Finite Group Databasebeta

← Group #397928

Character table — Group #397928

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222222222222222222244444444444488888888888888882244444444444444444444448888888822224444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111111111-1-111-1-1
χ91111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1-1-111
χ17222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022-2-2-2-20000000000000000220000000000000000
χ18222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-222220000000000000000-2-20000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002222-2-20000000000000000-2-20000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-2-2-2220000000000000000220000000000000000
χ212222222-2-2-2-2-22-2-2-20000000022-2-2-22-2200002222-2-2-2-20000000000000000002i2i−2i−2i00002i2i−2i−2i000000000000000000
χ222222222-2-2-2-2-22-2-2-20000000022-2-2-22-2200002222-2-2-2-2000000000000000000−2i−2i2i2i0000−2i−2i2i2i000000000000000000
χ232222222-2-2-2-2-22-2-2-20000000022-2-2-22-220000-2-2-2-222220000000000000000002i2i−2i−2i0000−2i−2i2i2i000000000000000000
χ242222222-2-2-2-2-22-2-2-20000000022-2-2-22-220000-2-2-2-22222000000000000000000−2i−2i2i2i00002i2i−2i−2i000000000000000000
χ252222-2-2-2222-2-2-2-2-222222-2-2-2-200000000000022−2−222−2−22222−2−2−2−2002i−2i2i−2i000000000000000000i2i2−i2−i2i2i2−i2−i200000000
χ262222-2-2-2222-2-2-2-2-222222-2-2-2-200000000000022−2−222−2−22222−2−2−2−200−2i2i−2i2i000000000000000000−i2−i2i2i2−i2−i2i2i200000000
χ272222-2-2-2222-2-2-2-2-222222-2-2-2-2000000000000−2−222−2−222−2−2−2−22222002i−2i2i−2i000000000000000000−i2−i2i2i2−i2−i2i2i200000000
χ282222-2-2-2222-2-2-2-2-222222-2-2-2-2000000000000−2−222−2−222−2−2−2−2222200−2i2i−2i2i000000000000000000i2i2−i2−i2i2i2−i2−i200000000
χ292222-2-2-2222-2-2-2-2-22-2-2-2-2222200000000000022−2−222−2−2−2−2−2−22222002i−2i−2i2i000000000000000000−i2−i2i2i2i2i2−i2−i200000000
χ302222-2-2-2222-2-2-2-2-22-2-2-2-2222200000000000022−2−222−2−2−2−2−2−2222200−2i2i2i−2i000000000000000000i2i2−i2−i2−i2−i2i2i200000000
χ312222-2-2-2222-2-2-2-2-22-2-2-2-22222000000000000−2−222−2−2222222−2−2−2−2002i−2i−2i2i000000000000000000i2i2−i2−i2−i2−i2i2i200000000
χ322222-2-2-2222-2-2-2-2-22-2-2-2-22222000000000000−2−222−2−2222222−2−2−2−200−2i2i2i−2i000000000000000000−i2−i2i2i2i2i2−i2−i200000000
χ3322-2-222-22-2-2-2-2-222222-2-222-2-20000000000002−22−22−22−222−2−222−2−22-2000000000000000000002-22−22−22−22−200000000
χ3422-2-222-22-2-2-2-2-222222-2-222-2-20000000000002−22−22−22−222−2−222−2−2-2200000000000000000000-22−22−22−22−2200000000
χ3522-2-222-22-2-2-2-2-222222-2-222-2-2000000000000−22−22−22−22−2−222−2−2222-2000000000000000000002-2−22−22−22−2200000000
χ3622-2-222-22-2-2-2-2-222222-2-222-2-2000000000000−22−22−22−22−2−222−2−222-2200000000000000000000-222−22−22−22−200000000
χ3722-2-222-22-2-2-2-2-2222-2-222-2-2220000000000002−22−22−22−2−2−222−2−2222-200000000000000000000-222−22−2−22−2200000000
χ3822-2-222-22-2-2-2-2-2222-2-222-2-2220000000000002−22−22−22−2−2−222−2−222-22000000000000000000002-2−22−222−22−200000000
