Finite Group Databasebeta

← Group #239386

Character table — Group #239386

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222222224444444444444444444444161616161616161616161616161616161616161616161616
order12222222224444444444444444448888888888888888244444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ91111111111-1-1-1-111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-111
χ111111111111-1-1-1-111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111
χ121111111111-1-1-1-111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1
χ131111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111-1-11111-1-1
χ141111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-111-1-1-1-111
χ151111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-111-1-1-1-111-1-111
χ161111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-11111-1-111-1-1
χ1722222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000002-22-200000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000-22-2200000000
χ192222222222-2-2-2-2-2-22222-2-2-2-2-2-22200000000000000000000000000002-2-2200000000
χ202222222222-2-2-2-2-2-22222-2-2-2-2-2-2220000000000000000000000000000-222-200000000
χ2122222-2-2-2-2222222222-2-2-2-2-2-22-22-20000000000000000000000002i−2i2i−2i000000000000
χ2222222-2-2-2-2222222222-2-2-2-2-2-22-22-2000000000000000000000000−2i2i−2i2i000000000000
χ2322222-2-2-2-222222-2-2-2-22222-2-2-22-22000000000000000000002-22-20000000000000000
χ2422222-2-2-2-222222-2-2-2-22222-2-2-22-2200000000000000000000-22-220000000000000000
χ2522222-2-2-2-22-2-2-2-222-2-222-2-2222-2-220000000000000000000000002i−2i−2i2i000000000000
χ2622222-2-2-2-22-2-2-2-222-2-222-2-2222-2-22000000000000000000000000−2i2i2i−2i000000000000
χ2722222-2-2-2-22-2-2-2-2-2-222-2-22222-222-2000000000000000000002-2-220000000000000000
χ2822222-2-2-2-22-2-2-2-2-2-222-2-22222-222-200000000000000000000-222-20000000000000000
χ292222-222-2-2-222-2-2222222-2-22-2-22-2-2000000000000000000000000000000002i−2i2i−2i0000
χ302222-222-2-2-222-2-2222222-2-22-2-22-2-200000000000000000000000000000000−2i2i−2i2i0000
χ312222-222-2-2-222-2-2-2-2-2-2-2-2222-22-22200000000000000002-22-200000000000000000000
χ322222-222-2-2-222-2-2-2-2-2-2-2-2222-22-2220000000000000000-22-2200000000000000000000
χ332222-222-2-2-2-2-22222-2-2-2-2-2-2-22-2222000000000000000000000000000000002i−2i−2i2i0000
χ342222-222-2-2-2-2-22222-2-2-2-2-2-2-22-222200000000000000000000000000000000−2i2i2i−2i0000
χ352222-222-2-2-2-2-222-2-2222222-222-2-2-200000000000000002-2-2200000000000000000000
χ362222-222-2-2-2-2-222-2-2222222-222-2-2-20000000000000000-222-200000000000000000000
χ372222-2-2-222-222-2-22222-2-222-22-2-2-220000000000000000000000000000000000002-22-2
χ382222-2-2-222-222-2-22222-2-222-22-2-2-22000000000000000000000000000000000000-22-22
χ392222-2-2-222-222-2-2-2-2-2-222-2-2-22222-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ402222-2-2-222-222-2-2-2-2-2-222-2-2-22222-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ412222-2-2-222-2-2-22222-2-222222-2-2-22-20000000000000000000000000000000000002-2-22
χ422222-2-2-222-2-2-22222-2-222222-2-2-22-2000000000000000000000000000000000000-222-2
χ432222-2-2-222-2-2-222-2-222-2-2-2-22-222-222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ442222-2-2-222-2-2-222-2-222-2-2-2-22-222-22−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ4544-4-444-44-4-4000000000000000000000000002222−22−222222−22−22000000000000000000000000
χ4644-4-444-44-4-400000000000000000000000000−22−222222−22−222222000000000000000000000000
χ4744-4-44-44-44-40000000000000000002222−22−222222−22−2200000000000000000000000000000000
χ4844-4-44-44-44-4000000000000000000−22−222222−22−22222200000000000000000000000000000000
χ4944-4-4-44-4-4440000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000
χ5044-4-4-44-4-444000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000
χ5144-4-4-4-444-44000000000000000000000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000
χ5244-4-4-4-444-4400000000000000000000000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000
χ534-44-4000000004i−4i00004i−4i4-40000002-22-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ544-44-4000000004i−4i00004i−4i4-4000000-22-22-22-22−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ554-44-4000000004i−4i0000−4i4i-440000002i−2i2i−2i−2i2i−2i2i2-22-2-22-22000000000000000000000000
χ564-44-4000000004i−4i0000−4i4i-44000000−2i2i−2i2i2i−2i2i−2i-22-222-22-2000000000000000000000000
χ574-44-400000000−4i4i00004i−4i-440000002i−2i2i−2i−2i2i−2i2i-22-222-22-2000000000000000000000000
χ584-44-400000000−4i4i00004i−4i-44000000−2i2i−2i2i2i−2i2i−2i2-22-2-22-22000000000000000000000000
χ594-44-400000000−4i4i0000−4i4i4-40000002-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ604-44-400000000−4i4i0000−4i4i4-4000000-22-22-22-222i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ614-4-440000004i−4i004i−4i4-400000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ624-4-440000004i−4i004i−4i4-40000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ634-4-440000004i−4i00−4i4i-4400000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ644-4-440000004i−4i00−4i4i-440000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ654-4-44000000−4i4i004i−4i-4400000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ664-4-44000000−4i4i004i−4i-440000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ674-4-44000000−4i4i00−4i4i4-400000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ684-4-44000000−4i4i00−4i4i4-40000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000

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