Finite Group Databasebeta

← Group #396274

Character table — Group #396274

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222222222224444444444444444222244444444444444442222444444444444888888888888888822444444
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
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ121111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ131111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ141111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ151111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ161111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ172222222222222222-2-2-2-2-2-222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-222220000000000000000000000000000000000000000
χ2122222-2-2-2222-2-2-2-2-20000002i2i2i2i−2i−2i−2i−2i00000000002i2i−2i−2i22-2-20000000000000000000022−2−2i2i2−i2−i2i2i2−i2−i222−2−200000000
χ2222222-2-2-2222-2-2-2-2-20000002i2i2i2i−2i−2i−2i−2i00000000002i2i−2i−2i22-2-200000000000000000000−2−222−i2−i2i2i2−i2−i2i2i2−2−22200000000
χ2322222-2-2-2222-2-2-2-2-20000002i2i2i2i−2i−2i−2i−2i0000000000−2i−2i2i2i-2-2220000000000000000000022−2−2i2i2−i2−i2−i2−i2i2i2−2−22200000000
χ2422222-2-2-2222-2-2-2-2-20000002i2i2i2i−2i−2i−2i−2i0000000000−2i−2i2i2i-2-22200000000000000000000−2−222−i2−i2i2i2i2i2−i2−i222−2−200000000
χ2522222-2-2-2222-2-2-2-2-2000000−2i−2i−2i−2i2i2i2i2i00000000002i2i−2i−2i-2-2220000000000000000000022−2−2−i2−i2i2i2i2i2−i2−i2−2−22200000000
χ2622222-2-2-2222-2-2-2-2-2000000−2i−2i−2i−2i2i2i2i2i00000000002i2i−2i−2i-2-22200000000000000000000−2−222i2i2−i2−i2−i2−i2i2i222−2−200000000
χ2722222-2-2-2222-2-2-2-2-2000000−2i−2i−2i−2i2i2i2i2i0000000000−2i−2i2i2i22-2-20000000000000000000022−2−2−i2−i2i2i2−i2−i2i2i222−2−200000000
χ2822222-2-2-2222-2-2-2-2-2000000−2i−2i−2i−2i2i2i2i2i0000000000−2i−2i2i2i22-2-200000000000000000000−2−222i2i2−i2−i2i2i2−i2−i2−2−22200000000
χ29222-2-222-22-2-222-2-2-20000002i2i−2i−2i2i2i−2i−2i0022-2-20000000000002i2i−2i−2i00000000000000002−22−2i2−i2i2−i22−22−2i2−i2i2−i200000000
χ30222-2-222-22-2-222-2-2-20000002i2i−2i−2i2i2i−2i−2i0022-2-20000000000002i2i−2i−2i0000000000000000−22−22−i2i2−i2i2−22−22−i2i2−i2i200000000
χ31222-2-222-22-2-222-2-2-20000002i2i−2i−2i2i2i−2i−2i00-2-222000000000000−2i−2i2i2i00000000000000002−22−2i2−i2i2−i2−22−22−i2i2−i2i200000000
χ32222-2-222-22-2-222-2-2-20000002i2i−2i−2i2i2i−2i−2i00-2-222000000000000−2i−2i2i2i0000000000000000−22−22−i2i2−i2i22−22−2i2−i2i2−i200000000
χ33222-2-222-22-2-222-2-2-2000000−2i−2i2i2i−2i−2i2i2i0022-2-2000000000000−2i−2i2i2i00000000000000002−22−2−i2i2−i2i22−22−2−i2i2−i2i200000000
χ34222-2-222-22-2-222-2-2-2000000−2i−2i2i2i−2i−2i2i2i0022-2-2000000000000−2i−2i2i2i0000000000000000−22−22i2−i2i2−i2−22−22i2−i2i2−i200000000
χ35222-2-222-22-2-222-2-2-2000000−2i−2i2i2i−2i−2i2i2i00-2-2220000000000002i2i−2i−2i00000000000000002−22−2−i2i2−i2i2−22−22i2−i2i2−i200000000
χ36222-2-222-22-2-222-2-2-2000000−2i−2i2i2i−2i−2i2i2i00-2-2220000000000002i2i−2i−2i0000000000000000−22−22i2−i2i2−i22−22−2−i2i2−i2i200000000
