Finite Group Databasebeta

← Group #72321488

Character table — Group #72321488

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size1111222222222222224444444488888888888888888888161616161616161616161616161616161616161616161616161616161616161616163232323232323232
order12222222224444444488888888444444444444444444442244444444448888881616161616161616161616161616161624448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ911111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ1111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111
χ1211111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1411111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1511111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1611111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ17222222222222222222-2-2-2-2-2-2-2-222222222222200000000000000000000-2-2-2-2-2-2000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000-2-22222000000000000000000000000
χ19222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000022-2-222000000000000000000000000
χ20222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000002222-2-2000000000000000000000000
χ21222222-2-2-2-2222-22-2-2-222-2-2-22-220000000000002i2i2i2i−2i−2i−2i−2i0000000000000000002i2i−2i−2i0000000000002-2000000
χ22222222-2-2-2-2222-22-2-2-222-2-2-22-220000000000002i2i2i2i−2i−2i−2i−2i000000000000000000−2i−2i2i2i000000000000-22000000
χ23222222-2-2-2-2222-22-2-2-222-2-2-22-22000000000000−2i−2i−2i−2i2i2i2i2i0000000000000000002i2i−2i−2i000000000000-22000000
χ24222222-2-2-2-2222-22-2-2-222-2-2-22-22000000000000−2i−2i−2i−2i2i2i2i2i000000000000000000−2i−2i2i2i0000000000002-2000000
χ252222-2-222-2-22-2-2222-2-22-222-22-2-20000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000022-2-2000000000000002i−2i
χ262222-2-222-2-22-2-2222-2-22-222-22-2-20000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000-2-22200000000000000−2i2i
χ272222-2-222-2-22-2-2222-2-22-222-22-2-2000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000022-2-200000000000000−2i2i
χ282222-2-222-2-22-2-2222-2-22-222-22-2-2000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000-2-222000000000000002i−2i
χ292222-2-2-2-2222-2-2-22-2222-2-2-2222-222-2-20000000022-2-2-2-222002200-2-200002-20000000000000000000000000000
χ302222-2-2-2-2222-2-2-22-2222-2-2-2222-222-2-200000000-2-22222-2-200-2-2002200002-20000000000000000000000000000
χ312222-2-2-2-2222-2-2-22-2222-2-2-2222-2-2-2220000000022-2-2-2-22200-2-200220000-220000000000000000000000000000
χ322222-2-2-2-2222-2-2-22-2222-2-2-2222-2-2-22200000000-2-22222-2-2002200-2-20000-220000000000000000000000000000
χ332222-2-2-2-2222-2-2-22-222-2222-2-2-2222-2-200000000000000002200-2-20022-2-2-220000000000000000000000000000
χ342222-2-2-2-2222-2-2-22-222-2222-2-2-2222-2-20000000000000000-2-2002200-2-222-220000000000000000000000000000
χ352222-2-2-2-2222-2-2-22-222-2222-2-2-22-2-22200000000000000002200-2-200-2-2222-20000000000000000000000000000
χ362222-2-2-2-2222-2-2-22-222-2222-2-2-22-2-2220000000000000000-2-200220022-2-22-20000000000000000000000000000
χ372-22-22-22-22-2-22-222-22-2-2-22-222-220000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000022-2-2002i−2i0000
χ382-22-22-22-22-2-22-222-22-2-2-22-222-220000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000-2-22200−2i2i0000
χ392-22-22-22-22-2-22-222-22-2-2-22-222-22000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000022-2-200−2i2i0000
χ402-22-22-22-22-2-22-222-22-2-2-22-222-22000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000-2-222002i−2i0000
χ412-22-22-2-22-222-222-2-22-2000000002i−2i2i−2i2i2i−2i−2i22-2-2000000000000000000000000002−22−2i2−i2i2−i2i2i2−i2−i22−22−200000000
χ422-22-22-2-22-222-222-2-22-2000000002i−2i2i−2i2i2i−2i−2i22-2-200000000000000000000000000−22−22−i2i2−i2i2−i2−i2i2i2−22−2200000000
χ432-22-22-2-22-222-222-2-22-2000000002i−2i2i−2i−2i−2i2i2i-2-222000000000000000000000000002−22−2i2−i2i2−i2−i2−i2i2i2−22−2200000000
χ442-22-22-2-22-222-222-2-22-2000000002i−2i2i−2i−2i−2i2i2i-2-22200000000000000000000000000−22−22−i2i2−i2i2i2i2−i2−i22−22−200000000
χ452-22-22-2-22-222-222-2-22-200000000−2i2i−2i2i2i2i−2i−2i-2-222000000000000000000000000002−22−2−i2i2−i2i2i2i2−i2−i2−22−2200000000
χ462-22-22-2-22-222-222-2-22-200000000−2i2i−2i2i2i2i−2i−2i-2-22200000000000000000000000000−22−22i2−i2i2−i2−i2−i2i2i22−22−200000000
χ472-22-22-2-22-222-222-2-22-200000000−2i2i−2i2i−2i−2i2i2i22-2-2000000000000000000000000002−22−2−i2i2−i2i2−i2−i2i2i22−22−200000000
