Finite Group Databasebeta

← Group #243304

Character table — Group #243304

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444444444444488888888888888882244444488888888888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ911111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ1722222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ192222222222222222-2-2-2-2222222-2-2-2-222-2-2-2-2000000000000000022-2-2-2-22200000000000000000000000000000000
χ202222222222222222-2-2-2-2222222-2-2-2-222-2-2-2-20000000000000000-2-22222-2-200000000000000000000000000000000
χ212222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2322222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-222-2-222000000000000000022-2-222-2-200000000000000000000000000000000
χ2422222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2220000000000000000-2-222-2-22200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ2922-22-22-2-22i2i2i2i−2i−2i−2i−2i2i2i−2i−2i0000002-22-200000022-2-22i2i−2i−2i00000000000000000000000022−2−2i2i2−i2−i222−2−2i2i2−i2−i200000000
χ3022-22-22-2-22i2i2i2i−2i−2i−2i−2i2i2i−2i−2i0000002-22-200000022-2-22i2i−2i−2i000000000000000000000000−2−222−i2−i2i2i2−2−222−i2−i2i2i200000000
χ3122-22-22-2-22i2i2i2i−2i−2i−2i−2i2i2i−2i−2i0000002-22-2000000-2-222−2i−2i2i2i00000000000000000000000022−2−2i2i2−i2−i2−2−222−i2−i2i2i200000000
χ3222-22-22-2-22i2i2i2i−2i−2i−2i−2i2i2i−2i−2i0000002-22-2000000-2-222−2i−2i2i2i000000000000000000000000−2−222−i2−i2i2i222−2−2i2i2−i2−i200000000
χ3322-22-22-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i0000002-22-200000022-2-2−2i−2i2i2i00000000000000000000000022−2−2−i2−i2i2i222−2−2−i2−i2i2i200000000
χ3422-22-22-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i0000002-22-200000022-2-2−2i−2i2i2i000000000000000000000000−2−222i2i2−i2−i2−2−222i2i2−i2−i200000000
χ3522-22-22-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i0000002-22-2000000-2-2222i2i−2i−2i00000000000000000000000022−2−2−i2−i2i2i2−2−222i2i2−i2−i200000000
χ3622-22-22-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i0000002-22-2000000-2-2222i2i−2i−2i000000000000000000000000−2−222i2i2−i2−i222−2−2−i2−i2i2i200000000
χ372-222-2-22-22i2i−2i−2i2i2i−2i−2i2i−2i2i−2i2-22i2i−2i−2i2-2-222-22-22i−2i00000000000000000000000000000000000000002i−2i2i−2i2-22-200000000
χ382-222-2-22-22i2i−2i−2i2i2i−2i−2i2i−2i2i−2i2-22i2i−2i−2i2-2-222-22-22i−2i0000000000000000000000000000000000000000−2i2i−2i2i-22-2200000000
χ392-222-2-22-22i2i−2i−2i2i2i−2i−2i2i−2i2i−2i-22−2i−2i2i2i2-2-22-22-22−2i2i000000000000000000000000000000002-22-22i−2i2i−2i0000000000000000
χ402-222-2-22-22i2i−2i−2i2i2i−2i−2i2i−2i2i−2i-22−2i−2i2i2i2-2-22-22-22−2i2i00000000000000000000000000000000-22-22−2i2i−2i2i0000000000000000
χ412-222-2-22-22i2i−2i−2i2i2i−2i−2i−2i2i−2i2i2-22i2i−2i−2i-222-22-2-22−2i2i000000000000000000000000000000000000000000000000002i−2i2-200
χ422-222-2-22-22i2i−2i−2i2i2i−2i−2i−2i2i−2i2i2-22i2i−2i−2i-222-22-2-22−2i2i00000000000000000000000000000000000000000000000000−2i2i-2200
χ432-222-2-22-22i2i−2i−2i2i2i−2i−2i−2i2i−2i2i-22−2i−2i2i2i-222-2-222-22i−2i0000000000000000000000000000000000000000000000002-200002i−2i
