Finite Group Databasebeta

← Group #112554

Character table — Group #112554

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12224444222244444444244444444444444444444444888888884444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
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
χ91111-1-1-1-11111-1-111-1-1-1-11-1111-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−iii−i−i
χ101111-1-1-1-11111-1-111-1-1-1-11-1111-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii−i−iii
χ111111-1-1-1-11111-1-111-1-1-1-11-1111-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i−i−iii−i−iii
χ121111-1-1-1-11111-1-111-1-1-1-11-1111-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-111−i−iiiii−i−iii−i−i
χ131111-1-1-1-11111-1-111-1-1-1-11-1111-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i-1-111−i−iiiii−i−i−i−iii
χ141111-1-1-1-11111-1-111-1-1-1-11-1111-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i−i−iiiii−i−i
χ151111-1-1-1-11111-1-111-1-1-1-11-1111-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii−i−iiiii−i−i
χ161111-1-1-1-11111-1-111-1-1-1-11-1111-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−iii−i−i−i−iii
χ1722222222222222-2-222-2-222-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000
χ1822222222222222-2-222-2-222-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ192222222222-2-2-2-2222222-2-22-2-22-2-200000000000000000000000000002-22-200000000
χ202222222222-2-2-2-2222222-2-22-2-22-2-20000000000000000000000000000-22-2200000000
χ212222222222-2-2-2-2-2-222-2-2-2-2-222-222000000000000000022-2-222-2-20000000000000000
χ222222222222-2-2-2-2-2-222-2-2-2-2-222-2220000000000000000-2-222-2-2220000000000000000
χ2322222222-2-2222222-2-222-2-2-22-2-22-20000000000000000000000002-22-2000000000000
χ2422222222-2-2222222-2-222-2-2-22-2-22-2000000000000000000000000-22-22000000000000
χ2522222222-2-22222-2-2-2-2-2-2-2-22-222-220000000022-2-222-2-2000000000000000000000000
χ2622222222-2-22222-2-2-2-2-2-2-2-22-222-2200000000-2-222-2-222000000000000000000000000
χ2722222222-2-2-2-2-2-222-2-22222-2-22-2-22000000000000000000000000000000002-22-20000
χ2822222222-2-2-2-2-2-222-2-22222-2-22-2-2200000000000000000000000000000000-22-220000
χ2922222222-2-2-2-2-2-2-2-2-2-2-2-22222-222-20000000000000000000000000000000000002i−2i2i−2i
χ3022222222-2-2-2-2-2-2-2-2-2-2-2-22222-222-2000000000000000000000000000000000000−2i2i−2i2i
χ312222-2-2-2-22222-2-2-2-2-2-2222-2-2-2-222222-2-2-2-22200000000000000000000000000000000
χ322222-2-2-2-22222-2-2-2-2-2-2222-2-2-2-2222-2-22222-2-200000000000000000000000000000000
χ332222-2-2-2-222-2-22222-2-2-2-2-222-2-2-22200000000000000000000000000002i−2i−2i2i00000000
χ342222-2-2-2-222-2-22222-2-2-2-2-222-2-2-2220000000000000000000000000000−2i2i2i−2i00000000
χ352222-2-2-2-222-2-222-2-2-2-222-22-2222-2-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ362222-2-2-2-222-2-222-2-2-2-222-22-2222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ372222-2-2-2-2-2-222-2-22222-2-2-22-22-22-220000000000000000000000002-2-22000000000000
χ382222-2-2-2-2-2-222-2-22222-2-2-22-22-22-22000000000000000000000000-222-2000000000000
χ392222-2-2-2-2-2-222-2-2-2-22222-222-22-22-20000000022-2-2-2-222000000000000000000000000
χ402222-2-2-2-2-2-222-2-2-2-22222-222-22-22-200000000-2-22222-2-2000000000000000000000000
χ412222-2-2-2-2-2-2-2-2222222-2-22-2-2-2222-2000000000000000000000000000000002i−2i−2i2i0000
χ422222-2-2-2-2-2-2-2-2222222-2-22-2-2-2222-200000000000000000000000000000000−2i2i2i−2i0000
χ432222-2-2-2-2-2-2-2-222-2-222222-222-2-2-220000000000000000000000000000000000002-2-22
χ442222-2-2-2-2-2-2-2-222-2-222222-222-2-2-22000000000000000000000000000000000000-222-2
χ4544-4-444-4-44-40000004-40000000000000000002-22-22-22-2000000000000000000000000
χ4644-4-444-4-44-40000004-4000000000000000000-22-22-22-22000000000000000000000000
χ4744-4-444-4-4-44000000-440000000000000000002-2-222-2-22000000000000000000000000
χ4844-4-444-4-4-44000000-44000000000000000000-222-2-222-2000000000000000000000000
χ4944-4-4-4-4444-4000000-440000000000000000002-22-2-22-22000000000000000000000000
χ5044-4-4-4-4444-4000000-44000000000000000000-22-222-22-2000000000000000000000000
χ5144-4-4-4-444-440000004-40000000000000000002-2-22-222-2000000000000000000000000
χ5244-4-4-4-444-440000004-4000000000000000000-222-22-2-22000000000000000000000000
χ534-44-44i−4i4i−4i0000004-4004i−4i000000002-22-22i−2i2i−2i00000000000000000000000000000000
χ544-44-44i−4i4i−4i0000004-4004i−4i00000000-22-22−2i2i−2i2i00000000000000000000000000000000
χ554-44-44i−4i4i−4i000000-4400−4i4i000000002-2-222i−2i−2i2i00000000000000000000000000000000
χ564-44-44i−4i4i−4i000000-4400−4i4i00000000-222-2−2i2i2i−2i00000000000000000000000000000000
χ574-44-4−4i4i−4i4i0000004-400−4i4i000000002-22-2−2i2i−2i2i00000000000000000000000000000000
χ584-44-4−4i4i−4i4i0000004-400−4i4i00000000-22-222i−2i2i−2i00000000000000000000000000000000
χ594-44-4−4i4i−4i4i000000-44004i−4i000000002-2-22−2i2i2i−2i00000000000000000000000000000000
χ604-44-4−4i4i−4i4i000000-44004i−4i00000000-222-22i−2i−2i2i00000000000000000000000000000000
χ614-4-444i−4i−4i4i004-44i−4i0000000000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000
χ624-4-444i−4i−4i4i004-44i−4i000000000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000
χ634-4-444i−4i−4i4i00-44−4i4i0000000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ644-4-444i−4i−4i4i00-44−4i4i000000000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ654-4-44−4i4i4i−4i004-4−4i4i0000000000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000
χ664-4-44−4i4i4i−4i004-4−4i4i000000000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000
χ674-4-44−4i4i4i−4i00-444i−4i0000000000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ684-4-44−4i4i4i−4i00-444i−4i000000000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000

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