222-2-2-2-22-2-2-2-22-22222-20000220000-2-20000002i2i−2i−2i0000002i−2i000000000000
χ262222-2-2-2-22-2-2-2-22-22222-20000220000-2-2000000−2i−2i2i2i000000−2i2i000000000000
χ272222-2-2-2-22-2-2-2-22-22222-20000-2-20000220000002i2i−2i−2i000000−2i2i000000000000
χ282222-2-2-2-22-2-2-2-22-22222-20000-2-2000022000000−2i−2i2i2i0000002i−2i000000000000
χ292222-2-2-2-2-222-2-2-2222-2-2222-2-2000000002-200000000000000002i−2i2i−2i00000000
χ302222-2-2-2-2-222-2-2-2222-2-2222-2-2000000002-20000000000000000−2i2i−2i2i00000000
χ312222-2-2-2-2-222-2-2-2222-2-22-2-22200000000-2200000000000000002i−2i−2i2i00000000
χ322222-2-2-2-2-222-2-2-2222-2-22-2-22200000000-220000000000000000−2i2i2i−2i00000000
χ332222-2-2-2-2-2-2-222-22-2-222222-2-200000000-2200000000002i−2i2i−2i00000000000000
χ342222-2-2-2-2-2-2-222-22-2-222222-2-200000000-220000000000−2i2i−2i2i00000000000000
χ352222-2-2-2-2-2-2-222-22-2-2222-2-222000000002-200000000002i−2i−2i2i00000000000000
χ362222-2-2-2-2-2-2-222-22-2-2222-2-222000000002-20000000000−2i2i2i−2i00000000000000
χ372-2-22-2-222-22-22-2222-22-2-2000000000000002i−2i2i−2i0000000000000000002-22i−2i00
χ382-2-22-2-222-22-22-2222-22-2-2000000000000002i−2i2i−2i000000000000000000-22−2i2i00
χ392-2-22-2-222-22-22-2222-22-2-200000000000000−2i2i−2i2i0000000000000000002-2−2i2i00
χ402-2-22-2-222-22-22-2222-22-2-200000000000000−2i2i−2i2i000000000000000000-222i−2i00
χ412-2-22-2-222-2-22-2222-22-22-2000000000000002i−2i−2i2i00000000000000002-200002i−2i
χ422-2-22-2-222-2-22-2222-22-22-2000000000000002i−2i−2i2i0000000000000000-220000−2i2i
χ432-2-22-2-222-2-22-2222-22-22-200000000000000−2i2i2i−2i00000000000000002-20000−2i2i
χ442-2-22-2-222-2-22-2222-22-22-200000000000000−2i2i2i−2i0000000000000000-2200002i−2i
χ4544444444-444-4-4-4-4-4-444-4000000000000000000000000000000000000000000
χ4644444444-4-4-444-4-444-4-4-4000000000000000000000000000000000000000000
χ4744-4-44i−4i4i−4i0000000000002i2−2i222−22002-22i−2i000000002ζ−2ζ2ζ3−2ζ300000000000000000000
χ4844-4-44i−4i4i−4i0000000000002i2−2i222−2200-22−2i2i00000000−2ζ2ζ−2ζ32ζ300000000000000000000
χ4944-4-44i−4i4i−4i000000000000−2i22i2−2222002-22i−2i00000000−2ζ2ζ−2ζ32ζ300000000000000000000
χ5044-4-44i−4i4i−4i000000000000−2i22i2−222200-22−2i2i000000002ζ−2ζ2ζ3−2ζ300000000000000000000
χ5144-4-4−4i4i−4i4i0000000000002i2−2i2−2222002-2−2i2i000000002ζ3−2ζ32ζ−2ζ00000000000000000000
χ5244-4-4−4i4i−4i4i0000000000002i2−2i2−222200-222i−2i00000000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ5344-4-4−4i4i−4i4i000000000000−2i22i222−22002-2−2i2i00000000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ5444-4-4−4i4i−4i4i000000000000−2i22i222−2200-222i−2i000000002ζ3−2ζ32ζ−2ζ00000000000000000000
χ554-4-4444-4-444-4-44-444-4-44-4000000000000000000000000000000000000000000
χ564-4-4444-4-44-444-4-44-444-4-4000000000000000000000000000000000000000000
χ574-4-4444-4-4-44-44-44-4-44-444000000000000000000000000000000000000000000
χ584-4-4444-4-4-4-44-444-44-44-44000000000000000000000000000000000000000000
χ594-4-44-4-44444-4-44-4-4-444-44000000000000000000000000000000000000000000
χ604-4-44-4-4444-444-4-4-44-4-444000000000000000000000000000000000000000000
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.