χ442-222-2-22-22i2i−2i−2i2i2i−2i−2i−2i2i−2i2i-22−2i−2i2i2i-222-2-222-22i−2i000000000000000000000000000000000000000000000000-220000−2i2i
χ452-222-2-22-2−2i−2i2i2i−2i−2i2i2i2i−2i2i−2i2-2−2i−2i2i2i-222-22-2-222i−2i000000000000000000000000000000000000000000000000002i−2i-2200
χ462-222-2-22-2−2i−2i2i2i−2i−2i2i2i2i−2i2i−2i2-2−2i−2i2i2i-222-22-2-222i−2i00000000000000000000000000000000000000000000000000−2i2i2-200
χ472-222-2-22-2−2i−2i2i2i−2i−2i2i2i2i−2i2i−2i-222i2i−2i−2i-222-2-222-2−2i2i0000000000000000000000000000000000000000000000002-20000−2i2i
χ482-222-2-22-2−2i−2i2i2i−2i−2i2i2i2i−2i2i−2i-222i2i−2i−2i-222-2-222-2−2i2i000000000000000000000000000000000000000000000000-2200002i−2i
χ492-222-2-22-2−2i−2i2i2i−2i−2i2i2i−2i2i−2i2i2-2−2i−2i2i2i2-2-222-22-2−2i2i00000000000000000000000000000000000000002i−2i2i−2i-22-2200000000
χ502-222-2-22-2−2i−2i2i2i−2i−2i2i2i−2i2i−2i2i2-2−2i−2i2i2i2-2-222-22-2−2i2i0000000000000000000000000000000000000000−2i2i−2i2i2-22-200000000
χ512-222-2-22-2−2i−2i2i2i−2i−2i2i2i−2i2i−2i2i-222i2i−2i−2i2-2-22-22-222i−2i000000000000000000000000000000002-22-2−2i2i−2i2i0000000000000000
χ522-222-2-22-2−2i−2i2i2i−2i−2i2i2i−2i2i−2i2i-222i2i−2i−2i2-2-22-22-222i−2i00000000000000000000000000000000-22-222i−2i2i−2i0000000000000000
χ532-2-222-2-2222-2-2-2-2222-2-2200000022-2-2000000000000002i2i−2i−2i2i2i−2i−2i00000000000000002−2−222−2−22i2−i2−i2i2−i2i2i2−i200000000
χ542-2-222-2-2222-2-2-2-2222-2-2200000022-2-2000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000−222−2−222−2−i2i2i2−i2i2−i2−i2i200000000
χ552-2-222-2-2222-2-2-2-2222-2-2200000022-2-200000000000000−2i−2i2i2i−2i−2i2i2i00000000000000002−2−222−2−22−i2i2i2−i2i2−i2−i2i200000000
χ562-2-222-2-2222-2-2-2-2222-2-2200000022-2-200000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000−222−2−222−2i2−i2−i2i2−i2i2i2−i200000000
χ572-2-222-2-22-2-22222-2-2-222-200000022-2-2000000000000002i2i−2i−2i−2i−2i2i2i00000000000000002−2−22−222−2i2−i2−i2i2i2−i2−i2i200000000
χ582-2-222-2-22-2-22222-2-2-222-200000022-2-2000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000−222−22−2−22−i2i2i2−i2−i2i2i2−i200000000
χ592-2-222-2-22-2-22222-2-2-222-200000022-2-200000000000000−2i−2i2i2i2i2i−2i−2i00000000000000002−2−22−222−2−i2i2i2−i2−i2i2i2−i200000000
χ602-2-222-2-22-2-22222-2-2-222-200000022-2-200000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000−222−22−2−22i2−i2−i2i2i2−i2−i2i200000000
χ612-2-2-2-22222-22-22-22-20000222-22-20000-2-200002−22−22−22−22−22−22−22−2002i−2i2i−2i00i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ622-2-2-2-22222-22-22-22-20000222-22-20000-2-200002−22−22−22−22−22−22−22−200−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ632-2-2-2-22222-22-22-22-20000222-22-20000-2-20000−22−22−22−22−22−22−22−22002i−2i2i−2i00−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ642-2-2-2-22222-22-22-22-20000222-22-20000-2-20000−22−22−22−22−22−22−22−2200−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ652-2-2-2-22222-22-22-22-20000-2-2-22-2200002200002−22−22−22−2−22−22−22−222-200002-22−2−222−2−22000000000000000000000000
χ662-2-2-2-22222-22-22-22-20000-2-2-22-2200002200002−22−22−22−2−22−22−22−22-220000-22−222−2−222−2000000000000000000000000
