Finite Group Databasebeta

← Group #263003

Character table — Group #263003

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12224444224422444444888888884444448888888844444444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1
χ9111111111111-1-1-1-1111111111111-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-111-1-111-1-1
χ10111111111111-1-1-1-1111111111111-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1-1-111-1-111
χ11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-111
χ12111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111
χ14111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-111-1-1-1-111
χ172222222222222222-2-2-2-22222-2-2-2-2-2-2000022-2-2000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-20000-2-222000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-22222-2-2-2-2220000-2-222000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222000022-2-2000000000000000000000000
χ212222-2-2-2-222-2-222-2-222-2-2000000002-2000000002i2i−2i−2i00000000002i−2i00000000
χ222222-2-2-2-222-2-222-2-222-2-2000000002-200000000−2i−2i2i2i0000000000−2i2i00000000
χ232222-2-2-2-222-2-222-2-2-2-22200000000-2222-2-200000000000000002-20000000000
χ242222-2-2-2-222-2-222-2-2-2-22200000000-22-2-2220000000000000000-220000000000
χ252222-2-2-2-222-2-2-2-22222-2-200000000-22000000002i2i−2i−2i0000000000−2i2i00000000
χ262222-2-2-2-222-2-2-2-22222-2-200000000-2200000000−2i−2i2i2i00000000002i−2i00000000
χ272222-2-2-2-222-2-2-2-222-2-222000000002-222-2-20000000000000000-220000000000
χ282222-2-2-2-222-2-2-2-222-2-222000000002-2-2-22200000000000000002-20000000000
χ292222-2-2-2-2-2-22200002-22-222-2-222-2-200000000000000002-2002-2000000000000
χ302222-2-2-2-2-2-22200002-22-222-2-222-2-20000000000000000-2200-22000000000000
χ312222-2-2-2-2-2-22200002-22-2-2-222-2-22200000000000000002-200-22000000000000
χ322222-2-2-2-2-2-22200002-22-2-2-222-2-2220000000000000000-22002-2000000000000
χ332222-2-2-2-2-2-2220000-22-2222-2-2-2-222000000000000002-2002-200000000000000
χ342222-2-2-2-2-2-2220000-22-2222-2-2-2-22200000000000000-2200-2200000000000000
χ352222-2-2-2-2-2-2220000-22-22-2-22222-2-2000000000000002-200-2200000000000000
χ362222-2-2-2-2-2-2220000-22-22-2-22222-2-200000000000000-22002-200000000000000
χ3722-2-222-2-22-22-22-22-200002-22-200000000002-20000000000000000002−22−22−22−2
χ3822-2-222-2-22-22-22-22-200002-22-200000000002-2000000000000000000−22−22−22−22
χ3922-2-222-2-22-22-22-22-20000-22-220000000000-220000000000000000002−22−2−22−22
χ4022-2-222-2-22-22-22-22-20000-22-220000000000-22000000000000000000−22−222−22−2
χ4122-2-222-2-22-22-2-22-2200002-22-20000000000-220000000000000000002−2−222−2−22
χ4222-2-222-2-22-22-2-22-2200002-22-20000000000-22000000000000000000−222−2−222−2
χ4322-2-222-2-22-22-2-22-220000-22-2200000000002-20000000000000000002−2−22−222−2
χ4422-2-222-2-22-22-2-22-220000-22-2200000000002-2000000000000000000−222−22−2−22
χ4544444444-4-4-4-400004-4-44000000000000000000000000000000000000000000
χ4644444444-4-4-4-40000-444-4000000000000000000000000000000000000000000
χ4744-4-444-4-4-44-440000000000000000000000004-4000000000000000000000000
χ4844-4-444-4-4-44-44000000000000000000000000-44000000000000000000000000
χ4944-4-4-4-4444-4-444-4-440000000000000000000000000000000000000000000000
χ5044-4-4-4-4444-4-44-444-40000000000000000000000000000000000000000000000
χ5144-4-4-4-444-444-4000000004-4-4400000000000000000000000000000000000000
χ5244-4-4-4-444-444-400000000-444-400000000000000000000000000000000000000
χ534-44-44i−4i4i−4i00000000000000002i2−2i222−22002-22i−2i00002ζ−2ζ2ζ3−2ζ300000000000000000000
χ544-44-44i−4i4i−4i00000000000000002i2−2i222−2200-22−2i2i0000−2ζ2ζ−2ζ32ζ300000000000000000000
χ554-44-44i−4i4i−4i0000000000000000−2i22i2−2222002-22i−2i0000−2ζ2ζ−2ζ32ζ300000000000000000000
χ564-44-44i−4i4i−4i0000000000000000−2i22i2−222200-22−2i2i00002ζ−2ζ2ζ3−2ζ300000000000000000000
χ574-44-4−4i4i−4i4i00000000000000002i2−2i2−2222002-2−2i2i00002ζ3−2ζ32ζ−2ζ00000000000000000000
χ584-44-4−4i4i−4i4i00000000000000002i2−2i2−222200-222i−2i0000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ594-44-4−4i4i−4i4i0000000000000000−2i22i222−22002-2−2i2i0000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ604-44-4−4i4i−4i4i0000000000000000−2i22i222−2200-222i−2i00002ζ3−2ζ32ζ−2ζ00000000000000000000
χ618-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000
χ628-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000

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