Finite Group Databasebeta

← Group #490513

Character table — Group #490513

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order122244444444444488888888888888882488888888888888882244444488888888161616161616161616161616161616164444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ91111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1111-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1
χ101111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1111-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11
χ111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1111-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-11
χ121111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1111-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-1
χ131111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11
χ141111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1
χ151111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1111-1-1-1-111-1-1-1-11111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1
χ161111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1111-1-1-1-111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11
χ172222222222222222-2-2-2-222222222-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ192222222222-2-222-2-22222000000002222-2-2-2-2-2-20000000000002222-2-2-2-20000000000000000000000000000
χ202222222222-2-222-2-22222000000002222-2-2-2-2-2-2000000000000-2-2-2-222220000000000000000000000000000
χ212222222222-2-222-2-2-2-2-2-200000000-2-2-2-2-2-22222000000000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ222222222222-2-222-2-2-2-2-2-200000000-2-2-2-2-2-2222200000000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2322222222-2-222-2-2220000222222220000-2-20000-2-2-2-200000000000000000000000022−2−222−2−222−2−222−2−20000
χ2422222222-2-222-2-2220000222222220000-2-20000-2-2-2-2000000000000000000000000−2−222−2−222−2−222−2−2220000
χ2522222222-2-222-2-2220000-2-2-2-2-2-2-2-20000-2-20000222200000000000000000000000022−2−222−2−2−2−222−2−2220000
χ2622222222-2-222-2-2220000-2-2-2-2-2-2-2-20000-2-200002222000000000000000000000000−2−222−2−22222−2−222−2−20000
χ272222-2-2-2-222-2-2-2-22200002222-2-2-2-200002-20000-2-22200000000000000000000000022−2−2−2−22222−2−2−2−2220000
χ282222-2-2-2-222-2-2-2-22200002222-2-2-2-200002-20000-2-222000000000000000000000000−2−22222−2−2−2−22222−2−20000
χ292222-2-2-2-222-2-2-2-2220000-2-2-2-2222200002-2000022-2-200000000000000000000000022−2−2−2−222−2−22222−2−20000
χ302222-2-2-2-222-2-2-2-2220000-2-2-2-2222200002-2000022-2-2000000000000000000000000−2−22222−2−222−2−2−2−2220000
χ312222-2-2-2-2-2-22222-2-2222200000000-2-2-2-22-222-2-2000000000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ322222-2-2-2-2-2-22222-2-2222200000000-2-2-2-22-222-2-200000000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ332222-2-2-2-2-2-22222-2-2-2-2-2-20000000022222-2-2-22200000000000022-2-2-2-2220000000000000000000000000000
χ342222-2-2-2-2-2-22222-2-2-2-2-2-20000000022222-2-2-222000000000000-2-22222-2-20000000000000000000000000000
χ352222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-22-2-22222-2-2-2-2-2-22222000000000000000000000000000000000000
χ362222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-22-2-222-2-2222222-2-2-2-2000000000000000000000000000000000000
