Finite Group Databasebeta

← Group #118459

Character table — Group #118459

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12224444222244444444244444448888888888888888888888884444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
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
χ91111111111-1-111-1-1-1-1-1-1-1-111-111-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1i−iii−i−ii−i11-1-1
χ101111111111-1-111-1-1-1-1-1-1-1-111-111-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1111111-1-1−ii−i−iii−ii-1-111
χ111111111111-1-111-1-1-1-1-1-1-1-111-111-1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111i−i−i−iiii−i-1-111
χ121111111111-1-111-1-1-1-1-1-1-1-111-111-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-111−iiii−i−i−ii11-1-1
χ131111111111-1-111-1-1-1-1-1-1-1-111-111-1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111−iiii−i−i−ii-1-111
χ141111111111-1-111-1-1-1-1-1-1-1-111-111-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-111i−i−i−iiii−i11-1-1
χ151111111111-1-111-1-1-1-1-1-1-1-111-111-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1−ii−i−iii−ii11-1-1
χ161111111111-1-111-1-1-1-1-1-1-1-111-111-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1111111-1-1i−iii−i−ii−i-1-111
χ1722222222222222-2-22-2-2222-2-2-2-2-2-20000000000000000000000000000000000002i−2i2i−2i
χ1822222222222222-2-22-2-2222-2-2-2-2-2-2000000000000000000000000000000000000−2i2i−2i2i
χ192222222222-2-22222-222-2-2-2-2-22-2-220000000000000000000000000000000000002i−2i−2i2i
χ202222222222-2-22222-222-2-2-2-2-22-2-22000000000000000000000000000000000000−2i2i2i−2i
χ2122222222-2-222-2-2222222-2-22-2-22-2-20000000000000000000000000000220000-2-20000
χ2222222222-2-222-2-2222222-2-22-2-22-2-20000000000000000000000000000-2-20000220000
χ2322222222-2-222-2-2-2-22-2-22-2-2-222-2220000000022-2-222-2-2000000000000000000000000
χ2422222222-2-222-2-2-2-22-2-22-2-2-222-22200000000-2-222-2-222000000000000000000000000
χ2522222222-2-2-2-2-2-222-222-222-22-2-22-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2622222222-2-2-2-2-2-222-222-222-22-2-22-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222-222-2200000000000000000000000000002i−2i0000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222-222-220000000000000000000000000000−2i2i00002i−2i0000
χ292222-2-2-2-22222-2-222-2-2-2-22-2222-2-2-20000000000000000000000002-22-2000000000000
χ302222-2-2-2-22222-2-222-2-2-2-22-2222-2-2-2000000000000000000000000-22-22000000000000
χ312222-2-2-2-22222-2-2-2-2-222-22-2-2-2-2222000000000000000022-2-222-2-20000000000000000
χ322222-2-2-2-22222-2-2-2-2-222-22-2-2-2-22220000000000000000-2-222-2-2220000000000000000
χ332222-2-2-2-222-2-2-2-2222-2-22-22-2-2222-2000000000000000022-2-2-2-2220000000000000000
χ342222-2-2-2-222-2-2-2-2222-2-22-22-2-2222-20000000000000000-2-22222-2-20000000000000000
χ352222-2-2-2-222-2-2-2-2-2-22222-2222-2-2-220000000000000000000000002-2-22000000000000
χ362222-2-2-2-222-2-2-2-2-2-22222-2222-2-2-22000000000000000000000000-222-2000000000000
χ372222-2-2-2-2-2-2222222-2-2-2-2-222-2-2-2220000000000000000000000000000002i−2i2i−2i000000
χ382222-2-2-2-2-2-2222222-2-2-2-2-222-2-2-222000000000000000000000000000000−2i2i−2i2i000000
χ392222-2-2-2-2-2-22222-2-2-222-2-22-2222-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ402222-2-2-2-2-2-22222-2-2-222-2-22-2222-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ412222-2-2-2-2-2-2-2-222222-2-222-2-22-22-2222-2-2-2-22200000000000000000000000000000000
χ422222-2-2-2-2-2-2-2-222222-2-222-2-22-22-22-2-22222-2-200000000000000000000000000000000
χ432222-2-2-2-2-2-2-2-222-2-222222-22-22-22-20000000000000000000000000000002-2-22000000
χ442222-2-2-2-2-2-2-2-222-2-222222-22-22-22-2000000000000000000000000000000-222-2000000
χ4544-4-444-4-4004-40000400-400000000000000000022−220022−22000000000000000000000000
χ4644-4-444-4-4004-40000400-4000000000000000000−222200−2222000000000000000000000000
χ4744-4-444-4-400-440000-40040000000000000000002i2−2i200−2i22i2000000000000000000000000
χ4844-4-444-4-400-440000-4004000000000000000000−2i22i2002i2−2i2000000000000000000000000
χ4944-4-4-4-444004-40000-400400000000000000002i2−2i2002i2−2i200000000000000000000000000
χ5044-4-4-4-444004-40000-40040000000000000000−2i22i200−2i22i200000000000000000000000000
χ5144-4-4-4-44400-440000400-4000000000000000022−2200−222200000000000000000000000000
χ5244-4-4-4-44400-440000400-40000000000000000−22220022−2200000000000000000000000000
χ534-44-44i−4i4i−4i0000004i−4i04-40000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300000000000000000000000000000000
χ544-44-44i−4i4i−4i0000004i−4i04-4000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300000000000000000000000000000000
χ554-44-44i−4i4i−4i000000−4i4i0-440000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ00000000000000000000000000000000
χ564-44-44i−4i4i−4i000000−4i4i0-44000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ00000000000000000000000000000000
χ574-44-4−4i4i−4i4i0000004i−4i0-440000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ300000000000000000000000000000000
χ584-44-4−4i4i−4i4i0000004i−4i0-44000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ300000000000000000000000000000000
χ594-44-4−4i4i−4i4i000000−4i4i04-40000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ00000000000000000000000000000000
χ604-44-4−4i4i−4i4i000000−4i4i04-4000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ00000000000000000000000000000000
χ614-4-444i−4i−4i4i4-4004i−4i00000000000000000000000000000000002i2−2i222−220000000000000000
χ624-4-444i−4i−4i4i4-4004i−4i0000000000000000000000000000000000−2i22i2−22220000000000000000
χ634-4-444i−4i−4i4i-4400−4i4i0000000000000000000000000000002i2−2i222−2200000000000000000000
χ644-4-444i−4i−4i4i-4400−4i4i000000000000000000000000000000−2i22i2−222200000000000000000000
χ654-4-44−4i4i4i−4i4-400−4i4i00000000000000000000000000000000002i2−2i2−22220000000000000000
χ664-4-44−4i4i4i−4i4-400−4i4i0000000000000000000000000000000000−2i22i222−220000000000000000
χ674-4-44−4i4i4i−4i-44004i−4i0000000000000000000000000000002i2−2i2−222200000000000000000000
χ684-4-44−4i4i4i−4i-44004i−4i000000000000000000000000000000−2i22i222−2200000000000000000000

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