Finite Group Databasebeta

← Group #324403

Character table — Group #324403

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order12222222444444444444444488888888444444888888888888444444448888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ911111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1
χ1011111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-11
χ1111111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-11
χ1211111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-1
χ1311111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11
χ1411111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1
χ1511111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1
χ1611111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11-1-11
χ17222222222222222222-2-2-222-200000000-2-2-2-2-2-200000000000022-2-222-2-20000000000000000000000000000
χ18222222222222222222-2-2-222-200000000-2-2-2-2-2-2000000000000-2-222-2-2220000000000000000000000000000
χ19222222222222-2-2-2-2-2-2222-2-222222222222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2222-2-22-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-222220000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i0000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-22222000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000
χ2322222222-2-2-2-22222-2-2222-2-2222222222-2-2-2-222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ2422222222-2-2-2-22222-2-2222-2-22-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22222000000000000000000000000000000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-2000000002222-2-20000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i0000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-2000000002222-2-2000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000
χ2722222222-2-2-2-2-2-2-2-222-2-2-222-20000000022-2-22200000000000022-2-2-2-2220000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-2-222-20000000022-2-222000000000000-2-22222-2-20000000000000000000000000000
χ29222-22-2-2-222-2-222-2-222000-2-202222−2−2−2−200000022−2−222−2−222−2−2002-2002-200000000000000002−22−22−22−20000
χ30222-22-2-2-222-2-222-2-222000-2-202222−2−2−2−200000022−2−222−2−222−2−200-2200-220000000000000000−22−22−22−220000
χ31222-22-2-2-222-2-222-2-222000-2-20−2−2−2−22222000000−2−222−2−222−2−222002-2002-20000000000000000−22−22−22−220000
χ32222-22-2-2-222-2-222-2-222000-2-20−2−2−2−22222000000−2−222−2−222−2−22200-2200-2200000000000000002−22−22−22−20000
χ33222-22-2-2-222-2-2-2-222-2-20002202222−2−2−2−200000022−2−2−2−222−2−2222i−2i002i−2i000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ34222-22-2-2-222-2-2-2-222-2-20002202222−2−2−2−200000022−2−2−2−222−2−222−2i2i00−2i2i000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ35222-22-2-2-222-2-2-2-222-2-2000220−2−2−2−22222000000−2−22222−2−222−2−22i−2i002i−2i000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ36222-22-2-2-222-2-2-2-222-2-2000220−2−2−2−22222000000−2−22222−2−222−2−2−2i2i00−2i2i000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ37222-22-2-2-2-2-22222-2-2-2-20002202222−2−2−2−2000000−2−22222−2−2−2−2222i−2i00−2i2i000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ38222-22-2-2-2-2-22222-2-2-2-20002202222−2−2−2−2000000−2−22222−2−2−2−222−2i2i002i−2i000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ39222-22-2-2-2-2-22222-2-2-2-2000220−2−2−2−2222200000022−2−2−2−22222−2−22i−2i00−2i2i000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ40222-22-2-2-2-2-22222-2-2-2-2000220−2−2−2−2222200000022−2−2−2−22222−2−2−2i2i002i−2i000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ41222-22-2-2-2-2-222-2-22222000-2-202222−2−2−2−2000000−2−222−2−22222−2−2002-200-2200000000000000002−22−2−22−220000
χ42222-22-2-2-2-2-222-2-22222000-2-202222−2−2−2−2000000−2−222−2−22222−2−200-22002-20000000000000000−22−222−22−20000
χ43222-22-2-2-2-2-222-2-22222000-2-20−2−2−2−2222200000022−2−222−2−2−2−222002-200-220000000000000000−22−222−22−20000
χ44222-22-2-2-2-2-222-2-22222000-2-20−2−2−2−2222200000022−2−222−2−2−2−22200-22002-200000000000000002−22−2−22−220000
χ4522-22-2-22-22-22-20000002-2-20022i2i−2i−2i2i2i−2i−2i2-200002i−2i2i−2i0000000000000000i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000
χ4622-22-2-22-22-22-20000002-2-20022i2i−2i−2i2i2i−2i−2i2-200002i−2i2i−2i0000000000000000−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000
χ4722-22-2-22-22-22-20000002-2-2002−2i−2i2i2i−2i−2i2i2i2-20000−2i2i−2i2i0000000000000000i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000
χ4822-22-2-22-22-22-20000002-2-2002−2i−2i2i2i−2i−2i2i2i2-20000−2i2i−2i2i0000000000000000−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000
