Finite Group Databasebeta

← Group #398570

Character table — Group #398570

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222222222224444444444444444444488888888888888882222224444444444444444448888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
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
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-111
χ91111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11111
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-111
χ161111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1
χ17222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000002222000000000000-2-2-2-20000000000000000
χ18222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000-2-2-2-200000000000022220000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000022-2-200000000000022-2-20000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000-2-222000000000000-2-2220000000000000000
χ2122222-2-2-2-222-2-2-2-222i2i2i2i−2i−2i−2i−2i22-2-222-2-22i2i−2i−2i000000000000000000000000000000000000000022-2-22i2i−2i−2i00000000
χ2222222-2-2-2-222-2-2-2-222i2i2i2i−2i−2i−2i−2i22-2-222-2-22i2i−2i−2i0000000000000000000000000000000000000000-2-222−2i−2i2i2i00000000
χ2322222-2-2-2-222-2-2-2-222i2i2i2i−2i−2i−2i−2i-2-222-2-222−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i2222-2-2-2-20000000000000000000000000000000000000000
χ2422222-2-2-2-222-2-2-2-222i2i2i2i−2i−2i−2i−2i-2-222-2-222−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i-2-2-2-222220000000000000000000000000000000000000000
χ2522222-2-2-2-222-2-2-2-22−2i−2i−2i−2i2i2i2i2i22-2-222-2-2−2i−2i2i2i000000000000000000000000000000000000000022-2-2−2i−2i2i2i00000000
χ2622222-2-2-2-222-2-2-2-22−2i−2i−2i−2i2i2i2i2i22-2-222-2-2−2i−2i2i2i0000000000000000000000000000000000000000-2-2222i2i−2i−2i00000000
χ2722222-2-2-2-222-2-2-2-22−2i−2i−2i−2i2i2i2i2i-2-222-2-2222i2i−2i−2i2i2i2i2i−2i−2i−2i−2i-2-2-2-222220000000000000000000000000000000000000000
χ2822222-2-2-2-222-2-2-2-22−2i−2i−2i−2i2i2i2i2i-2-222-2-2222i2i−2i−2i−2i−2i−2i−2i2i2i2i2i2222-2-2-2-20000000000000000000000000000000000000000
χ29222-2-222-2-22-2-222-2-22i2i−2i−2i2i2i−2i−2i000000000000i2i2−i2−i2i2i2−i2−i222−2−222−2−200002-22i−2i0000000000000000i2−i2i2−i22−22−200000000
χ30222-2-222-2-22-2-222-2-22i2i−2i−2i2i2i−2i−2i000000000000i2i2−i2−i2i2i2−i2−i222−2−222−2−20000-22−2i2i0000000000000000−i2i2−i2i2−22−2200000000
χ31222-2-222-2-22-2-222-2-22i2i−2i−2i2i2i−2i−2i000000000000−i2−i2i2i2−i2−i2i2i2−2−222−2−22200002-22i−2i0000000000000000−i2i2−i2i2−22−2200000000
χ32222-2-222-2-22-2-222-2-22i2i−2i−2i2i2i−2i−2i000000000000−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000-22−2i2i0000000000000000i2−i2i2−i22−22−200000000
χ33222-2-222-2-22-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000i2i2−i2−i2i2i2−i2−i2−2−222−2−22200002-2−2i2i0000000000000000i2−i2i2−i2−22−2200000000
χ34222-2-222-2-22-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000-222i−2i0000000000000000−i2i2−i2i22−22−200000000
χ35222-2-222-2-22-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000−i2−i2i2i2−i2−i2i2i222−2−222−2−200002-2−2i2i0000000000000000−i2i2−i2i22−22−200000000
χ36222-2-222-2-22-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000−i2−i2i2i2−i2−i2i2i222−2−222−2−20000-222i−2i0000000000000000i2−i2i2−i2−22−2200000000
