Finite Group Databasebeta

← Group #117803

Character table — Group #117803

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12224444222222444444444444444444888888888888888844444444888888882244888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ91111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−i−iii−i−iii-1-111
χ111111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−i−iii−i−iii11-1-1
χ121111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11ii−i−iii−i−i-1-111
χ131111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111-1-11-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii1-11-1ii−i−i−i−iii-1-111
χ141111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111-1-11-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-11-11−i−iiiii−i−i11-1-1
χ151111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111-1-11-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i1-11-1−i−iiiii−i−i-1-111
χ161111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111-1-11-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-11-11ii−i−i−i−iii11-1-1
χ1722222222222222-2-2-2-2-2-222222-2-22-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ1822222222222222-2-2-2-2-2-222222-2-22-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ192222222222-2-2-2-222-2-222-2-2-222-2-2-222-2-2000000000000000000000000000000000000000000002i−2i2i−2i
χ202222222222-2-2-2-222-2-222-2-2-222-2-2-222-2-200000000000000000000000000000000000000000000−2i2i−2i2i
χ212222222222-2-2-2-2-2-222-2-2-2-2-22222-2-2-22200000000000000000000000000000000000000002-22-20000
χ222222222222-2-2-2-2-2-222-2-2-2-2-22222-2-2-2220000000000000000000000000000000000000000-22-220000
χ2322222222-2-222-2-222-2-2222-2-2-2-2-2-22-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2422222222-2-222-2-222-2-2222-2-2-2-2-2-22-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2522222222-2-222-2-2-2-222-2-22-2-2-2-222222-2-200000000000000000000000022-2-222-2-20000000000000000
χ2622222222-2-222-2-2-2-222-2-22-2-2-2-222222-2-2000000000000000000000000-2-222-2-2220000000000000000
χ2722222222-2-2-2-222222222-222-2-222-2-2-2-2-2000000000000000000000000000000002-2-22000000000000
χ2822222222-2-2-2-222222222-222-2-222-2-2-2-2-200000000000000000000000000000000-222-2000000000000
χ2922222222-2-2-2-222-2-2-2-2-2-2-222-2-2-2-2-222220000000000000000000000000000000000002-22-200000000
χ3022222222-2-2-2-222-2-2-2-2-2-2-222-2-2-2-2-22222000000000000000000000000000000000000-22-2200000000
χ312222-2-2-2-222222222-2-2-2-2-2-2-2-2-222-22-22-2000000000000000000000000000000000000000000002i−2i−2i2i
χ322222-2-2-2-222222222-2-2-2-2-2-2-2-2-222-22-22-200000000000000000000000000000000000000000000−2i2i2i−2i
χ332222-2-2-2-2222222-2-22222-2-2-2-2-2-2-2-2-22-2200000000000000000000000000000000000000002i−2i−2i2i0000
χ342222-2-2-2-2222222-2-22222-2-2-2-2-2-2-2-2-22-220000000000000000000000000000000000000000−2i2i2i−2i0000
χ352222-2-2-2-222-2-2-2-2-2-2-2-222222-2-2222-222-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ362222-2-2-2-222-2-2-2-2-2-2-2-222222-2-2222-222-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ372222-2-2-2-2-2-222-2-22222-2-2-22222-2-2-2-222-20000000000000000000000000000000022-2-2000000000000
χ382222-2-2-2-2-2-222-2-22222-2-2-22222-2-2-2-222-200000000000000000000000000000000-2-222000000000000
χ392222-2-2-2-2-2-222-2-2-2-2-2-222-2222222-22-2-220000000000000000000000000000000000002i−2i−2i2i00000000
χ402222-2-2-2-2-2-222-2-2-2-2-2-222-2222222-22-2-22000000000000000000000000000000000000−2i2i2i−2i00000000
