Finite Group Databasebeta

← Group #398657

Character table — Group #398657

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111111111111222222224444444444444444444488888888888888888888888888888888881616161616161616
order12222222222222224444444444444444444444444444444444444444444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ10111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ11111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ12111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ14111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ172222222222222222-2-2-2-2-2-2-2-222222222222200000000-2-2-2-200000000-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000-2-22200000000220000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000000022-2-200000000220000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000222200000000-2-20000000000000000000000000000
χ21222222-2-2-2-2-22-2-2-22222-2-2-2-220000000000002222-2-2-2-20000000000000000002i2i−2i−2i0000000000002i−2i000000
χ22222222-2-2-2-2-22-2-2-22222-2-2-2-220000000000002222-2-2-2-2000000000000000000−2i−2i2i2i000000000000−2i2i000000
χ23222222-2-2-2-2-22-2-2-22222-2-2-2-22000000000000-2-2-2-222220000000000000000002i2i−2i−2i000000000000−2i2i000000
χ24222222-2-2-2-2-22-2-2-22222-2-2-2-22000000000000-2-2-2-22222000000000000000000−2i−2i2i2i0000000000002i−2i000000
χ252222-2-22-2222-2-2-2-2-20000000022-2-222-2-222-2-2000000000000000000000000002−22−222−2−222−2−222−2−200000000
χ262222-2-22-2222-2-2-2-2-20000000022-2-222-2-222-2-200000000000000000000000000−22−22−2−222−2−222−2−22200000000
χ272222-2-22-2222-2-2-2-2-20000000022-2-2-2-222-2-222000000000000000000000000002−22−222−2−2−2−222−2−22200000000
χ282222-2-22-2222-2-2-2-2-20000000022-2-2-2-222-2-22200000000000000000000000000−22−22−2−22222−2−222−2−200000000
χ292222-2-22-2222-2-2-2-2-200000000-2-22222-2-2-2-222000000000000000000000000002−22−2−2−22222−2−2−2−22200000000
χ302222-2-22-2222-2-2-2-2-200000000-2-22222-2-2-2-22200000000000000000000000000−22−2222−2−2−2−22222−2−200000000
χ312222-2-22-2222-2-2-2-2-200000000-2-222-2-22222-2-2000000000000000000000000002−22−2−2−222−2−22222−2−200000000
χ322222-2-22-2222-2-2-2-2-200000000-2-222-2-22222-2-200000000000000000000000000−22−2222−2−222−2−2−2−22200000000
χ3322-2-22-2222-2-222-2-2-222-222-2-2-200002-22-2000022-2-222-2-2002-2000022-2-2000000000000000000000000000000
χ3422-2-22-2222-2-222-2-2-222-222-2-2-200002-22-20000-2-222-2-222002-20000-2-222000000000000000000000000000000
χ3522-2-22-2222-2-222-2-2-222-222-2-2-20000-22-22000022-2-222-2-200-220000-2-222000000000000000000000000000000
χ3622-2-22-2222-2-222-2-2-222-222-2-2-20000-22-220000-2-222-2-22200-22000022-2-2000000000000000000000000000000
χ3722-2-22-2222-2-222-2-2-2-2-22-2-222200002-22-200000000000000-222i2i−2i−2i0000002i2i−2i−2i000000000000000000000000
χ3822-2-22-2222-2-222-2-2-2-2-22-2-222200002-22-200000000000000-22−2i−2i2i2i000000−2i−2i2i2i000000000000000000000000
χ3922-2-22-2222-2-222-2-2-2-2-22-2-22220000-22-22000000000000002-22i2i−2i−2i000000−2i−2i2i2i000000000000000000000000
χ4022-2-22-2222-2-222-2-2-2-2-22-2-22220000-22-22000000000000002-2−2i−2i2i2i0000002i2i−2i−2i000000000000000000000000
χ4122-2-22-2-2-2-2222-222-222-2-2-222-200000000000022-2-2-2-222000000000000000000000000002i−2i2i−2i000000002i−2i00
χ4222-2-22-2-2-2-2222-222-222-2-2-222-200000000000022-2-2-2-22200000000000000000000000000−2i2i−2i2i00000000−2i2i00
χ4322-2-22-2-2-2-2222-222-222-2-2-222-2000000000000-2-22222-2-2000000000000000000000000002i−2i2i−2i00000000−2i2i00
χ4422-2-22-2-2-2-2222-222-222-2-2-222-2000000000000-2-22222-2-200000000000000000000000000−2i2i−2i2i000000002i−2i00
χ452-22-2-2222-22-22-22-2-22-222-22-2-22-22-2000000002-22-22-22-22-2002-22-20000000000000000000000000000000000
χ462-22-2-2222-22-22-22-2-22-222-22-2-22-22-200000000-22-22-22-222-200-22-220000000000000000000000000000000000
χ472-22-2-2222-22-22-22-2-22-222-22-2-2-22-22000000002-22-22-22-2-2200-22-220000000000000000000000000000000000
χ482-22-2-2222-22-22-22-2-22-222-22-2-2-22-2200000000-22-22-22-22-22002-22-20000000000000000000000000000000000
