Finite Group Databasebeta

← Group #116207

Character table — Group #116207

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12224444222222444444222244444444444444444444444444442444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
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
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ91111-1-1-1-1-1-111-1-11111-1-111-1-11-1-111111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-1-1-111-1-11111-1-111-1-11-1-111111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i-1-111−i−iii−i−iii-1-111
χ111111-1-1-1-1-1-111-1-11111-1-111-1-11-1-111111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-1
χ121111-1-1-1-1-1-111-1-11111-1-111-1-11-1-111111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii-1-111ii−i−iii−i−i-1-111
χ131111-1-1-1-1-1-111-1-11111-1-111-1-11-1-11-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiii11-1-1−i−iiiii−i−i-1-111
χ141111-1-1-1-1-1-111-1-11111-1-111-1-11-1-11-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiii-1-111ii−i−i−i−iii11-1-1
χ151111-1-1-1-1-1-111-1-11111-1-111-1-11-1-11-1-1-1-11111−i−iii−i−iiiiiii−i−i−i−i11-1-1ii−i−i−i−iii-1-111
χ161111-1-1-1-1-1-111-1-11111-1-111-1-11-1-11-1-1-1-11111−i−iii−i−iiiiiii−i−i−i−i-1-111−i−iiiii−i−i11-1-1
χ1722222222222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-200000000-2-2-2-22222000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-22-22-2-22-2200000000000000000000000000002i−2i2i−2i00000000
χ202222222222-2-2-2-222-2-2-2-22-22-2-22-220000000000000000000000000000−2i2i−2i2i00000000
χ212222222222-2-2-2-222-2-2-2-2-22-222-22-20000000000000000000000000000000000002i−2i2i−2i
χ222222222222-2-2-2-222-2-2-2-2-22-222-22-2000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-2-222-2-2-2-2-2-22222-2-2-222-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2422222222-2-222-2-2-2-2-2-22222-2-2-222-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2522222222-2-222-2-2-2-2-2-222-2-2222-2-2222-2-222-2-200000000000000000000000000000000
χ2622222222-2-222-2-2-2-2-2-222-2-2222-2-22-2-222-2-22200000000000000000000000000000000
χ2722222222-2-2-2-222-2-222-2-22-2-2222-2-20000000000000000000000002-2-22000000000000
χ2822222222-2-2-2-222-2-222-2-22-2-2222-2-2000000000000000000000000-222-2000000000000
χ2922222222-2-2-2-222-2-222-2-2-222-2-2-222000000000000000000000000000000002-22-20000
χ3022222222-2-2-2-222-2-222-2-2-222-2-2-22200000000000000000000000000000000-22-220000
χ312222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-2000000000000000022-2-2-2-2220000000000000000
χ322222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-20000000000000000-2-22222-2-20000000000000000
χ332222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22200000000000000000000000000000000
χ342222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-22222-2-22222-2-200000000000000000000000000000000
χ352222-2-2-2-222-2-2-2-2-2-222222-22-22-22-20000000000000000000000002-22-2000000000000
χ362222-2-2-2-222-2-2-2-2-2-222222-22-22-22-2000000000000000000000000-22-22000000000000
χ372222-2-2-2-222-2-2-2-2-2-22222-22-22-22-22000000000000000000000000000000002i−2i−2i2i0000
χ382222-2-2-2-222-2-2-2-2-2-22222-22-22-22-2200000000000000000000000000000000−2i2i2i−2i0000
χ392222-2-2-2-2-2-222-2-22222-2-2-2-222-222-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ402222-2-2-2-2-2-222-2-22222-2-2-2-222-222-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ412222-2-2-2-2-2-2-2-22222-2-2222-2-22-2-22200000000000000000000000000002-2-2200000000
χ422222-2-2-2-2-2-2-2-22222-2-2222-2-22-2-2220000000000000000000000000000-222-200000000
χ432222-2-2-2-2-2-2-2-22222-2-222-222-222-2-20000000000000000000000000000000000002i−2i−2i2i
χ442222-2-2-2-2-2-2-2-22222-2-222-222-222-2-2000000000000000000000000000000000000−2i2i2i−2i
χ4544-4-44i4i−4i−4i004-40000004i−4i000000000000000000002+2i−2−2i2−2i−2+2i000000000000000000000000
χ4644-4-44i4i−4i−4i004-40000004i−4i00000000000000000000−2−2i2+2i−2+2i2−2i000000000000000000000000
χ4744-4-44i4i−4i−4i00-44000000−4i4i00000000000000002+2i−2−2i2−2i−2+2i0000000000000000000000000000
χ4844-4-44i4i−4i−4i00-44000000−4i4i0000000000000000−2−2i2+2i−2+2i2−2i0000000000000000000000000000
χ4944-4-4−4i−4i4i4i004-4000000−4i4i000000000000000000002−2i−2+2i2+2i−2−2i000000000000000000000000
χ5044-4-4−4i−4i4i4i004-4000000−4i4i00000000000000000000−2+2i2−2i−2−2i2+2i000000000000000000000000
χ5144-4-4−4i−4i4i4i00-440000004i−4i00000000000000002−2i−2+2i2+2i−2−2i0000000000000000000000000000
χ5244-4-4−4i−4i4i4i00-440000004i−4i0000000000000000−2+2i2−2i−2−2i2+2i0000000000000000000000000000
χ534-44-44i−4i4i−4i4-400004i−4i0000000000002-22i−2i2i−2i2-200000000000000000000000000000000
χ544-44-44i−4i4i−4i4-400004i−4i000000000000-22−2i2i−2i2i-2200000000000000000000000000000000
χ554-44-44i−4i4i−4i-440000−4i4i0000000000002-2−2i2i2i−2i-2200000000000000000000000000000000
χ564-44-44i−4i4i−4i-440000−4i4i000000000000-222i−2i−2i2i2-200000000000000000000000000000000
χ574-44-4−4i4i−4i4i4-40000−4i4i0000000000002-2−2i2i−2i2i2-200000000000000000000000000000000
χ584-44-4−4i4i−4i4i4-40000−4i4i000000000000-222i−2i2i−2i-2200000000000000000000000000000000
χ594-44-4−4i4i−4i4i-4400004i−4i0000000000002-22i−2i−2i2i-2200000000000000000000000000000000
χ604-44-4−4i4i−4i4i-4400004i−4i000000000000-22−2i2i2i−2i2-200000000000000000000000000000000
χ614-4-444-4-4400004-4004-4000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ624-4-444-4-4400004-4004-400000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ634-4-444-4-440000-4400-44000000000000000000000000002-2-222-2-220000000000000000
χ644-4-444-4-440000-4400-4400000000000000000000000000-222-2-222-20000000000000000
χ654-4-44-444-400004-400-44000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ664-4-44-444-400004-400-4400000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ674-4-44-444-40000-44004-4000000000000000000000000002-22-2-22-220000000000000000
χ684-4-44-444-40000-44004-400000000000000000000000000-22-222-22-20000000000000000

Here i is the imaginary unit (i² = −1).