Finite Group Databasebeta

← Group #321521

Character table — Group #321521

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order12222222444444444444444488888888444444888888888888224444448888888888888888888888882244
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-11
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-11-1
χ911111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ1111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ1211111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ1311111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11
χ1411111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1
χ1511111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1
χ1611111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11
χ17222222222222222222-2-2-2-22200000000-2-2-2-2-2-200000000000022-2-2-2-2220000000000000000000000000000
χ18222222222222222222-2-2-2-22200000000-2-2-2-2-2-2000000000000-2-22222-2-20000000000000000000000000000
χ19222222222222-2-2-2-2-2-22222-2-22222222222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ20222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-22222000000000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2222200000000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2322222222-2-2-2-22222-2-22222-2-222222222-2-222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ2422222222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-22222000000000000000000000000000000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-20000000022-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-20000000022-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-2-2-222000000002222-2-200000000000022-2-222-2-20000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-2-2-222000000002222-2-2000000000000-2-222-2-2220000000000000000000000000000
χ29222-2-22-2-200002i2i−2i−2i002-22-2002222-2-2-2-2002i−2i0000002i2i−2i−2i0000000000000000000022−2−2i2i2−i2−i222−2−2i2i2−i2−i20000
χ30222-2-22-2-200002i2i−2i−2i002-22-2002222-2-2-2-2002i−2i0000002i2i−2i−2i00000000000000000000−2−222−i2−i2i2i2−2−222−i2−i2i2i20000
χ31222-2-22-2-200002i2i−2i−2i002-22-200-2-2-2-22222002i−2i000000−2i−2i2i2i0000000000000000000022−2−2i2i2−i2−i2−2−222−i2−i2i2i20000
χ32222-2-22-2-200002i2i−2i−2i002-22-200-2-2-2-22222002i−2i000000−2i−2i2i2i00000000000000000000−2−222−i2−i2i2i222−2−2i2i2−i2−i20000
χ33222-2-22-2-20000−2i−2i2i2i002-22-2002222-2-2-2-200−2i2i000000−2i−2i2i2i0000000000000000000022−2−2−i2−i2i2i222−2−2−i2−i2i2i20000
χ34222-2-22-2-20000−2i−2i2i2i002-22-2002222-2-2-2-200−2i2i000000−2i−2i2i2i00000000000000000000−2−222i2i2−i2−i2−2−222i2i2−i2−i20000
χ35222-2-22-2-20000−2i−2i2i2i002-22-200-2-2-2-2222200−2i2i0000002i2i−2i−2i0000000000000000000022−2−2−i2−i2i2i2−2−222i2i2−i2−i20000
χ36222-2-22-2-20000−2i−2i2i2i002-22-200-2-2-2-2222200−2i2i0000002i2i−2i−2i00000000000000000000−2−222i2i2−i2−i222−2−2−i2−i2i2i20000
χ3722-22-2-22-22i2i−2i−2i2i−2i2i−2i2-200002-222−2−222−2−2000000i2i2−i2−i2i2−i2i2−i222−2−2002i−2i2-200i2−i2i2−i22−22−200000000000000000000