χ672-2-2-2-22222-22-22-22-20000-2-2-22-220000220000−22−22−22−222−22−22−22−22-200002-2−222−2−222−2000000000000000000000000
χ682-2-2-2-22222-22-22-22-20000-2-2-22-220000220000−22−22−22−222−22−22−22−2-220000-222−2−222−2−22000000000000000000000000
χ692-2-2-2-2222-22-22-22-22000022-22-220000-2-200002−22−2−22−222−22−2−22−22002i−2i−2i2i00i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ702-2-2-2-2222-22-22-22-22000022-22-220000-2-200002−22−2−22−222−22−2−22−2200−2i2i2i−2i00−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ712-2-2-2-2222-22-22-22-22000022-22-220000-2-20000−22−222−22−2−22−222−22−2002i−2i−2i2i00−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ722-2-2-2-2222-22-22-22-22000022-22-220000-2-20000−22−222−22−2−22−222−22−200−2i2i2i−2i00i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ732-2-2-2-2222-22-22-22-220000-2-22-22-200002200002−22−2−22−22−22−222−22−22-20000-222−2−22−222−2000000000000000000000000
χ742-2-2-2-2222-22-22-22-220000-2-22-22-200002200002−22−2−22−22−22−222−22−2-2200002-2−222−22−2−22000000000000000000000000
χ752-2-2-2-2222-22-22-22-220000-2-22-22-20000220000−22−222−22−22−22−2−22−222-20000-22−222−22−2−22000000000000000000000000
χ762-2-2-2-2222-22-22-22-220000-2-22-22-20000220000−22−222−22−22−22−2−22−22-2200002-22−2−22−222−2000000000000000000000000
χ77444-4-4-4-444-4-44-444-400000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ78444-4-4-4-444-4-44-444-40000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ79444-4-4-4-44-444-44-4-4400000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ80444-4-4-4-44-444-44-4-440000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ8144-44-44-4-44i4i4i4i−4i−4i−4i−4i−4i−4i4i4i000000-44-4400000000000000000000000000000000000000000000000000000000000000
χ8244-44-44-4-4−4i−4i−4i−4i4i4i4i4i4i4i−4i−4i000000-44-4400000000000000000000000000000000000000000000000000000000000000
χ8344-4-44-44-44i−4i−4i4i4i−4i−4i4i00004-44i−4i−4i4i0000-44000000000000000000000000000000000000000000000000000000000000
χ8444-4-44-44-44i−4i−4i4i4i−4i−4i4i0000-44−4i4i4i−4i00004-4000000000000000000000000000000000000000000000000000000000000
χ8544-4-44-44-4−4i4i4i−4i−4i4i4i−4i00004-4−4i4i4i−4i0000-44000000000000000000000000000000000000000000000000000000000000
χ8644-4-44-44-4−4i4i4i−4i−4i4i4i−4i0000-444i−4i−4i4i00004-4000000000000000000000000000000000000000000000000000000000000
χ874-44-444-4-44i−4i4i−4i−4i4i−4i4i0000000000000000000022−22−22222i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ884-44-444-4-44i−4i4i−4i−4i4i−4i4i00000000000000000000−222222−22−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ894-44-444-4-4−4i4i−4i4i4i−4i4i−4i0000000000000000000022−22−2222−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ904-44-444-4-4−4i4i−4i4i4i−4i4i−4i00000000000000000000−222222−222i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ914-4-444-4-4444-4-4-4-444-444-4000000-4-44400000000000000000000000000000000000000000000000000000000000000
χ924-4-444-4-44-4-44444-4-44-4-44000000-4-44400000000000000000000000000000000000000000000000000000000000000

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