Finite Group Databasebeta

← Group #72322193

Character table — Group #72322193

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size11112222222222222244444444888888888888888888888888888816161616161616161616161616161616161616161616323232323232323232323232
order1222222222444444448888888822444444888816161616161616161616161616161616224444444488881616161616161616224488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-11111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-111-1-111-1-111
χ81111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1
χ911111111111111111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ1011111111111111111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1
χ1111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1
χ1211111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-111
χ1311111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-11111111111-1-1-1-1-1-1
χ1411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1111111
χ1511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-11111
χ1611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1111111-1-1-1-11111-1-111-1-1-1-1
χ17222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000022-2-2-2-200000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-2000000000000000000000000-2-2222200000000000000000000
χ19222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-22222000000000000000000000000-2-2-2-22200000000000000000000
χ20222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000002222-2-200000000000000000000
χ21222222-2-2-2-22-2-22-222-2222-2-22-2-2000000000000000000002i2i2i2i−2i−2i−2i−2i0022-2-20000000000000000002i−2i00000000
χ22222222-2-2-2-22-2-22-222-2222-2-22-2-2000000000000000000002i2i2i2i−2i−2i−2i−2i00-2-222000000000000000000−2i2i00000000
χ23222222-2-2-2-22-2-22-222-2222-2-22-2-200000000000000000000−2i−2i−2i−2i2i2i2i2i0022-2-2000000000000000000−2i2i00000000
χ24222222-2-2-2-22-2-22-222-2222-2-22-2-200000000000000000000−2i−2i−2i−2i2i2i2i2i00-2-2220000000000000000002i−2i00000000
χ252222-2-222-2-2-22-22-22-222-2-22-22-220000000000002222-2-2-2-200000000220000-2-2000000000000002-20000000000
χ262222-2-222-2-2-22-22-22-222-2-22-22-220000000000002222-2-2-2-200000000-2-200002200000000000000-220000000000
χ272222-2-222-2-2-22-22-22-222-2-22-22-22000000000000-2-2-2-2222200000000220000-2-200000000000000-220000000000
χ282222-2-222-2-2-22-22-22-222-2-22-22-22000000000000-2-2-2-2222200000000-2-2000022000000000000002-20000000000
χ292222-2-2-2-22222-2-2-2-222000000002222-2-2-2-2000022−2−222−2−222−2−222−2−2000000002-2000022−2−222−2−2000000000000
χ302222-2-2-2-22222-2-2-2-222000000002222-2-2-2-20000−2−222−2−222−2−222−2−222000000002-20000−2−222−2−222000000000000
χ312222-2-2-2-22222-2-2-2-2220000000022-2-222-2-2000022−2−222−2−222−2−222−2−200000000-220000−2−222−2−222000000000000
χ322222-2-2-2-22222-2-2-2-2220000000022-2-222-2-20000−2−222−2−222−2−222−2−22200000000-22000022−2−222−2−2000000000000
χ332222-2-2-2-22222-2-2-2-22200000000-2-222-2-222000022−2−222−2−2−2−222−2−22200000000-22000022−2−2−2−222000000000000
χ342222-2-2-2-22222-2-2-2-22200000000-2-222-2-2220000−2−222−2−22222−2−222−2−200000000-220000−2−22222−2−2000000000000
