Finite Group Databasebeta

← Group #418165

Character table — Group #418165

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111111111112222222244444444444444444444444444448888888888888888888888161616161616161616161616
order12222222222222224444444444444444444488888888888888884444444444444488888888222244444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ51111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ71111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111
χ9111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111-1-1-1-1
χ10111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111
χ11111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-11111-1-111-1-1-1-111-1-1
χ12111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1
χ172222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000022-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000-2-222220000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000-2-222-2-20000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000022-2-2220000000000000000000000000000
χ2122222-2-2-222-2-2-2-2-2222-2-222-2-200002i2i−2i−2i0000000000002222-2-2-2-200002i−2i0000000000002i2i−2i−2i000000000000
χ2222222-2-2-222-2-2-2-2-2222-2-222-2-200002i2i−2i−2i000000000000-2-2-2-2222200002i−2i000000000000−2i−2i2i2i000000000000
χ2322222-2-2-222-2-2-2-2-2222-2-222-2-20000−2i−2i2i2i0000000000002222-2-2-2-20000−2i2i000000000000−2i−2i2i2i000000000000
χ2422222-2-2-222-2-2-2-2-2222-2-222-2-20000−2i−2i2i2i000000000000-2-2-2-222220000−2i2i0000000000002i2i−2i−2i000000000000
χ2522222-2-2-222-2-2-2-2-22-2-222-2-22200002i2i−2i−2i00002222-2-2-2-2000000000000−2i2i000000002i2i−2i−2i0000000000000000
χ2622222-2-2-222-2-2-2-2-22-2-222-2-22200002i2i−2i−2i0000-2-2-2-22222000000000000−2i2i00000000−2i−2i2i2i0000000000000000
χ2722222-2-2-222-2-2-2-2-22-2-222-2-2220000−2i−2i2i2i00002222-2-2-2-20000000000002i−2i00000000−2i−2i2i2i0000000000000000
χ2822222-2-2-222-2-2-2-2-22-2-222-2-2220000−2i−2i2i2i0000-2-2-2-222220000000000002i−2i000000002i2i−2i−2i0000000000000000
χ29222-2-222-22-22-2-2-22-20000000000002i−2i2i−2i22-2-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002i−2i00000000002−22−22−22−2000000000000
χ30222-2-222-22-22-2-2-22-20000000000002i−2i2i−2i22-2-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002i−2i0000000000−22−22−22−22000000000000
χ31222-2-222-22-22-2-2-22-20000000000002i−2i2i−2i-2-222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200−2i2i00000000002−22−2−22−22000000000000
χ32222-2-222-22-22-2-2-22-20000000000002i−2i2i−2i-2-222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200−2i2i0000000000−22−222−22−2000000000000
χ33222-2-222-22-22-2-2-22-2000000000000−2i2i−2i2i22-2-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200−2i2i0000000000−22−22−22−22000000000000
χ34222-2-222-22-22-2-2-22-2000000000000−2i2i−2i2i22-2-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200−2i2i00000000002−22−22−22−2000000000000
χ35222-2-222-22-22-2-2-22-2000000000000−2i2i−2i2i-2-222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2002i−2i0000000000−22−222−22−2000000000000
χ36222-2-222-22-22-2-2-22-2000000000000−2i2i−2i2i-2-222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2002i−2i00000000002−22−2−22−22000000000000
χ37222-2-2-2-222-2-2222-2-20000000022-2-22-2-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22-2000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ38222-2-2-2-222-2-2222-2-20000000022-2-22-2-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i22-2000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ39222-2-2-2-222-2-2222-2-20000000022-2-2-222-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2-22000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ40222-2-2-2-222-2-2222-2-20000000022-2-2-222-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2-22000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ41222-2-2-2-222-2-2222-2-200000000-2-2222-2-220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2-22000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ42222-2-2-2-222-2-2222-2-200000000-2-2222-2-220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2-22000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ43222-2-2-2-222-2-2222-2-200000000-2-222-222-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i22-2000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ44222-2-2-2-222-2-2222-2-200000000-2-222-222-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i22-2000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ4522-22-22-22-2-222-2-2-22222-2-2-22-20000000000002-22-22-22-2000000000000002i2i−2i−2i0000000000000000002i−2i0000