χ37222-2-2-2-2222-22-2-22-222-2-2-2-22200000000000022−2−2−2−22222−2−2−2−222000000000000000000002i−2i2i−2ii2−i2−i2i2−i2i2i2−i200000000
χ38222-2-2-2-2222-22-2-22-222-2-2-2-22200000000000022−2−2−2−22222−2−2−2−22200000000000000000000−2i2i−2i2i−i2i2i2−i2i2−i2−i2i200000000
χ39222-2-2-2-2222-22-2-22-222-2-2-2-222000000000000−2−22222−2−2−2−22222−2−2000000000000000000002i−2i2i−2i−i2i2i2−i2i2−i2−i2i200000000
χ40222-2-2-2-2222-22-2-22-222-2-2-2-222000000000000−2−22222−2−2−2−22222−2−200000000000000000000−2i2i−2i2ii2−i2−i2i2−i2i2i2−i200000000
χ41222-2-2-2-2222-22-2-22-2-2-22222-2-200000000000022−2−2−2−222−2−22222−2−2000000000000000000002i−2i−2i2i−i2i2i2−i2−i2i2i2−i200000000
χ42222-2-2-2-2222-22-2-22-2-2-22222-2-200000000000022−2−2−2−222−2−22222−2−200000000000000000000−2i2i2i−2ii2−i2−i2i2i2−i2−i2i200000000
χ43222-2-2-2-2222-22-2-22-2-2-22222-2-2000000000000−2−22222−2−222−2−2−2−222000000000000000000002i−2i−2i2ii2−i2−i2i2i2−i2−i2i200000000
χ44222-2-2-2-2222-22-2-22-2-2-22222-2-2000000000000−2−22222−2−222−2−2−2−22200000000000000000000−2i2i2i−2i−i2i2i2−i2−i2i2i2−i200000000
χ4522-22-22-22-2-2-2-22-222000000002-2222-2-2-20000000000002i−2i2i−2i2i−2i2i−2i000000002i2i−2i−2i000022-2-200000000000000000000
χ4622-22-22-22-2-2-2-22-222000000002-2222-2-2-20000000000002i−2i2i−2i2i−2i2i−2i00000000−2i−2i2i2i0000-2-22200000000000000000000
χ4722-22-22-22-2-2-2-22-222000000002-2222-2-2-2000000000000−2i2i−2i2i−2i2i−2i2i000000002i2i−2i−2i0000-2-22200000000000000000000
χ4822-22-22-22-2-2-2-22-222000000002-2222-2-2-2000000000000−2i2i−2i2i−2i2i−2i2i00000000−2i−2i2i2i000022-2-200000000000000000000
χ4922-22-2-22-22-2-22-22-2200000000-2222-22-2-20000000000002i−2i2i−2i−2i2i−2i2i22-2-2000000002i2i−2i−2i000000000000000000000000
χ5022-22-2-22-22-2-22-22-2200000000-2222-22-2-20000000000002i−2i2i−2i−2i2i−2i2i-2-22200000000−2i−2i2i2i000000000000000000000000
χ5122-22-2-22-22-2-22-22-2200000000-2222-22-2-2000000000000−2i2i−2i2i2i−2i2i−2i22-2-200000000−2i−2i2i2i000000000000000000000000
χ5222-22-2-22-22-2-22-22-2200000000-2222-22-2-2000000000000−2i2i−2i2i2i−2i2i−2i-2-222000000002i2i−2i−2i000000000000000000000000
χ532-22-2-2222-2-222-2-2-222i−2i2i−2i2i−2i2i−2i2-22-2-222-22i−2i2i−2i0000000000000000000000002-22-22i−2i2i−2i000000000000000000000000
χ542-22-2-2222-2-222-2-2-222i−2i2i−2i2i−2i2i−2i2-22-2-222-22i−2i2i−2i000000000000000000000000-22-22−2i2i−2i2i000000000000000000000000
χ552-22-2-2222-2-222-2-2-222i−2i2i−2i2i−2i2i−2i-22-222-2-22−2i2i−2i2i0000000000000000000000000000000000000000000000002-2002i−2i00
χ562-22-2-2222-2-222-2-2-222i−2i2i−2i2i−2i2i−2i-22-222-2-22−2i2i−2i2i000000000000000000000000000000000000000000000000-2200−2i2i00
χ572-22-2-2222-2-222-2-2-22−2i2i−2i2i−2i2i−2i2i2-22-2-222-2−2i2i−2i2i0000000000000000000000002-22-2−2i2i−2i2i000000000000000000000000
χ582-22-2-2222-2-222-2-2-22−2i2i−2i2i−2i2i−2i2i2-22-2-222-2−2i2i−2i2i000000000000000000000000-22-222i−2i2i−2i000000000000000000000000
χ592-22-2-2222-2-222-2-2-22−2i2i−2i2i−2i2i−2i2i-22-222-2-222i−2i2i−2i0000000000000000000000000000000000000000000000002-200−2i2i00
χ602-22-2-2222-2-222-2-2-22−2i2i−2i2i−2i2i−2i2i-22-222-2-222i−2i2i−2i000000000000000000000000000000000000000000000000-22002i−2i00
χ612-22-2-2-2-2-22-22-222222-22-2-22-222-2-22-22-222-2-22000000000000000000000000000000000000000000000000002-2002-2