χ352222-2-2-2-22222-2-2-2-22200000000-2-2-2-22222000022−2−222−2−2−2−222−2−222000000002-20000−2−22222−2−2000000000000
χ362222-2-2-2-22222-2-2-2-22200000000-2-2-2-222220000−2−222−2−22222−2−222−2−2000000002-2000022−2−2−2−222000000000000
χ372-2-222-22-22-222-2-222-2-222-2-2-2-2220000000000002-22-22-22-200000000002i−2i2i−2i000000000000000000000000002i−2i
χ382-2-222-22-22-222-2-222-2-222-2-2-2-2220000000000002-22-22-22-20000000000−2i2i−2i2i00000000000000000000000000−2i2i
χ392-2-222-22-22-222-2-222-2-222-2-2-2-222000000000000-22-22-22-2200000000002i−2i2i−2i00000000000000000000000000−2i2i
χ402-2-222-22-22-222-2-222-2-222-2-2-2-222000000000000-22-22-22-220000000000−2i2i−2i2i000000000000000000000000002i−2i
χ412-2-222-2-22-222-22-2-22-2222-222-2-2-22-200002-222-2-20000000000000000002i−2i−2i2i000000000000000000002i−2i000000
χ422-2-222-2-22-222-22-2-22-2222-222-2-2-22-200002-222-2-2000000000000000000−2i2i2i−2i00000000000000000000−2i2i000000
χ432-2-222-2-22-222-22-2-22-2222-222-2-2-2-220000-22-2-2220000000000000000002i−2i−2i2i00000000000000000000−2i2i000000
χ442-2-222-2-22-222-22-2-22-2222-222-2-2-2-220000-22-2-222000000000000000000−2i2i2i−2i000000000000000000002i−2i000000
χ452-2-222-2-22-222-22-2-22-22-2-22-2-22222-200002-2-2-22200000000000000002-200002-2000000000000000000002-20000
χ462-2-222-2-22-222-22-2-22-22-2-22-2-22222-200002-2-2-2220000000000000000-220000-2200000000000000000000-220000
χ472-2-222-2-22-222-22-2-22-22-2-22-2-2222-220000-2222-2-200000000000000002-200002-200000000000000000000-220000
χ482-2-222-2-22-222-22-2-22-22-2-22-2-2222-220000-2222-2-20000000000000000-220000-22000000000000000000002-20000
χ492-2-222-2-22-22-22-222-22-200000000002i−2i2i−2i002i−2i2i−2i2−2−22−222−2i2−i2i2−i2i2−i2i2−i20000000000002-2i2−i2i2−i22−22−2000000000000
χ502-2-222-2-22-22-22-222-22-200000000002i−2i2i−2i002i−2i2i−2i−222−22−2−22−i2i2−i2i2−i2i2−i2i20000000000002-2−i2i2−i2i2−22−22000000000000
χ512-2-222-2-22-22-22-222-22-200000000002i−2i2i−2i00−2i2i−2i2i2−2−22−222−2−i2i2−i2i2−i2i2−i2i2000000000000-22i2−i2i2−i2−22−22000000000000
χ522-2-222-2-22-22-22-222-22-200000000002i−2i2i−2i00−2i2i−2i2i−222−22−2−22i2−i2i2−i2i2−i2i2−i2000000000000-22−i2i2−i2i22−22−2000000000000
χ532-2-222-2-22-22-22-222-22-20000000000−2i2i−2i2i002i−2i2i−2i2−2−22−222−2i2−i2i2−i2i2−i2i2−i2000000000000-22−i2i2−i2i2−22−22000000000000
χ542-2-222-2-22-22-22-222-22-20000000000−2i2i−2i2i002i−2i2i−2i−222−22−2−22−i2i2−i2i2−i2i2−i2i2000000000000-22i2−i2i2−i22−22−2000000000000
χ552-2-222-2-22-22-22-222-22-20000000000−2i2i−2i2i00−2i2i−2i2i2−2−22−222−2−i2i2−i2i2−i2i2−i2i20000000000002-2−i2i2−i2i22−22−2000000000000
χ562-2-222-2-22-22-22-222-22-20000000000−2i2i−2i2i00−2i2i−2i2i−222−22−2−22i2−i2i2−i2i2−i2i2−i20000000000002-2i2−i2i2−i2−22−22000000000000
χ572-2-22-222-2-22-222-2-222-22-22-22-2-22002i−2i−2i2i0000002-22-2-22-220000000000000000002i−2i002i−2i−2i2i0000000000000000
χ582-2-22-222-2-22-222-2-222-22-22-22-2-22002i−2i−2i2i000000-22-222-22-20000000000000000002i−2i00−2i2i2i−2i0000000000000000
χ592-2-22-222-2-22-222-2-222-22-22-22-2-2200−2i2i2i−2i0000002-22-2-22-22000000000000000000−2i2i00−2i2i2i−2i0000000000000000