χ3922-2-222-22-2-2-2-2-2222-2-222-2-222000000000000−22−22−22−2222−2−222−2−22-200000000000000000000-22−22−222−22−200000000
χ4022-2-222-22-2-2-2-2-2222-2-222-2-222000000000000−22−22−22−2222−2−222−2−2-22000000000000000000002-22−22−2−22−2200000000
χ4122-2-2-2-222-2-2222-2-2222-2-2-2-2222222-2-2-2-222-2-200000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ4222-2-2-2-222-2-2222-2-2222-2-2-2-2222222-2-2-2-222-2-20000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ4322-2-2-2-222-2-2222-2-2222-2-2-2-222-2-2-2-22222-2-2222-2-222-2-2222-2-2-2-2220000000000000000000000000000000000000000
χ4422-2-2-2-222-2-2222-2-2222-2-2-2-222-2-2-2-22222-2-222-222-2-222-2-2-22222-2-20000000000000000000000000000000000000000
χ4522-2-2-2-222-2-2222-2-22-2-22222-2-22222-2-2-2-2-2-22200000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ4622-2-2-2-222-2-2222-2-22-2-22222-2-22222-2-2-2-2-2-2220000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ4722-2-2-2-222-2-2222-2-22-2-22222-2-2-2-2-2-2222222-2-22-2-222-2-22-2-22222-2-20000000000000000000000000000000000000000
χ4822-2-2-2-222-2-2222-2-22-2-22222-2-2-2-2-2-2222222-2-2-222-2-222-222-2-2-2-2220000000000000000000000000000000000000000
χ4922-2-2-2-22-222-2-2222-200000000-2-222-22-2200002-2-22-222-20000000000000022-2-2000022-2-20000000000000000000000
χ5022-2-2-2-22-222-2-2222-200000000-2-222-22-2200002-2-22-222-200000000000000-2-2220000-2-2220000000000000000000000
χ5122-2-2-2-22-222-2-2222-200000000-2-222-22-220000-222-22-2-220000000000000022-2-20000-2-2220000000000000000000000
χ5222-2-2-2-22-222-2-2222-200000000-2-222-22-220000-222-22-2-2200000000000000-2-222000022-2-20000000000000000000000
χ532-22-22-2-222-22-222-2-2000000002-22-222-2-20000000000002i−2i2i−2i2i−2i2i−2i00000000002i−2i2i−2i2-22-20000000000000000000000
χ542-22-22-2-222-22-222-2-2000000002-22-222-2-20000000000002i−2i2i−2i2i−2i2i−2i0000000000−2i2i−2i2i-22-220000000000000000000000
χ552-22-22-2-222-22-222-2-2000000002-22-222-2-2000000000000−2i2i−2i2i−2i2i−2i2i00000000002i−2i2i−2i-22-220000000000000000000000
χ562-22-22-2-222-22-222-2-2000000002-22-222-2-2000000000000−2i2i−2i2i−2i2i−2i2i0000000000−2i2i−2i2i2-22-20000000000000000000000
χ572-22-22-2-2-2-22-222-2222-22-22-22-22-2-22-222-22-22-200000000000000000000002-22-22-2-2200000000000000000000000000
χ582-22-22-2-2-2-22-222-2222-22-22-22-22-2-22-222-22-22-20000000000000000000000-22-22-222-200000000000000000000000000
χ592-22-22-2-2-2-22-222-2222-22-22-22-2-222-22-2-22-22-220000000000000000000000000000000000000000000000002-2002-200
χ602-22-22-2-2-2-22-222-2222-22-22-22-2-222-22-2-22-22-22000000000000000000000000000000000000000000000000-2200-2200
χ612-22-22-2-2-2-22-222-222-22-22-22-222-2-22-222-2-22-2200000000000000000000002-22-2-222-200000000000000000000000000
χ622-22-22-2-2-2-22-222-222-22-22-22-222-2-22-222-2-22-220000000000000000000000-22-222-2-2200000000000000000000000000
χ632-22-22-2-2-2-22-222-222-22-22-22-22-222-22-2-222-22-20000000000000000000000000000000000000000000000002-200-2200
χ642-22-22-2-2-2-22-222-222-22-22-22-22-222-22-2-222-22-2000000000000000000000000000000000000000000000000-22002-200