χ622-22-2-2-2-2-22-22-222222-22-2-22-222-2-22-22-222-2-2200000000000000000000000000000000000000000000000000-2200-22
χ632-22-2-2-2-2-22-22-222222-22-2-22-22-222-22-22-2-222-200000000000000002-22-20000000000002-22-200000000000000000000
χ642-22-2-2-2-2-22-22-222222-22-2-22-22-222-22-22-2-222-20000000000000000-22-22000000000000-22-2200000000000000000000
χ652-22-2-2-2-2-22-22-22222-22-222-22-22-2-22-22-22-222-2000000000000000000000000000000000000000000000000002-200-22
χ662-22-2-2-2-2-22-22-22222-22-222-22-22-2-22-22-22-222-200000000000000000000000000000000000000000000000000-22002-2
χ672-22-2-2-2-2-22-22-22222-22-222-22-2-222-22-22-22-2-2200000000000000002-22-2000000000000-22-2200000000000000000000
χ682-22-2-2-2-2-22-22-22222-22-222-22-2-222-22-22-22-2-220000000000000000-22-220000000000002-22-200000000000000000000
χ692-2-2-222-2222-2-2-22-2200000000222-2-2-2-2200002i−2i2i−2i2i−2i2i−2i000000002-2-2200002i−2i−2i2i0000000000000000000000000000
χ702-2-2-222-2222-2-2-22-2200000000222-2-2-2-2200002i−2i2i−2i2i−2i2i−2i00000000-222-20000−2i2i2i−2i0000000000000000000000000000
χ712-2-2-222-2222-2-2-22-2200000000222-2-2-2-220000−2i2i−2i2i−2i2i−2i2i000000002-2-220000−2i2i2i−2i0000000000000000000000000000
χ722-2-2-222-2222-2-2-22-2200000000222-2-2-2-220000−2i2i−2i2i−2i2i−2i2i00000000-222-200002i−2i−2i2i0000000000000000000000000000
χ732-2-2-22-22-2-22-222-22200000000-2-22-222-2200002-22-2-22-22000000000000000000002-2-22-222-200000000000000000000
χ742-2-2-22-22-2-22-222-22200000000-2-22-222-2200002-22-2-22-2200000000000000000000-222-22-2-2200000000000000000000
χ752-2-2-22-22-2-22-222-22200000000-2-22-222-220000-22-222-22-2000000000000000000002-2-222-2-2200000000000000000000
χ762-2-2-22-22-2-22-222-22200000000-2-22-222-220000-22-222-22-200000000000000000000-222-2-222-200000000000000000000
χ7744-44-44-44-4-4-4-44-44400000000-44-4-4-4444000000000000000000000000000000000000000000000000000000000000
χ7844-44-4-44-44-4-44-44-44000000004-4-4-44-444000000000000000000000000000000000000000000000000000000000000
χ7944-4-444-4-44-4444-4-4-400000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ8044-4-444-4-44-4444-4-4-40000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ8144-4-44-444-4-44-4-444-400000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ8244-4-44-444-4-44-4-444-40000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ834-444444-44-4-4-4-4-44-44-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ844-444444-44-4-4-4-4-44-4-444-4-444-400000000000000000000000000000000000000000000000000000000000000000000
χ854-4444-4-44-4-4-4444-4-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ864-4444-4-44-4-4-4444-4-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ874-4-44-44-4-4-4444-444-40000000000000000000022−22−222222−22−2222000000000000000000000000000000000000000000000000
χ884-4-44-44-4-4-4444-444-400000000000000000000−222222−22−222222−22000000000000000000000000000000000000000000000000
χ894-4-44-4-444444-44-4-4-4000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ904-4-44-4-444444-44-4-4-400000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ914-4-4-444-4444-4-4-44-4400000000-4-4-44444-4000000000000000000000000000000000000000000000000000000000000
χ924-4-4-44-44-4-44-444-4440000000044-44-4-44-4000000000000000000000000000000000000000000000000000000000000

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