χ3822-22-2-22-22i2i−2i−2i2i−2i2i−2i2-200002-222−2−222−2−2000000i2i2−i2−i2i2−i2i2−i222−2−200−2i2i-2200−i2i2−i2i2−22−2200000000000000000000
χ3922-22-2-22-22i2i−2i−2i2i−2i2i−2i2-200002-2−2−222−2−222000000−i2−i2i2i2−i2i2−i2i2−2−222002i−2i2-200−i2i2−i2i2−22−2200000000000000000000
χ4022-22-2-22-22i2i−2i−2i2i−2i2i−2i2-200002-2−2−222−2−222000000−i2−i2i2i2−i2i2−i2i2−2−22200−2i2i-2200i2−i2i2−i22−22−200000000000000000000
χ4122-22-2-22-22i2i−2i−2i−2i2i−2i2i-220000-2222−2−222−2−2000000i2i2−i2−i2−i2i2−i2i2−2−2222-200002i−2i2−2−22−i2i2i2−i200000000000000000000
χ4222-22-2-22-22i2i−2i−2i−2i2i−2i2i-220000-2222−2−222−2−2000000i2i2−i2−i2−i2i2−i2i2−2−222-220000−2i2i−222−2i2−i2−i2i200000000000000000000
χ4322-22-2-22-22i2i−2i−2i−2i2i−2i2i-220000-22−2−222−2−222000000−i2−i2i2i2i2−i2i2−i222−2−22-200002i−2i−222−2i2−i2−i2i200000000000000000000
χ4422-22-2-22-22i2i−2i−2i−2i2i−2i2i-220000-22−2−222−2−222000000−i2−i2i2i2i2−i2i2−i222−2−2-220000−2i2i2−2−22−i2i2i2−i200000000000000000000
χ4522-22-2-22-2−2i−2i2i2i2i−2i2i−2i-220000-2222−2−222−2−2000000−i2−i2i2i2i2−i2i2−i2−2−2222-20000−2i2i2−2−22i2−i2−i2i200000000000000000000
χ4622-22-2-22-2−2i−2i2i2i2i−2i2i−2i-220000-2222−2−222−2−2000000−i2−i2i2i2i2−i2i2−i2−2−222-2200002i−2i−222−2−i2i2i2−i200000000000000000000
χ4722-22-2-22-2−2i−2i2i2i2i−2i2i−2i-220000-22−2−222−2−222000000i2i2−i2−i2−i2i2−i2i222−2−22-20000−2i2i−222−2−i2i2i2−i200000000000000000000
χ4822-22-2-22-2−2i−2i2i2i2i−2i2i−2i-220000-22−2−222−2−222000000i2i2−i2−i2−i2i2−i2i222−2−2-2200002i−2i2−2−22i2−i2−i2i200000000000000000000
χ4922-22-2-22-2−2i−2i2i2i−2i2i−2i2i2-200002-222−2−222−2−2000000−i2−i2i2i2−i2i2−i2i222−2−2002i−2i-2200i2−i2i2−i2−22−2200000000000000000000
χ5022-22-2-22-2−2i−2i2i2i−2i2i−2i2i2-200002-222−2−222−2−2000000−i2−i2i2i2−i2i2−i2i222−2−200−2i2i2-200−i2i2−i2i22−22−200000000000000000000
χ5122-22-2-22-2−2i−2i2i2i−2i2i−2i2i2-200002-2−2−222−2−222000000i2i2−i2−i2i2−i2i2−i2−2−222002i−2i-2200−i2i2−i2i22−22−200000000000000000000
χ5222-22-2-22-2−2i−2i2i2i−2i2i−2i2i2-200002-2−2−222−2−222000000i2i2−i2−i2i2−i2i2−i2−2−22200−2i2i2-200i2−i2i2−i2−22−2200000000000000000000
χ532-2-2222-2-22i−2i2i−2i000000-222-2002-22-22-22-22i−2i00002i−2i2i−2i0000000000000000000000002−22−2i2−i2i2−i22−22−2i2−i2i2−i20000
χ542-2-2222-2-22i−2i2i−2i000000-222-2002-22-22-22-22i−2i00002i−2i2i−2i000000000000000000000000−22−22−i2i2−i2i2−22−22−i2i2−i2i20000
χ552-2-2222-2-22i−2i2i−2i000000-222-200-22-22-22-222i−2i0000−2i2i−2i2i0000000000000000000000002−22−2i2−i2i2−i2−22−22−i2i2−i2i20000
χ562-2-2222-2-22i−2i2i−2i000000-222-200-22-22-22-222i−2i0000−2i2i−2i2i000000000000000000000000−22−22−i2i2−i2i22−22−2i2−i2i2−i20000
χ572-2-2222-2-2−2i2i−2i2i000000-222-2002-22-22-22-2−2i2i0000−2i2i−2i2i0000000000000000000000002−22−2−i2i2−i2i22−22−2−i2i2−i2i20000
χ582-2-2222-2-2−2i2i−2i2i000000-222-2002-22-22-22-2−2i2i0000−2i2i−2i2i000000000000000000000000−22−22i2−i2i2−i2−22−22i2−i2i2−i20000
χ592-2-2222-2-2−2i2i−2i2i000000-222-200-22-22-22-22−2i2i00002i−2i2i−2i0000000000000000000000002−22−2−i2i2−i2i2−22−22i2−i2i2−i20000