χ602-2-22-222-2-22-222-2-222-22-22-22-2-2200−2i2i2i−2i000000-22-222-22-2000000000000000000−2i2i002i−2i−2i2i0000000000000000
χ612-2-22-222-2-22-222-2-222-2-22-22-222-2002i−2i−2i2i000000000000002i−2i−2i2i2i−2i−2i2i0000000000−2i2i0000002-2-22000000000000
χ622-2-22-222-2-22-222-2-222-2-22-22-222-2002i−2i−2i2i00000000000000−2i2i2i−2i−2i2i2i−2i0000000000−2i2i000000-222-2000000000000
χ632-2-22-222-2-22-222-2-222-2-22-22-222-200−2i2i2i−2i000000000000002i−2i−2i2i2i−2i−2i2i00000000002i−2i000000-222-2000000000000
χ642-2-22-222-2-22-222-2-222-2-22-22-222-200−2i2i2i−2i00000000000000−2i2i2i−2i−2i2i2i−2i00000000002i−2i0000002-2-22000000000000
χ652-2-22-22-222-2-2-2-2-22222-22-2-222-22000000000000000000002-2-22-222-22-20000-2200000000000000000000002-200
χ662-2-22-22-222-2-2-2-2-22222-22-2-222-22000000000000000000002-2-22-222-2-2200002-20000000000000000000000-2200
χ672-2-22-22-222-2-2-2-2-22222-22-2-222-2200000000000000000000-222-22-2-222-20000-220000000000000000000000-2200
χ682-2-22-22-222-2-2-2-2-22222-22-2-222-2200000000000000000000-222-22-2-22-2200002-200000000000000000000002-200
χ694444444444-4-4-4-4-4-4-4-400000000000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ704444444444-4-4-4-4-4-4-4-40000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ71444444-4-4-4-44-4-44-444-4-4-4-444-44400000000000000000000000000000000000000000000000000000000000000
χ72444444-4-4-4-4-444-44-4-44000000000000000000002222−22−22−22−222222000000000000000000000000000000000000000000
χ73444444-4-4-4-4-444-44-4-4400000000000000000000−22−2222222222−22−22000000000000000000000000000000000000000000
χ744444-4-444-4-44-44-44-44-400000000000000000000000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ754444-4-444-4-44-44-44-44-40000000000000000000000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ764444-4-444-4-4-44-44-44-44-444-44-44-400000000000000000000000000000000000000000000000000000000000000
χ774444-4-4-4-444-4-44444-4-44-4-4-4444-400000000000000000000000000000000000000000000000000000000000000
χ784444-4-4-4-444-4-44444-4-4-4444-4-4-4400000000000000000000000000000000000000000000000000000000000000
χ794-4-444-44-44-444-4-444-4-4-4-44444-4-400000000000000000000000000000000000000000000000000000000000000
χ804-4-444-44-44-4-4-444-4-444000000000000000000000000000022−2222−22−2222−22220000000000000000000000000000000000
χ814-4-444-44-44-4-4-444-4-4440000000000000000000000000000−2222−222222−2222−220000000000000000000000000000000000
χ824-4-44-444-4-444-4-444-4-44000000004-40000-44000000000000000000000000000000000000000000000000000000
χ834-4-44-444-4-444-4-444-4-4400000000-4400004-4000000000000000000000000000000000000000000000000000000
χ844-4-44-44-444-44444-4-4-4-40000000000000000000022−22−222222−22−2222000000000000000000000000000000000000000000
χ854-4-44-44-444-44444-4-4-4-400000000000000000000−222222−22−222222−22000000000000000000000000000000000000000000
χ864-4-44-44-444-4-4-4-4-444444-444-4-44-400000000000000000000000000000000000000000000000000000000000000
χ871616-16-16000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8816-1616-16000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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