χ412222-2-2-2-2-2-2-2-22222-2-2-2-22-2-222222-22-222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ422222-2-2-2-2-2-2-2-22222-2-2-2-22-2-222222-22-22-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ432222-2-2-2-2-2-2-2-222-2-222222-2-222-2-222-22-20000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ442222-2-2-2-2-2-2-2-222-2-222222-2-222-2-222-22-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ452-2-2222-2-22-22-22-2000000-22-22-2002000022−2−222−2−222−2−222−2−2002i−2i002i−2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ462-2-2222-2-22-22-22-2000000-22-22-2002000022−2−222−2−222−2−222−2−200−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ472-2-2222-2-22-22-22-2000000-22-22-20020000−2−222−2−222−2−222−2−222002i−2i002i−2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ482-2-2222-2-22-22-22-2000000-22-22-20020000−2−222−2−222−2−222−2−22200−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ492-2-2222-2-2-222-2-22000000-2-22-22002000022−2−2−2−22222−2−2−2−2222i−2i002i−2i00i2−i2−i2i2i2−i2−i2i20000000000000000
χ502-2-2222-2-2-222-2-22000000-2-22-22002000022−2−2−2−22222−2−2−2−222−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i20000000000000000
χ512-2-2222-2-2-222-2-22000000-2-22-220020000−2−22222−2−2−2−22222−2−22i−2i002i−2i00−i2i2i2−i2−i2i2i2−i20000000000000000
χ522-2-2222-2-2-222-2-22000000-2-22-220020000−2−22222−2−2−2−22222−2−2−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i20000000000000000
χ532-2-22-2-2222-2-22-22000000-22-2-22002000022−2−222−2−2−2−222−2−222002-200-222−22−2−22−220000000000000000
χ542-2-22-2-2222-2-22-22000000-22-2-22002000022−2−222−2−2−2−222−2−22200-22002-2−22−222−22−20000000000000000
χ552-2-22-2-2222-2-22-22000000-22-2-220020000−2−222−2−22222−2−222−2−2002-200-22−22−222−22−20000000000000000
χ562-2-22-2-2222-2-22-22000000-22-2-220020000−2−222−2−22222−2−222−2−200-22002-22−22−2−22−220000000000000000
χ572-2-22-2-222-22-222-2000000-2-222-2002000022−2−2−2−222−2−22222−2−22-200-22002−2−22−222−20000000000000000
χ582-2-22-2-222-22-222-2000000-2-222-2002000022−2−2−2−222−2−22222−2−2-22002-200−222−22−2−220000000000000000
χ592-2-22-2-222-22-222-2000000-2-222-20020000−2−22222−2−222−2−2−2−2222-200-2200−222−22−2−220000000000000000
χ602-2-22-2-222-22-222-2000000-2-222-20020000−2−22222−2−222−2−2−2−222-22002-2002−2−22−222−20000000000000000
χ6144-4-44i−4i4i−4i000000004-400000004i−4i000002-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ6244-4-44i−4i4i−4i000000004-400000004i−4i00000-22-22-22-22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ6344-4-44i−4i4i−4i00000000-440000000−4i4i000002-22-2-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ6444-4-44i−4i4i−4i00000000-440000000−4i4i00000-22-222-22-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6544-4-4−4i4i−4i4i000000004-40000000−4i4i000002-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ6644-4-4−4i4i−4i4i000000004-40000000−4i4i00000-22-22-22-222i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ6744-4-4−4i4i−4i4i00000000-4400000004i−4i000002-22-2-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6844-4-4−4i4i−4i4i00000000-4400000004i−4i00000-22-222-22-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ694-44-44i−4i−4i4i0000004-4004i−4i000000000000000022−22−222200002i2−2i2−2i22i200000000000000000000000000000000
χ704-44-44i−4i−4i4i0000004-4004i−4i0000000000000000−222222−220000−2i22i22i2−2i200000000000000000000000000000000
χ714-44-44i−4i−4i4i000000-4400−4i4i00000000000022−22−222200002i2−2i2−2i22i2000000000000000000000000000000000000
χ724-44-44i−4i−4i4i000000-4400−4i4i000000000000−222222−220000−2i22i22i2−2i2000000000000000000000000000000000000
χ734-44-4−4i4i4i−4i0000004-400−4i4i000000000000000022−22−22220000−2i22i22i2−2i200000000000000000000000000000000
χ744-44-4−4i4i4i−4i0000004-400−4i4i0000000000000000−222222−2200002i2−2i2−2i22i200000000000000000000000000000000
χ754-44-4−4i4i4i−4i000000-44004i−4i00000000000022−22−22220000−2i22i22i2−2i2000000000000000000000000000000000000
χ764-44-4−4i4i4i−4i000000-44004i−4i000000000000−222222−2200002i2−2i2−2i22i2000000000000000000000000000000000000
χ774-4-4444-4-44-4-44-440000004-444-400-40000000000000000000000000000000000000000000000000000
χ784-4-4444-4-4-44-444-400000044-4-4400-40000000000000000000000000000000000000000000000000000
χ794-4-44-4-4444-44-44-40000004-44-4400-40000000000000000000000000000000000000000000000000000
χ804-4-44-4-444-444-4-4400000044-44-400-40000000000000000000000000000000000000000000000000000

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