Finite Group Databasebeta

← Group #419129

Character table — Group #419129

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111111111112222222244444444444444444444444444448888888888888888888888161616161616161616161616
order12222222222222224444444444444444444488888888888888882222222244444488888888444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ511111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ611111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1111111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ9111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1
χ10111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111
χ11111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ12111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111
χ172222222222222222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000-2-2220000-2-2000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000022-2-2000022000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000-2-2-2-2000022000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000022220000-2-2000000000000000000000000
χ21222222-2-2-2-2-2-2-222-200000000000022-2-22i2i−2i−2ii2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2000000002i−2i000022−2−222−2−2000000000000
χ22222222-2-2-2-2-2-2-222-200000000000022-2-22i2i−2i−2i−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2000000002i−2i0000−2−222−2−222000000000000
χ23222222-2-2-2-2-2-2-222-200000000000022-2-2−2i−2i2i2ii2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200000000−2i2i0000−2−222−2−222000000000000
χ24222222-2-2-2-2-2-2-222-200000000000022-2-2−2i−2i2i2i−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200000000−2i2i000022−2−222−2−2000000000000
χ25222222-2-2-2-2-2-2-222-2000000000000-2-2222i2i−2i−2ii2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200000000−2i2i000022−2−2−2−222000000000000
χ26222222-2-2-2-2-2-2-222-2000000000000-2-2222i2i−2i−2i−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200000000−2i2i0000−2−22222−2−2000000000000
χ27222222-2-2-2-2-2-2-222-2000000000000-2-222−2i−2i2i2ii2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2000000002i−2i0000−2−22222−2−2000000000000
χ28222222-2-2-2-2-2-2-222-2000000000000-2-222−2i−2i2i2i−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2000000002i−2i000022−2−2−2−222000000000000
χ292222-2-22-2-2-222-2-2-22222-2-22-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i000022-2-20000000000000000002i−2i000000
χ302222-2-22-2-2-222-2-2-22222-2-22-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i0000-2-222000000000000000000−2i2i000000
χ312222-2-22-2-2-222-2-2-22222-2-22-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i000022-2-2000000000000000000−2i2i000000
χ322222-2-22-2-2-222-2-2-22222-2-22-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i0000-2-2220000000000000000002i−2i000000
χ3322-2-222-22-2-22-22-2-2222-22-2-22-20000000000002i2i−2i−2i2i2i−2i−2i0000000000002-22-200000000000000002i−2i00000000
χ3422-2-222-22-2-22-22-2-2222-22-2-22-20000000000002i2i−2i−2i2i2i−2i−2i000000000000-22-220000000000000000−2i2i00000000
χ3522-2-222-22-2-22-22-2-2222-22-2-22-2000000000000−2i−2i2i2i−2i−2i2i2i0000000000002-22-20000000000000000−2i2i00000000
χ3622-2-222-22-2-22-22-2-2222-22-2-22-2000000000000−2i−2i2i2i−2i−2i2i2i000000000000-22-2200000000000000002i−2i00000000
χ3722-2-2-2-2-2-2222-2-222222-2-22-2-2222-2-22-22-20000000000000000000000002-2-2200000000000000000000002-200
χ3822-2-2-2-2-2-2222-2-222222-2-22-2-2222-2-22-22-2000000000000000000000000-222-20000000000000000000000-2200
χ3922-2-2-2-2-2-2222-2-222222-2-22-2-22-2-222-22-220000000000000000000000002-2-220000000000000000000000-2200
χ4022-2-2-2-2-2-2222-2-222222-2-22-2-22-2-222-22-22000000000000000000000000-222-200000000000000000000002-200
χ4122-2-2-2-2-2-2222-2-2222-2-222-222-222-2-2-22-2200000000000000000000000000000022-2-2000000002-20000000000
χ4222-2-2-2-2-2-2222-2-2222-2-222-222-222-2-2-22-22000000000000000000000000000000-2-22200000000-220000000000
χ4322-2-2-2-2-2-2222-2-2222-2-222-222-2-2-2222-22-200000000000000000000000000000022-2-200000000-220000000000
χ4422-2-2-2-2-2-2222-2-2222-2-222-222-2-2-2222-22-2000000000000000000000000000000-2-222000000002-20000000000
χ452-22-22-2222-2-2-2-2-2222-22-22-22-20000000000002i−2i2i−2i2i−2i2i−2i0000000000000000002-22-2000000000000002i−2i0000
χ462-22-22-2222-2-2-2-2-2222-22-22-22-20000000000002i−2i2i−2i2i−2i2i−2i000000000000000000-22-2200000000000000−2i2i0000
