Finite Group Databasebeta

← Group #239289

Character table — Group #239289

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12224444222244444444244444444444444488888888888888882224444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1111-1-11-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111111-1-11-1-1-1-1-1-111-111-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1-11-1111-1-111-1-1
χ10111111111-1-11-1-1-1-1-1-111-111-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-111-11-111-1-1-1-111
χ11111111111-1-11-1-1-1-1-1-111-111-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-111-1-111
χ12111111111-1-11-1-1-1-1-1-111-111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-111-1-11111-1-1
χ13111111111-1-11-1-1-1-1-1-111-111-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-1-1-111-1-111-1-111
χ14111111111-1-11-1-1-1-1-1-111-111-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-11111-1-1
χ15111111111-1-11-1-1-1-1-1-111-111-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-111-11-111-1-111-1-1
χ16111111111-1-11-1-1-1-1-1-111-111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-1-11-1111-1-1-1-111
χ17222222222222-2-2-2-222222-2-2-2-22-2-2000000000000000000000000000000002-22-20000
χ18222222222222-2-2-2-222222-2-2-2-22-2-200000000000000000000000000000000-22-220000
χ19222222222-2-222222-2-222-2-2-222-2-2-2000000000000000000000000000000002-2-220000
χ20222222222-2-222222-2-222-2-2-222-2-2-200000000000000000000000000000000-222-20000
χ2122222222-222-2222222-2-2-22-2-2-2-22-20000000000000000000000000000000000002i−2i2i−2i
χ2222222222-222-2222222-2-2-22-2-2-2-22-2000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-222-2-2-2-2-222-2-2-2-2222-2-2200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2422222222-222-2-2-2-2-222-2-2-2-2222-2-220000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2522222222-2-2-2-22222-2-2-2-22-22-2-22-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2622222222-2-2-2-22222-2-2-2-22-22-2-22-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222-22222-20000000000000000000000000000000000002i−2i−2i2i
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222-22222-2000000000000000000000000000000000000−2i2i2i−2i
χ292222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ302222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ312222-2-2-2-22222-2-222-2-2-2-22-2-2-22-22222-2-222-2-200000000000000000000000000000000
χ322222-2-2-2-22222-2-222-2-2-2-22-2-2-22-222-2-222-2-22200000000000000000000000000000000
χ332222-2-2-2-22-2-2222-2-222-2-2-2-2-22-222222-2-2-2-22200000000000000000000000000000000
χ342222-2-2-2-22-2-2222-2-222-2-2-2-2-22-2222-2-22222-2-200000000000000000000000000000000
χ352222-2-2-2-22-2-22-2-22222-2-2-222-222-2-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ362222-2-2-2-22-2-22-2-22222-2-2-222-222-2-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ372222-2-2-2-2-222-222-2-2-2-222-22-2-222-2200000000000000000000000022000-2-2000000000
χ382222-2-2-2-2-222-222-2-2-2-222-22-2-222-22000000000000000000000000-2-200022000000000
χ392222-2-2-2-2-222-2-2-222-2-222-2-222-222-20000000000000000000000000022-200-200000000
χ402222-2-2-2-2-222-2-2-222-2-222-2-222-222-200000000000000000000000000-2-2200200000000
χ412222-2-2-2-2-2-2-2-222-2-222222-22-22-22-2000000000000000000000000002-2200-200000000
χ422222-2-2-2-2-2-2-2-222-2-222222-22-22-22-200000000000000000000000000-22-200200000000
χ432222-2-2-2-2-2-2-2-2-2-222222222-22-2-2-220000000000000000000000002-2000-22000000000
χ442222-2-2-2-2-2-2-2-2-2-222222222-22-2-2-22000000000000000000000000-220002-2000000000
χ4544-4-44i4i−4i−4i00004-44i−4i0000000000002-22i−2i2i−2i2-200000000000000000000000000000000
χ4644-4-44i4i−4i−4i00004-44i−4i000000000000-22−2i2i−2i2i-2200000000000000000000000000000000
χ4744-4-44i4i−4i−4i0000-44−4i4i0000000000002-22i−2i−2i2i-2200000000000000000000000000000000
χ4844-4-44i4i−4i−4i0000-44−4i4i000000000000-22−2i2i2i−2i2-200000000000000000000000000000000
χ4944-4-4−4i−4i4i4i00004-4−4i4i0000000000002-2−2i2i−2i2i2-200000000000000000000000000000000
χ5044-4-4−4i−4i4i4i00004-4−4i4i000000000000-222i−2i2i−2i-2200000000000000000000000000000000
χ5144-4-4−4i−4i4i4i0000-444i−4i0000000000002-2−2i2i2i−2i-2200000000000000000000000000000000
χ5244-4-4−4i−4i4i4i0000-444i−4i000000000000-222i−2i−2i2i2-200000000000000000000000000000000
χ534-44-44i−4i4i−4i04-4000004i−4i0000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ544-44-44i−4i4i−4i04-4000004i−4i000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ554-44-44i−4i4i−4i0-4400000−4i4i0000000000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ564-44-44i−4i4i−4i0-4400000−4i4i000000000000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ574-44-4−4i4i−4i4i04-400000−4i4i0000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ584-44-4−4i4i−4i4i04-400000−4i4i000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ594-44-4−4i4i−4i4i0-44000004i−4i0000000000000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ604-44-4−4i4i−4i4i0-44000004i−4i000000000000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ614-4-444-4-44400-40000004-400000000000000000000000000002i2−2i22i2−2i20000000000000000
χ624-4-444-4-44400-40000004-40000000000000000000000000000−2i22i2−2i22i20000000000000000
χ634-4-444-4-44-4004000000-44000000000000000000000000000022−22−22220000000000000000
χ644-4-444-4-44-4004000000-440000000000000000000000000000−222222−220000000000000000
χ654-4-44-444-4400-4000000-440000000000000000000000002i2−2i22i2−2i200000000000000000000
χ664-4-44-444-4400-4000000-44000000000000000000000000−2i22i2−2i22i200000000000000000000
χ674-4-44-444-4-40040000004-400000000000000000000000022−22−222200000000000000000000
χ684-4-44-444-4-40040000004-4000000000000000000000000−222222−2200000000000000000000

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