χ602-2-2222-2-2−2i2i−2i2i000000-222-200-22-22-22-22−2i2i00002i−2i2i−2i000000000000000000000000−22−22i2−i2i2−i22−22−2−i2i2−i2i20000
χ612-2-2-2-2222000000002-2-2-222-222-22-2-22-2200002-2000000002-22-200000000000000002-2-2200002-2-2200000000
χ622-2-2-2-2222000000002-2-2-222-222-22-2-22-2200002-2000000002-22-20000000000000000-222-20000-222-200000000
χ632-2-2-2-2222000000002-2-2-222-22-22-222-22-200002-200000000-22-2200000000000000002-2-220000-222-200000000
χ642-2-2-2-2222000000002-2-2-222-22-22-222-22-200002-200000000-22-220000000000000000-222-200002-2-2200000000
χ652-2-2-2-222200000000-22-2-2222-22-22-2-22-220000-2200000000-22-22000000000000000000002-2-2200002-2-220000
χ662-2-2-2-222200000000-22-2-2222-22-22-2-22-220000-2200000000-22-2200000000000000000000-222-20000-222-20000
χ672-2-2-2-222200000000-22-2-2222-2-22-222-22-20000-22000000002-22-2000000000000000000002-2-220000-222-20000
χ682-2-2-2-222200000000-22-2-2222-2-22-222-22-20000-22000000002-22-200000000000000000000-222-200002-2-220000
χ69444-4-44-4-400004i4i−4i−4i00-44-44000000000000−4i4i00000000000000000000000000000000000000000000000000
χ70444-4-44-4-40000−4i−4i4i4i00-44-440000000000004i−4i00000000000000000000000000000000000000000000000000
χ7144-4-44-4-4400004-4-44000000002222−22−22−22−222222000000000022−22−22220000000000000000000000000000000000000000
χ7244-4-44-4-4400004-4-4400000000−22−2222222222−22−220000000000−222222−220000000000000000000000000000000000000000
χ7344-4-44-4-440000-444-4000000002222−22−22−22−2222220000000000−222222−220000000000000000000000000000000000000000
χ7444-4-44-4-440000-444-400000000−22−2222222222−22−22000000000022−22−22220000000000000000000000000000000000000000
χ754-444-4-4-444-4-4400000000000022−22−222222−22−222200000022−22−222200000000000000000000000000000000000000000000
χ764-444-4-4-444-4-44000000000000−222222−22−222222−22000000−222222−2200000000000000000000000000000000000000000000
χ774-444-4-4-44-444-400000000000022−22−222222−22−2222000000−222222−2200000000000000000000000000000000000000000000
χ784-444-4-4-44-444-4000000000000−222222−22−222222−2200000022−22−222200000000000000000000000000000000000000000000
χ794-44-44-44-400000000440000-4-422−22−2222−222222−220000000000000022−22−2222000000000000000000000000000000000000
χ804-44-44-44-400000000440000-4-4−222222−2222−22−222200000000000000−222222−22000000000000000000000000000000000000
χ814-44-44-44-400000000-4-400004422−22−2222−222222−2200000000000000−222222−22000000000000000000000000000000000000
χ824-44-44-44-400000000-4-4000044−222222−2222−22−22220000000000000022−22−2222000000000000000000000000000000000000
χ834-4-4444-4-44i−4i4i−4i0000004-4-440000000000−4i4i0000000000000000000000000000000000000000000000000000
χ844-4-4444-4-4−4i4i−4i4i0000004-4-4400000000004i−4i0000000000000000000000000000000000000000000000000000
χ854-4-4-4-4444000000004-444-4-4-44000000000000-44000000000000000000000000000000000000000000000000
χ864-4-4-4-444400000000-4444-4-44-40000000000004-4000000000000000000000000000000000000000000000000

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