χ37222-2-2-2-222-2-2-2-22222222-2-222-2-2-2-222-2-2000022-2-20000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ38222-2-2-2-222-2-2-2-22222222-2-222-2-2-2-222-2-2000022-2-2000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ39222-2-2-2-222-2-2-2-22222222-2-2-2-22222-2-2-2-20000-2-2220000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ40222-2-2-2-222-2-2-2-22222222-2-2-2-22222-2-2-2-20000-2-222000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ41222-2-2-2-222-2-2-2-2222-2-2-2-22222-2-2-2-222220000-2-22200000000000000000000000000002-2-222-2-220000000000000000
χ42222-2-2-2-222-2-2-2-2222-2-2-2-22222-2-2-2-222220000-2-2220000000000000000000000000000-222-2-222-20000000000000000
χ43222-2-2-2-222-2-2-2-2222-2-2-2-222-2-22222-2-222000022-2-200000000000000000000000000002-2-22-222-20000000000000000
χ44222-2-2-2-222-2-2-2-2222-2-2-2-222-2-22222-2-222000022-2-20000000000000000000000000000-222-22-2-220000000000000000
χ4522-22-22-22-22-22-22-2-222-2-22-22i−2i2i−2i2i−2i2i−2i2-200002i−2i2i−2i000000000000000000000000000000000000000000002-22i−2i0000
χ4622-22-22-22-22-22-22-2-222-2-22-22i−2i2i−2i2i−2i2i−2i2-200002i−2i2i−2i00000000000000000000000000000000000000000000-22−2i2i0000
χ4722-22-22-22-22-22-22-2-222-2-22-2−2i2i−2i2i−2i2i−2i2i2-20000−2i2i−2i2i000000000000000000000000000000000000000000002-2−2i2i0000
χ4822-22-22-22-22-22-22-2-222-2-22-2−2i2i−2i2i−2i2i−2i2i2-20000−2i2i−2i2i00000000000000000000000000000000000000000000-222i−2i0000
χ4922-22-22-22-22-22-22-2-2-2-222-222i−2i2i−2i2i−2i2i−2i-220000−2i2i−2i2i0000000000000000000000000000000000000000000000002-22i−2i
χ5022-22-22-22-22-22-22-2-2-2-222-222i−2i2i−2i2i−2i2i−2i-220000−2i2i−2i2i000000000000000000000000000000000000000000000000-22−2i2i
χ5122-22-22-22-22-22-22-2-2-2-222-22−2i2i−2i2i−2i2i−2i2i-2200002i−2i2i−2i0000000000000000000000000000000000000000000000002-2−2i2i
χ5222-22-22-22-22-22-22-2-2-2-222-22−2i2i−2i2i−2i2i−2i2i-2200002i−2i2i−2i000000000000000000000000000000000000000000000000-222i−2i
χ5322-2-22-222-2-22-222-2-222-2-2-222i−2i−2i2i−2i2i2i−2i-2200002i−2i−2i2i000000000000000022-2-22i2i−2i−2i0000000000000000000000000000
χ5422-2-22-222-2-22-222-2-222-2-2-222i−2i−2i2i−2i2i2i−2i-2200002i−2i−2i2i0000000000000000-2-222−2i−2i2i2i0000000000000000000000000000
χ5522-2-22-222-2-22-222-2-222-2-2-22−2i2i2i−2i2i−2i−2i2i-220000−2i2i2i−2i000000000000000022-2-2−2i−2i2i2i0000000000000000000000000000
χ5622-2-22-222-2-22-222-2-222-2-2-22−2i2i2i−2i2i−2i−2i2i-220000−2i2i2i−2i0000000000000000-2-2222i2i−2i−2i0000000000000000000000000000
χ5722-2-22-222-2-22-222-2-2-2-2222-22i−2i−2i2i−2i2i2i−2i2-20000−2i2i2i−2i00000000000022-2-2000000002i2i−2i−2i000000000000000000000000
χ5822-2-22-222-2-22-222-2-2-2-2222-22i−2i−2i2i−2i2i2i−2i2-20000−2i2i2i−2i000000000000-2-22200000000−2i−2i2i2i000000000000000000000000
χ5922-2-22-222-2-22-222-2-2-2-2222-2−2i2i2i−2i2i−2i−2i2i2-200002i−2i−2i2i00000000000022-2-200000000−2i−2i2i2i000000000000000000000000
χ6022-2-22-222-2-22-222-2-2-2-2222-2−2i2i2i−2i2i−2i−2i2i2-200002i−2i−2i2i000000000000-2-222000000002i2i−2i−2i000000000000000000000000
χ612-222-2-2-2-2-2-222222-22-22-22200000000-2-22-22-200002-22-200000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ622-222-2-2-2-2-2-222222-22-22-22200000000-2-22-22-200002-22-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ632-222-2-2-2-2-2-222222-22-22-22200000000-2-2-22-220000-22-2200000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ642-222-2-2-2-2-2-222222-22-22-22200000000-2-2-22-220000-22-220000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ652-222-2-2-2-2-2-222222-2-22-22-2-200000000222-22-20000-22-22000000002-22-22-22-200000000000000000000000000000000