χ472-22-22-2222-2-2-2-2-2222-22-22-22-2000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000002-22-200000000000000−2i2i0000
χ482-22-22-2222-2-2-2-2-2222-22-22-22-2000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000-22-22000000000000002i−2i0000
χ492-2-222-22-22-22-222-2-2000000002i−2i2i−2i00002i−2i2i−2ii2−i2−i2i2−i2i2i2−i22−22−22−22−2002-200000000002−22−2i2−i2i2−i2000000000000
χ502-2-222-22-22-22-222-2-2000000002i−2i2i−2i00002i−2i2i−2i−i2i2i2−i2i2−i2−i2i2−22−22−22−22002-20000000000−22−22−i2i2−i2i2000000000000
χ512-2-222-22-22-22-222-2-2000000002i−2i2i−2i0000−2i2i−2i2ii2−i2−i2i2−i2i2i2−i22−22−22−22−200-220000000000−22−22−i2i2−i2i2000000000000
χ522-2-222-22-22-22-222-2-2000000002i−2i2i−2i0000−2i2i−2i2i−i2i2i2−i2i2−i2−i2i2−22−22−22−2200-2200000000002−22−2i2−i2i2−i2000000000000
χ532-2-222-22-22-22-222-2-200000000−2i2i−2i2i00002i−2i2i−2ii2−i2−i2i2−i2i2i2−i2−22−22−22−2200-2200000000002−22−2−i2i2−i2i2000000000000
χ542-2-222-22-22-22-222-2-200000000−2i2i−2i2i00002i−2i2i−2i−i2i2i2−i2i2−i2−i2i22−22−22−22−200-220000000000−22−22i2−i2i2−i2000000000000
χ552-2-222-22-22-22-222-2-200000000−2i2i−2i2i0000−2i2i−2i2ii2−i2−i2i2−i2i2i2−i2−22−22−22−22002-20000000000−22−22i2−i2i2−i2000000000000
χ562-2-222-22-22-22-222-2-200000000−2i2i−2i2i0000−2i2i−2i2i−i2i2i2−i2i2−i2−i2i22−22−22−22−2002-200000000002−22−2−i2i2−i2i2000000000000
χ572-2-222-2-22-22-22-22-222-2-2-2-2222000000002-2-222-2-222-2-22000000002-20000000000002-2-220000000000000000
χ582-2-222-2-22-22-22-22-222-2-2-2-2222000000002-2-22-222-2-222-2000000002-2000000000000-222-20000000000000000
χ592-2-222-2-22-22-22-22-222-2-2-2-222200000000-222-22-2-222-2-2200000000-22000000000000-222-20000000000000000
χ602-2-222-2-22-22-22-22-222-2-2-2-222200000000-222-2-222-2-222-200000000-220000000000002-2-220000000000000000
χ612-2-222-2-22-22-22-22-22-22222-2-2-2000000002-2-22000000002i−2i2i−2i−2i2i−2i2i-220000000000000000−2i2i2i−2i000000000000
χ622-2-222-2-22-22-22-22-22-22222-2-2-2000000002-2-2200000000−2i2i−2i2i2i−2i2i−2i-2200000000000000002i−2i−2i2i000000000000
χ632-2-222-2-22-22-22-22-22-22222-2-2-200000000-222-2000000002i−2i2i−2i−2i2i−2i2i2-200000000000000002i−2i−2i2i000000000000
χ642-2-222-2-22-22-22-22-22-22222-2-2-200000000-222-200000000−2i2i−2i2i2i−2i2i−2i2-20000000000000000−2i2i2i−2i000000000000
χ652-2-22-22-2-22-2-222-222-222-2-2-222000000000000000000002-2-22-222-200000000002-2-220000000000000000002-2
χ662-2-22-22-2-22-2-222-222-222-2-2-222000000000000000000002-2-22-222-20000000000-222-2000000000000000000-22
χ672-2-22-22-2-22-2-222-222-222-2-2-22200000000000000000000-222-22-2-2200000000002-2-22000000000000000000-22
χ682-2-22-22-2-22-2-222-222-222-2-2-22200000000000000000000-222-22-2-220000000000-222-20000000000000000002-2
χ694444-4-44-4-4-444-4-4-44-4-4-444-44400000000000000000000000000000000000000000000000000000000000000
χ704444-4-4-4444-4-44-4-4-400000000000000000000000000002222−22−22−22−2222220000000000000000000000000000000000
χ714444-4-4-4444-4-44-4-4-40000000000000000000000000000−22−2222222222−22−220000000000000000000000000000000000
χ7244-4-4444-444-44-4-4-4-4000000000000000000002222−22−22−22−222222000000000000000000000000000000000000000000
χ7344-4-4444-444-44-4-4-4-400000000000000000000−22−2222222222−22−22000000000000000000000000000000000000000000
χ7444-4-444-44-4-44-44-4-44-4-44-444-4400000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-4-444-4-4-44444-40000000000004-4-44000000000000000000000000000000000000000000000000000000
χ7644-4-4-4-444-4-4-44444-4000000000000-444-4000000000000000000000000000000000000000000000000000000
χ774-44-44-4444-4-4-4-4-444-44-44-44-4400000000000000000000000000000000000000000000000000000000000000
χ784-44-44-4-4-4-44444-44-40000000000000000000022−2222−22−2222−2222000000000000000000000000000000000000000000
χ794-44-44-4-4-4-44444-44-400000000000000000000−2222−222222−2222−22000000000000000000000000000000000000000000
χ804-44-4-444-4-44-4-444-444-444-4-4-4400000000000000000000000000000000000000000000000000000000000000
χ814-44-4-444-4-44-4-444-44-44-4-4444-400000000000000000000000000000000000000000000000000000000000000
χ824-44-4-44-444-444-44-4-4000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ834-44-4-44-444-444-44-4-400000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ844-4-44-4444-444-4-4-44-400000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000
χ854-4-44-4444-444-4-4-44-40000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000
χ864-4-44-44-4-44-4-444-4444-4-4444-4-400000000000000000000000000000000000000000000000000000000000000

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