χ652-2-22-22-22-222-22-22-200000000-22-2222-2-20000000000002i−2i−2i2i−2i2i2i−2i0000002-2-22000000002i−2i2i−2i000000000000000000
χ662-2-22-22-22-222-22-22-200000000-22-2222-2-20000000000002i−2i−2i2i−2i2i2i−2i000000-222-200000000−2i2i−2i2i000000000000000000
χ672-2-22-22-22-222-22-22-200000000-22-2222-2-2000000000000−2i2i2i−2i2i−2i−2i2i0000002-2-2200000000−2i2i−2i2i000000000000000000
χ682-2-22-22-22-222-22-22-200000000-22-2222-2-2000000000000−2i2i2i−2i2i−2i−2i2i000000-222-2000000002i−2i2i−2i000000000000000000
χ692-2-22-22-2-22-2-2222-222-2-22-222-22-2-222-2-222-2-22000000000000000000000000000000000000000000000000002-2002-2
χ702-2-22-22-2-22-2-2222-222-2-22-222-22-2-222-2-222-2-2200000000000000000000000000000000000000000000000000-2200-22
χ712-2-22-22-2-22-2-2222-222-2-22-222-2-222-2-222-2-222-20000000000000000000000000000002-2-22-222-2000000000000000000
χ722-2-22-22-2-22-2-2222-222-2-22-222-2-222-2-222-2-222-2000000000000000000000000000000-222-22-2-22000000000000000000
χ732-2-22-22-2-22-2-2222-22-222-22-2-222-2-222-2-22-222-2000000000000000000000000000000000000000000000000002-200-22
χ742-2-22-22-2-22-2-2222-22-222-22-2-222-2-222-2-22-222-200000000000000000000000000000000000000000000000000-22002-2
χ752-2-22-22-2-22-2-2222-22-222-22-2-22-222-2-222-22-2-220000000000000000000000000000002-2-222-2-22000000000000000000
χ762-2-22-22-2-22-2-2222-22-222-22-2-22-222-2-222-22-2-22000000000000000000000000000000-222-2-222-2000000000000000000
χ774444444-4-4-4-4-44-4-4-400000000-4-4444-44-4000000000000000000000000000000000000000000000000000000000000
χ784444-4-4-4-4-4-444-444-4000000000000000000002222−22−22−22−222222000000000000000000000000000000000000000000000000
χ794444-4-4-4-4-4-444-444-400000000000000000000−22−2222222222−22−22000000000000000000000000000000000000000000000000
χ8044-4-444-4-44444-4-4-4-40000000000000000000022−2222−22−2222−2222000000000000000000000000000000000000000000000000
χ8144-4-444-4-44444-4-4-4-400000000000000000000−2222−222222−2222−22000000000000000000000000000000000000000000000000
χ8244-4-4-4-44-444-4-4444-40000000044-4-44-44-4000000000000000000000000000000000000000000000000000000000000
χ834-44-44-4-444-44-444-4-400000000-44-44-4-444000000000000000000000000000000000000000000000000000000000000
χ844-44-4-44444-4-44-4-44-400000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000
χ854-44-4-44444-4-44-4-44-40000000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000
χ864-44-4-444-4-444-4-44-444-44-4-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ874-44-4-444-4-444-4-44-44-44-444-44-400000000000000000000000000000000000000000000000000000000000000000000
χ884-4-444-444-44-44-44-4-400000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ894-4-444-444-44-44-44-4-40000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ904-4-444-44-44-44-4-4-4444-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ914-4-444-44-44-44-4-4-444-444-4-444-400000000000000000000000000000000000000000000000000000000000000000000
χ924-4-44-44-44-444-44-44-4000000004-44-4-4-444000000000000000000000000000000000000000000000000000000000000

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