χ492-22-2-2222-22-22-22-2-2-22-2-22-2222-22-20000000000000000-220000002i−2i2i−2i002i−2i2i−2i000000000000000000000000
χ502-22-2-2222-22-22-22-2-2-22-2-22-2222-22-20000000000000000-22000000−2i2i−2i2i00−2i2i−2i2i000000000000000000000000
χ512-22-2-2222-22-22-22-2-2-22-2-22-222-22-2200000000000000002-20000002i−2i2i−2i00−2i2i−2i2i000000000000000000000000
χ522-22-2-2222-22-22-22-2-2-22-2-22-222-22-2200000000000000002-2000000−2i2i−2i2i002i−2i2i−2i000000000000000000000000
χ532-22-2-22-2-22-2222-22-22-22-22-22-20000000000002-22-2-22-2200000000000000000000002i−2i2i−2i00000000002i−2i0000
χ542-22-2-22-2-22-2222-22-22-22-22-22-20000000000002-22-2-22-220000000000000000000000−2i2i−2i2i0000000000−2i2i0000
χ552-22-2-22-2-22-2222-22-22-22-22-22-2000000000000-22-222-22-200000000000000000000002i−2i2i−2i0000000000−2i2i0000
χ562-22-2-22-2-22-2222-22-22-22-22-22-2000000000000-22-222-22-20000000000000000000000−2i2i−2i2i00000000002i−2i0000
χ572-2-22-2-222-2-222-2-2222-2-22-2-222000000002-22-22-2-222-2-220000000000002-22-2-22000000000000000000000000
χ582-2-22-2-222-2-222-2-2222-2-22-2-222000000002-22-2-222-2-222-20000000000002-2-222-2000000000000000000000000
χ592-2-22-2-222-2-222-2-2222-2-22-2-22200000000-22-222-2-222-2-22000000000000-22-222-2000000000000000000000000
χ602-2-22-2-222-2-222-2-2222-2-22-2-22200000000-22-22-222-2-222-2000000000000-222-2-22000000000000000000000000
χ612-2-22-2-222-2-222-2-222-222-222-2-2000000002-22-20000000000002i−2i−2i2i−2i2i2i−2i-220000000000000000000000000000
χ622-2-22-2-222-2-222-2-222-222-222-2-2000000002-22-2000000000000−2i2i2i−2i2i−2i−2i2i-220000000000000000000000000000
χ632-2-22-2-222-2-222-2-222-222-222-2-200000000-22-220000000000002i−2i−2i2i2i−2i−2i2i2-20000000000000000000000000000
χ642-2-22-2-222-2-222-2-222-222-222-2-200000000-22-22000000000000−2i2i2i−2i−2i2i2i−2i2-20000000000000000000000000000
χ652-2-22-2-2-2-222-2222-222-2-2-222-220000000000002-2-22-222-20000000000000000000000000000002-22-20000002-2
χ662-2-22-2-2-2-222-2222-222-2-2-222-220000000000002-2-22-222-2000000000000000000000000000000-22-22000000-22
χ672-2-22-2-2-2-222-2222-222-2-2-222-22000000000000-222-22-2-220000000000000000000000000000002-22-2000000-22
χ682-2-22-2-2-2-222-2222-222-2-2-222-22000000000000-222-22-2-22000000000000000000000000000000-22-220000002-2
χ69444444-4-4-4-4-44-4-4-44-4-4-44444-400000000000000000000000000000000000000000000000000000000000000
χ704444-4-4-44-4-4-4-4444-400000000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ714444-4-4-44-4-4-4-4444-40000000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ7244-4-44-4-4-4-4444-444-4-4-4444-4-4400000000000000000000000000000000000000000000000000000000000000
χ7344-4-4-444-44-4-4-4-44440000000000004-4-44000000000000000000000000000000000000000000000000000000
χ7444-4-4-444-44-4-4-4-4444000000000000-444-4000000000000000000000000000000000000000000000000000000
χ7544-4-4-44-44-444-44-4-440000000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ7644-4-4-44-44-444-44-4-44000000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ774-44-44-44-4-44-4-44-444000000004-4-440000000000000000000000000000000000000000000000000000000000
χ784-44-44-44-4-44-4-44-44400000000-444-40000000000000000000000000000000000000000000000000000000000
χ794-44-44-4-444-44-4-44-44000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ804-44-44-4-444-44-4-44-4400000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ814-44-4-44-4-44-4444-44-4-44-44-44-4400000000000000000000000000000000000000000000000000000000000000
χ824-4-44444-4-4-44-444-4-400000000000000004-4-4400000000000000000000000000000000000000000000000000
χ834-4-44444-4-4-44-444-4-40000000000000000-444-400000000000000000000000000000000000000000000000000
χ844-4-4444-4444-4-4-4-44-4000000000000000000000000000000000000000000000000000000000022−22−222200000000
χ854-4-4444-4444-4-4-4-44-40000000000000000000000000000000000000000000000000000000000−222222−2200000000
χ864-4-44-4-4-4-444-4444-44-4444-4-44-400000000000000000000000000000000000000000000000000000000000000

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