χ482-22-22-2-22-222-222-2-22-200000000−2i2i−2i2i−2i−2i2i2i22-2-200000000000000000000000000−22−22i2−i2i2−i2i2i2−i2−i2−22−2200000000
χ492-22-22-2-22-22-22-2-222-22222-22-2-2-2000000002-22-200000000002i−2i002i−2i2i−2i2i−2i00002-2000000000000000000000000
χ502-22-22-2-22-22-22-2-222-22222-22-2-2-2000000002-22-20000000000−2i2i00−2i2i−2i2i−2i2i00002-2000000000000000000000000
χ512-22-22-2-22-22-22-2-222-22222-22-2-2-200000000-22-2200000000002i−2i002i−2i−2i2i−2i2i0000-22000000000000000000000000
χ522-22-22-2-22-22-22-2-222-22222-22-2-2-200000000-22-220000000000−2i2i00−2i2i2i−2i2i−2i0000-22000000000000000000000000
χ532-22-22-2-22-22-22-2-222-22-2-2-22-2222000000002-22-22-22-2-22-222-2002-20000000000-22000000000000000000000000
χ542-22-22-2-22-22-22-2-222-22-2-2-22-2222000000002-22-2-22-222-22-2-2200-220000000000-22000000000000000000000000
χ552-22-22-2-22-22-22-2-222-22-2-2-22-222200000000-22-222-22-2-22-22-2200-2200000000002-2000000000000000000000000
χ562-22-22-2-22-22-22-2-222-22-2-2-22-222200000000-22-22-22-222-22-22-2002-200000000002-2000000000000000000000000
χ572-22-2-222-2-22-2-2222-2-222-2-222-2-2200002i−2i2i−2i0000000000002-22i−2i-22−2i2i0000002i−2i00000000000000000000000000
χ582-22-2-222-2-22-2-2222-2-222-2-222-2-2200002i−2i2i−2i000000000000-22−2i2i2-22i−2i0000002i−2i00000000000000000000000000
χ592-22-2-222-2-22-2-2222-2-222-2-222-2-220000−2i2i−2i2i0000000000002-2−2i2i-222i−2i000000−2i2i00000000000000000000000000
χ602-22-2-222-2-22-2-2222-2-222-2-222-2-220000−2i2i−2i2i000000000000-222i−2i2-2−2i2i000000−2i2i00000000000000000000000000
χ612-22-2-222-2-22-2-2222-2-22-222-2-222-200002i−2i2i−2i00002-2-222-2-22000000002i−2i−2i2i00−2i2i00000000000000000000000000
χ622-22-2-222-2-22-2-2222-2-22-222-2-222-200002i−2i2i−2i0000-222-2-222-200000000−2i2i2i−2i00−2i2i00000000000000000000000000
χ632-22-2-222-2-22-2-2222-2-22-222-2-222-20000−2i2i−2i2i00002-2-222-2-2200000000−2i2i2i−2i002i−2i00000000000000000000000000
χ642-22-2-222-2-22-2-2222-2-22-222-2-222-20000−2i2i−2i2i0000-222-2-222-2000000002i−2i−2i2i002i−2i00000000000000000000000000
χ652-22-2-22-222-2-2-22-2222-2-22-2222-2-20000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000002i−2i2i−2i000000002-200
χ662-22-2-22-222-2-2-22-2222-2-22-2222-2-20000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000−2i2i−2i2i00000000-2200
χ672-22-2-22-222-2-2-22-2222-2-22-2222-2-2000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000002i−2i2i−2i00000000-2200
χ682-22-2-22-222-2-2-22-2222-2-22-2222-2-2000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000−2i2i−2i2i000000002-200
χ694444444444-4-4-4-4-4-4-4-400000000000000004-4-4400000000000000000000000000000000000000000000000000
χ704444444444-4-4-4-4-4-4-4-40000000000000000-444-400000000000000000000000000000000000000000000000000
χ71444444-4-4-4-4444-44-4-4-4-4-4444-44-400000000000000000000000000000000000000000000000000000000000000
χ72444444-4-4-4-4-4-4-44-4444000000000000000000000000000000000000000000000000000000000022−22−222200000000
χ73444444-4-4-4-4-4-4-44-44440000000000000000000000000000000000000000000000000000000000−222222−2200000000
χ744444-4-444-4-44-4-4444-4-4-44-4-44-44400000000000000000000000000000000000000000000000000000000000000
χ754444-4-444-4-4-444-4-4-44400000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ764444-4-444-4-4-444-4-4-444000000000000000000000000000000000000000000000000000000−222222−22000000000000
χ774444-4-4-4-444-4444-44-4-40000000000004-4-44000000000000000000000000000000000000000000000000000000
χ784444-4-4-4-444-4444-44-4-4000000000000-444-4000000000000000000000000000000000000000000000000000000
χ794-44-44-44-44-44-44-4-44-4400000000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ804-44-44-44-44-44-44-4-44-440000000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ814-44-44-44-44-4-44-444-44-444-44-4-44-400000000000000000000000000000000000000000000000000000000000000
χ824-44-4-444-4-4444-4-4-444-4000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ834-44-4-444-4-4444-4-4-444-400000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ844-44-4-44-444-444-44-4-4-44000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ854-44-4-44-444-444-44-4-4-4400000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ864-44-4-44-444-4-4-44-4444-44-44-4-4-44400000000000000000000000000000000000000000000000000000000000000
χ871616-16-16000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8816-16-1616000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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