χ372-22-22i2i−2i−2i002i−2i002-2i2i2−i2−i222-2-22i2i−2i−2i22−2−2002−2i2−i2000022−2−2i2i2−i2−i20000000000000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ382-22-22i2i−2i−2i002i−2i002-2i2i2−i2−i222-2-22i2i−2i−2i22−2−2002−2i2−i2000022−2−2i2i2−i2−i20000000000000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ392-22-22i2i−2i−2i002i−2i002-2i2i2−i2−i2-2-222−2i−2i2i2i22−2−2002−2i2−i20000−2−222−i2−i2i2i20000000000000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ402-22-22i2i−2i−2i002i−2i002-2i2i2−i2−i2-2-222−2i−2i2i2i22−2−2002−2i2−i20000−2−222−i2−i2i2i20000000000000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ412-22-22i2i−2i−2i002i−2i002-2−i2−i2i2i222-2-22i2i−2i−2i−2−22200−22−i2i20000−2−222−i2−i2i2i20000000000000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ422-22-22i2i−2i−2i002i−2i002-2−i2−i2i2i222-2-22i2i−2i−2i−2−22200−22−i2i20000−2−222−i2−i2i2i20000000000000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ432-22-22i2i−2i−2i002i−2i002-2−i2−i2i2i2-2-222−2i−2i2i2i−2−22200−22−i2i2000022−2−2i2i2−i2−i20000000000000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ442-22-22i2i−2i−2i002i−2i002-2−i2−i2i2i2-2-222−2i−2i2i2i−2−22200−22−i2i2000022−2−2i2i2−i2−i20000000000000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ452-22-2−2i−2i2i2i00−2i2i002-2i2i2−i2−i222-2-2−2i−2i2i2i−2−22200−22i2−i20000−2−222i2i2−i2−i20000000000000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ462-22-2−2i−2i2i2i00−2i2i002-2i2i2−i2−i222-2-2−2i−2i2i2i−2−22200−22i2−i20000−2−222i2i2−i2−i20000000000000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ472-22-2−2i−2i2i2i00−2i2i002-2i2i2−i2−i2-2-2222i2i−2i−2i−2−22200−22i2−i2000022−2−2−i2−i2i2i20000000000000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ482-22-2−2i−2i2i2i00−2i2i002-2i2i2−i2−i2-2-2222i2i−2i−2i−2−22200−22i2−i2000022−2−2−i2−i2i2i20000000000000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ492-22-2−2i−2i2i2i00−2i2i002-2−i2−i2i2i222-2-2−2i−2i2i2i22−2−2002−2−i2i2000022−2−2−i2−i2i2i20000000000000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ502-22-2−2i−2i2i2i00−2i2i002-2−i2−i2i2i222-2-2−2i−2i2i2i22−2−2002−2−i2i2000022−2−2−i2−i2i2i20000000000000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ512-22-2−2i−2i2i2i00−2i2i002-2−i2−i2i2i2-2-2222i2i−2i−2i22−2−2002−2−i2i20000−2−222i2i2−i2−i20000000000000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ522-22-2−2i−2i2i2i00−2i2i002-2−i2−i2i2i2-2-2222i2i−2i−2i22−2−2002−2−i2i20000−2−222i2i2−i2−i20000000000000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ532-2-222i−2i2i−2i2i−2i002-2002i−2i2i−2i2−22−2i2−i2i2−i22-22-20000002−2i2−i22−22−2i2−i2i2−i200002i−2i2-2i2−i2i2−i22−22−200000000000000000000
χ542-2-222i−2i2i−2i2i−2i002-2002i−2i2i−2i2−22−2i2−i2i2−i22-22-20000002−2i2−i22−22−2i2−i2i2−i20000−2i2i-22−i2i2−i2i2−22−2200000000000000000000
χ552-2-222i−2i2i−2i2i−2i002-2002i−2i2i−2i−22−22−i2i2−i2i22-22-2000000−22−i2i2−22−22−i2i2−i2i200002i−2i2-2−i2i2−i2i2−22−2200000000000000000000
χ562-2-222i−2i2i−2i2i−2i002-2002i−2i2i−2i−22−22−i2i2−i2i22-22-2000000−22−i2i2−22−22−i2i2−i2i20000−2i2i-22i2−i2i2−i22−22−200000000000000000000
χ572-2-222i−2i2i−2i2i−2i002-200−2i2i−2i2i2−22−2i2−i2i2−i2-22-220000002−2i2−i2−22−22−i2i2−i2i22-22i−2i00002−2−22−i2i2i2−i200000000000000000000
χ582-2-222i−2i2i−2i2i−2i002-200−2i2i−2i2i2−22−2i2−i2i2−i2-22-220000002−2i2−i2−22−22−i2i2−i2i2-22−2i2i0000−222−2i2−i2−i2i200000000000000000000
χ592-2-222i−2i2i−2i2i−2i002-200−2i2i−2i2i−22−22−i2i2−i2i2-22-22000000−22−i2i22−22−2i2−i2i2−i22-22i−2i0000−222−2i2−i2−i2i200000000000000000000