χ4922-22-2-22-2-22-220000002-2-20022i2i−2i−2i2i2i−2i−2i-220000−2i2i−2i2i0000000000000000i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000
χ5022-22-2-22-2-22-220000002-2-20022i2i−2i−2i2i2i−2i−2i-220000−2i2i−2i2i0000000000000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000
χ5122-22-2-22-2-22-220000002-2-2002−2i−2i2i2i−2i−2i2i2i-2200002i−2i2i−2i0000000000000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000
χ5222-22-2-22-2-22-220000002-2-2002−2i−2i2i2i−2i−2i2i2i-2200002i−2i2i−2i0000000000000000−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000
χ532-22-2-2-22200002-22-20022-200-22-22-22-22-200002-200002-22-2000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ542-22-2-2-22200002-22-20022-200-22-22-22-22-200002-200002-22-2000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ552-22-2-2-22200002-22-20022-200-2-22-22-22-2200002-20000-22-22000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ562-22-2-2-22200002-22-20022-200-2-22-22-22-2200002-20000-22-22000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ572-22-2-2-2220000-22-220022-200-22-22-22-22-20000-220000-22-22000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ582-22-2-2-2220000-22-220022-200-22-22-22-22-20000-220000-22-22000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ592-22-2-2-2220000-22-220022-200-2-22-22-22-220000-2200002-22-2000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ602-22-2-2-2220000-22-220022-200-2-22-22-22-220000-2200002-22-2000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ612-2-2-2222-2000000002-22-222-2-22i−2i−2i2i2i−2i−2i2i002-200000000002i−2i2i−2i0000000000002-2-220000−2i2i2i−2i000000000000
χ622-2-2-2222-2000000002-22-222-2-22i−2i−2i2i2i−2i−2i2i002-200000000002i−2i2i−2i000000000000-222-200002i−2i−2i2i000000000000
χ632-2-2-2222-2000000002-22-222-2-2−2i2i2i−2i−2i2i2i−2i002-20000000000−2i2i−2i2i0000000000002-2-2200002i−2i−2i2i000000000000
χ642-2-2-2222-2000000002-22-222-2-2−2i2i2i−2i−2i2i2i−2i002-20000000000−2i2i−2i2i000000000000-222-20000−2i2i2i−2i000000000000
χ652-2-2-2222-200000000-222-22-22-22i−2i−2i2i2i−2i−2i2i00-220000000000−2i2i−2i2i000000002-2-220000−2i2i2i−2i0000000000000000
χ662-2-2-2222-200000000-222-22-22-22i−2i−2i2i2i−2i−2i2i00-220000000000−2i2i−2i2i00000000-222-200002i−2i−2i2i0000000000000000
χ672-2-2-2222-200000000-222-22-22-2−2i2i2i−2i−2i2i2i−2i00-2200000000002i−2i2i−2i000000002-2-2200002i−2i−2i2i0000000000000000
χ682-2-2-2222-200000000-222-22-22-2−2i2i2i−2i−2i2i2i−2i00-2200000000002i−2i2i−2i00000000-222-20000−2i2i2i−2i0000000000000000
χ6944-44-4-44-44-44-4000000-44400-400000000-440000000000000000000000000000000000000000000000000000
χ7044-44-4-44-4-44-44000000-44400-4000000004-40000000000000000000000000000000000000000000000000000
χ7144-4-4-44-444-4-440000000000002i22i2−2i2−2i2−2i2−2i22i22i20000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ7244-4-4-44-444-4-44000000000000−2i2−2i22i22i22i22i2−2i2−2i2000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ7344-4-4-44-44-444-40000000000002i22i2−2i2−2i2−2i2−2i22i22i2000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ7444-4-4-44-44-444-4000000000000−2i2−2i22i22i22i22i2−2i2−2i20000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ754-444-44-4-400004-4-440000000022−2222−22−2222−2222000000000022−22−22220000000000000000000000000000000000000000
χ764-444-44-4-400004-4-4400000000−2222−222222−2222−220000000000−222222−220000000000000000000000000000000000000000
χ774-444-44-4-40000-444-40000000022−2222−22−2222−22220000000000−222222−220000000000000000000000000000000000000000
χ784-444-44-4-40000-444-400000000−2222−222222−2222−22000000000022−22−22220000000000000000000000000000000000000000
χ794-44-4-4-44400004-44-400-4-44004000000000000-44000000000000000000000000000000000000000000000000
χ804-44-4-4-4440000-44-4400-4-440040000000000004-4000000000000000000000000000000000000000000000000
χ814-4-444-4-44000000004-4000-4402i2−2i2−2i22i2−2i22i22i2−2i2000000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ824-4-444-4-44000000004-4000-440−2i22i22i2−2i22i2−2i2−2i22i200000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ834-4-444-4-4400000000-440004-402i2−2i2−2i22i2−2i22i22i2−2i200000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ844-4-444-4-4400000000-440004-40−2i22i22i2−2i22i2−2i2−2i22i2000000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ854-4-4-4444-4000000004-4-44-44-440000000000-4400000000000000000000000000000000000000000000000000
χ864-4-4-4444-400000000-44-44-4-44400000000004-400000000000000000000000000000000000000000000000000

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