χ4622-22-22-22-2-222-2-2-22222-2-2-22-20000000000002-22-22-22-200000000000000−2i−2i2i2i000000000000000000−2i2i0000
χ4722-22-22-22-2-222-2-2-22222-2-2-22-2000000000000-22-22-22-22000000000000002i2i−2i−2i000000000000000000−2i2i0000
χ4822-22-22-22-2-222-2-2-22222-2-2-22-2000000000000-22-22-22-2200000000000000−2i−2i2i2i0000000000000000002i−2i0000
χ4922-22-2-22-2-2-2-2-22222-2-22-2222-20000000000002-22-2-22-2200000000000000000022-2-2000000002-20000000000
χ5022-22-2-22-2-2-2-2-22222-2-22-2222-20000000000002-22-2-22-22000000000000000000-2-22200000000-220000000000
χ5122-22-2-22-2-2-2-2-22222-2-22-2222-2000000000000-22-222-22-200000000000000000022-2-200000000-220000000000
χ5222-22-2-22-2-2-2-2-22222-2-22-2222-2000000000000-22-222-22-2000000000000000000-2-222000000002-20000000000
χ532-22-222-2-2-2-2-222-2222-2-2-22-222000000000000000000002-22-22-22-200000000002-22-200000000002-200000000
χ542-22-222-2-2-2-2-222-2222-2-2-22-222000000000000000000002-22-22-22-20000000000-22-220000000000-2200000000
χ552-22-222-2-2-2-2-222-2222-2-2-22-22200000000000000000000-22-22-22-2200000000002-22-20000000000-2200000000
χ562-22-222-2-2-2-2-222-2222-2-2-22-22200000000000000000000-22-22-22-220000000000-22-2200000000002-200000000
χ572-22-22-222-2-22-2-22-222-2222-2-2-2000000000000000000002-22-2-22-220000002i−2i2i−2i000000000000000000002i−2i00
χ582-22-22-222-2-22-2-22-222-2222-2-2-2000000000000000000002-22-2-22-22000000−2i2i−2i2i00000000000000000000−2i2i00
χ592-22-22-222-2-22-2-22-222-2222-2-2-200000000000000000000-22-222-22-20000002i−2i2i−2i00000000000000000000−2i2i00
χ602-22-22-222-2-22-2-22-222-2222-2-2-200000000000000000000-22-222-22-2000000−2i2i−2i2i000000000000000000002i−2i00
χ612-2-2-2-2-2-22222-22-2222-22-2-22-222-22-200002-22-200000000000000000000002-2-2200000000000000002-2000000
χ622-2-2-2-2-2-22222-22-2222-22-2-22-222-22-200002-22-20000000000000000000000-222-20000000000000000-22000000
χ632-2-2-2-2-2-22222-22-2222-22-2-22-22-22-220000-22-2200000000000000000000002-2-220000000000000000-22000000
χ642-2-2-2-2-2-22222-22-2222-22-2-22-22-22-220000-22-220000000000000000000000-222-200000000000000002-2000000
χ652-2-2-2-2-2-22222-22-222-22-222-22-22-22-20000-22-22000000000000000000000000002-2-220000000000000000002-2
χ662-2-2-2-2-2-22222-22-222-22-222-22-22-22-20000-22-2200000000000000000000000000-222-2000000000000000000-22
χ672-2-2-2-2-2-22222-22-222-22-222-22-2-22-2200002-22-2000000000000000000000000002-2-22000000000000000000-22
χ682-2-2-2-2-2-22222-22-222-22-222-22-2-22-2200002-22-200000000000000000000000000-222-20000000000000000002-2
χ6944-44-44-44-4-444-4-4-44-4-4-4444-4400000000000000000000000000000000000000000000000000000000000000
χ7044-44-4-44-4-4-4-4-4444444-44-4-4-4400000000000000000000000000000000000000000000000000000000000000
χ7144-4-444-4-4-444-444-4-4000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ7244-4-444-4-4-444-444-4-400000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ7344-4-44-444-44-44-4-44-4000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ7444-4-44-444-44-44-4-44-400000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ754-444-44-44-44-4-4-444-400000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000
χ764-444-44-44-44-4-4-444-40000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000
χ774-444-4-44-4-44444-4-4-400000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000
χ784-444-4-44-4-44444-4-4-40000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000
χ794-44-444-4-4-4-4-444-444-4444-44-4-400000000000000000000000000000000000000000000000000000000000000
χ804-44-44-444-4-44-4-44-44-44-4-4-444400000000000000000000000000000000000000000000000000000000000000
χ814-4-4444444-4-4-44-4-4-4000000004-4-440000000000000000000000000000000000000000000000000000000000
χ824-4-4444444-4-4-44-4-4-400000000-444-40000000000000000000000000000000000000000000000000000000000
χ834-4-444-4-4-44-444-444-400000000000000004-4-4400000000000000000000000000000000000000000000000000
χ844-4-444-4-4-44-444-444-40000000000000000-444-400000000000000000000000000000000000000000000000000
χ854-4-4-4-444-444-44-44-444-4-44-444-400000000000000000000000000000000000000000000000000000000000000
χ864-4-4-4-444-444-44-44-44-444-44-4-4400000000000000000000000000000000000000000000000000000000000000

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