χ602-2-222i−2i2i−2i2i−2i002-200−2i2i−2i2i−22−22−i2i2−i2i2-22-22000000−22−i2i22−22−2i2−i2i2−i2-22−2i2i00002−2−22−i2i2i2−i200000000000000000000
χ612-2-22−2i2i−2i2i−2i2i002-2002i−2i2i−2i2−22−2−i2i2−i2i2-22-220000002−2−i2i2−22−22i2−i2i2−i22-2−2i2i00002−2−22i2−i2−i2i200000000000000000000
χ622-2-22−2i2i−2i2i−2i2i002-2002i−2i2i−2i2−22−2−i2i2−i2i2-22-220000002−2−i2i2−22−22i2−i2i2−i2-222i−2i0000−222−2−i2i2i2−i200000000000000000000
χ632-2-22−2i2i−2i2i−2i2i002-2002i−2i2i−2i−22−22i2−i2i2−i2-22-22000000−22i2−i22−22−2−i2i2−i2i22-2−2i2i0000−222−2−i2i2i2−i200000000000000000000
χ642-2-22−2i2i−2i2i−2i2i002-2002i−2i2i−2i−22−22i2−i2i2−i2-22-22000000−22i2−i22−22−2−i2i2−i2i2-222i−2i00002−2−22i2−i2−i2i200000000000000000000
χ652-2-22−2i2i−2i2i−2i2i002-200−2i2i−2i2i2−22−2−i2i2−i2i22-22-20000002−2−i2i22−22−2−i2i2−i2i200002i−2i-22i2−i2i2−i2−22−2200000000000000000000
χ662-2-22−2i2i−2i2i−2i2i002-200−2i2i−2i2i2−22−2−i2i2−i2i22-22-20000002−2−i2i22−22−2−i2i2−i2i20000−2i2i2-2−i2i2−i2i22−22−200000000000000000000
χ672-2-22−2i2i−2i2i−2i2i002-200−2i2i−2i2i−22−22i2−i2i2−i22-22-2000000−22i2−i2−22−22i2−i2i2−i200002i−2i-22−i2i2−i2i22−22−200000000000000000000
χ682-2-22−2i2i−2i2i−2i2i002-200−2i2i−2i2i−22−22i2−i2i2−i22-22-2000000−22i2−i2−22−22i2−i2i2−i20000−2i2i2-2i2−i2i2−i2−22−2200000000000000000000
χ6944444444-4-4-4-4-4-4-4-40000000000000000440000000000000000000000000000000000000000000000000000
χ704444-4-4-4-44444-4-4-4-40000000000000000-440000000000000000000000000000000000000000000000000000
χ7144-4-44-4-440000000022−22−222222−22−222222−22−222222−22−222200000000002-2-222-2-22000000000000000000000000000000000000
χ7244-4-44-4-440000000022−22−2222−222222−22−222222−2222−22−22220000000000-222-2-222-2000000000000000000000000000000000000
χ7344-4-44-4-4400000000−222222−2222−22−222222−22−2222−222222−220000000000-222-2-222-2000000000000000000000000000000000000
χ7444-4-44-4-4400000000−222222−22−222222−22−222222−22−222222−2200000000002-2-222-2-22000000000000000000000000000000000000
χ7544-4-4-444-40000000022−22−222222−22−2222−222222−22−222222−220000000000-222-22-2-22000000000000000000000000000000000000
χ7644-4-4-444-40000000022−22−2222−222222−2222−22−2222−222222−2200000000002-2-22-222-2000000000000000000000000000000000000
χ7744-4-4-444-400000000−222222−2222−22−2222−222222−2222−22−222200000000002-2-22-222-2000000000000000000000000000000000000
χ7844-4-4-444-400000000−222222−22−222222−2222−22−222222−22−22220000000000-222-22-2-22000000000000000000000000000000000000
χ794-44-44i4i−4i−4i00−4i4i00-442i22i2−2i2−2i2000000002222−22−2200−2222−2i22i2000000000000000000000000000000000000000000000000
χ804-44-44i4i−4i−4i00−4i4i00-44−2i2−2i22i22i200000000−22−2222220022−222i2−2i2000000000000000000000000000000000000000000000000
χ814-44-4−4i−4i4i4i004i−4i00-442i22i2−2i2−2i200000000−22−2222220022−22−2i22i2000000000000000000000000000000000000000000000000
χ824-44-4−4i−4i4i4i004i−4i00-44−2i2−2i22i22i2000000002222−22−2200−22222i2−2i2000000000000000000000000000000000000000000000000
χ834-4-444i−4i4i−4i−4i4i00-4400000022−2222−222i2−2i22i2−2i20000000000−2222−2i22i200000000000000000000000000000000000000000000
χ844-4-444i−4i4i−4i−4i4i00-44000000−2222−2222−2i22i2−2i22i2000000000022−222i2−2i200000000000000000000000000000000000000000000
χ854-4-44−4i4i−4i4i4i−4i00-4400000022−2222−22−2i22i2−2i22i20000000000−22222i2−2i200000000000000000000000000000000000000000000
χ864-4-44−4i4i−4i4i4i−4i00-44000000−2222−22222i2−2i22i2−2i2000000000022−22−2i22i200000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.