χ662-222-2-2-2-2-2-222222-2-22-22-2-200000000222-22-20000-22-2200000000-22-22-22-2200000000000000000000000000000000
χ672-222-2-2-2-2-2-222222-2-22-22-2-20000000022-22-2200002-22-2000000002-22-2-22-2200000000000000000000000000000000
χ682-222-2-2-2-2-2-222222-2-22-22-2-20000000022-22-2200002-22-200000000-22-222-22-200000000000000000000000000000000
χ692-2-2-2-22-2-2222-222-222-2-22-22000000002-20000000000002-22-22-22-22-2-2200002-2-220000000000000000000000000000
χ702-2-2-2-22-2-2222-222-222-2-22-22000000002-20000000000002-22-22-22-2-222-20000-222-20000000000000000000000000000
χ712-2-2-2-22-2-2222-222-222-2-22-22000000002-2000000000000-22-22-22-222-2-220000-222-20000000000000000000000000000
χ722-2-2-2-22-2-2222-222-222-2-22-22000000002-2000000000000-22-22-22-22-222-200002-2-220000000000000000000000000000
χ732-2-2-2-22-2-2222-222-22-222-22-200000000-220000000000002-22-2-22-2200002-2-220000-222-2000000000000000000000000
χ742-2-2-2-22-2-2222-222-22-222-22-200000000-220000000000002-22-2-22-220000-222-200002-2-22000000000000000000000000
χ752-2-2-2-22-2-2222-222-22-222-22-200000000-22000000000000-22-222-22-200002-2-2200002-2-22000000000000000000000000
χ762-2-2-2-22-2-2222-222-22-222-22-200000000-22000000000000-22-222-22-20000-222-20000-222-2000000000000000000000000
χ7744-44-4-44-4-44-4-44-4440000004-44-4-44-4400000000000000000000000000000000000000000000000000000000000000
χ7844-44-4-44-4-44-4-44-444000000-44-444-44-400000000000000000000000000000000000000000000000000000000000000
χ7944-4-444-4-4-4-444-4-4440000004-4-444-4-4400000000000000000000000000000000000000000000000000000000000000
χ8044-4-444-4-4-4-444-4-444000000-444-4-444-400000000000000000000000000000000000000000000000000000000000000
χ814-444-4444-4-44-4-4-4-440000000000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ824-444-4444-4-44-4-4-4-44000000000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ834-44-4444-4-44-4-4-444-44-44-4-4-40000000044000000000000000000000000000000000000000000000000000000000000
χ844-44-4444-4-44-4-4-444-4-44-444400000000-4-4000000000000000000000000000000000000000000000000000000000000
χ854-44-44-4-44-44-444-4-4400000000000000004-4-4400000000000000000000000000000000000000000000000000000000
χ864-44-44-4-44-44-444-4-440000000000000000-444-400000000000000000000000000000000000000000000000000000000
χ874-4-4444-444-4-4-44-44-4000000000000000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ884-4-4444-444-4-4-44-44-400000000000000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ894-4-444-44-44-4-44-44-444-4-444-400000000-44000000000000000000000000000000000000000000000000000000000000
χ904-4-444-44-44-4-44-44-44-444-4-44000000004-4000000000000000000000000000000000000000000000000000000000000
χ914-4-4-4-4-4444444-4-44-400000000000000000000000000004-4-4400000000000000000000000000000000000000000000
χ924-4-4-4-4-4444444-4-44-40000000000000000000000000000-444-400000000000000000000000000000000000000000000

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