Finite Group Databasebeta

← Group #449095

Character table — Group #449095

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111111111112222222244444444444444444444444444448888888888888888888888161616161616161616161616
order12222222222222224444444444444444444488888888888888884444444444444488888888224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ611111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1111111-1-1
χ9111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111111111-1-11111-1-1-1-111-1-1-1-1-1-111-1-1
χ10111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111
χ11111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ12111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111111111-1-111-1-1-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1
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
χ172222222222222222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000-2-22200000000-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000022-2-2000000002200000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000-2-2-2-2000000002200000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000222200000000-2-200000000000000000000
χ212222-22-2-2-2-2-2222-2-22-2-2-2222-20000000000002i2i2i2i−2i−2i−2i−2i00000000000000002i2i−2i−2i00000000002-20000000000
χ222222-22-2-2-2-2-2222-2-22-2-2-2222-20000000000002i2i2i2i−2i−2i−2i−2i0000000000000000−2i−2i2i2i0000000000-220000000000
χ232222-22-2-2-2-2-2222-2-22-2-2-2222-2000000000000−2i−2i−2i−2i2i2i2i2i00000000000000002i2i−2i−2i0000000000-220000000000
χ242222-22-2-2-2-2-2222-2-22-2-2-2222-2000000000000−2i−2i−2i−2i2i2i2i2i0000000000000000−2i−2i2i2i00000000002-20000000000
χ25222-2-2-2222-2-22-2-22-2000000002i2i−2i−2i00002i2i−2i−2i22−2−222−2−2i2i2i2i2−i2−i2−i2−i2002-20000000000i2i2−i2−i222−2−2000000000000
χ26222-2-2-2222-2-22-2-22-2000000002i2i−2i−2i00002i2i−2i−2i−2−222−2−222−i2−i2−i2−i2i2i2i2i2002-20000000000−i2−i2i2i2−2−222000000000000
χ27222-2-2-2222-2-22-2-22-2000000002i2i−2i−2i0000−2i−2i2i2i22−2−222−2−2i2i2i2i2−i2−i2−i2−i200-220000000000−i2−i2i2i2−2−222000000000000
χ28222-2-2-2222-2-22-2-22-2000000002i2i−2i−2i0000−2i−2i2i2i−2−222−2−222−i2−i2−i2−i2i2i2i2i200-220000000000i2i2−i2−i222−2−2000000000000
χ29222-2-2-2222-2-22-2-22-200000000−2i−2i2i2i00002i2i−2i−2i22−2−222−2−2−i2−i2−i2−i2i2i2i2i200-220000000000i2i2−i2−i2−2−222000000000000
χ30222-2-2-2222-2-22-2-22-200000000−2i−2i2i2i00002i2i−2i−2i−2−222−2−222i2i2i2i2−i2−i2−i2−i200-220000000000−i2−i2i2i222−2−2000000000000
χ31222-2-2-2222-2-22-2-22-200000000−2i−2i2i2i0000−2i−2i2i2i22−2−222−2−2−i2−i2−i2−i2i2i2i2i2002-20000000000−i2−i2i2i222−2−2000000000000
χ32222-2-2-2222-2-22-2-22-200000000−2i−2i2i2i0000−2i−2i2i2i−2−222−2−222i2i2i2i2−i2−i2−i2−i2002-20000000000i2i2−i2−i2−2−222000000000000
χ3322-2-2222-2-22-2-22-22-222-2-22-2-222i−2i2i−2i2i2i−2i−2i00000000000000000000000000002-22-2000000000000002i−2i000000
χ3422-2-2222-2-22-2-22-22-222-2-22-2-222i−2i2i−2i2i2i−2i−2i0000000000000000000000000000-22-2200000000000000−2i2i000000
χ3522-2-2222-2-22-2-22-22-222-2-22-2-22−2i2i−2i2i−2i−2i2i2i00000000000000000000000000002-22-200000000000000−2i2i000000
χ3622-2-2222-2-22-2-22-22-222-2-22-2-22−2i2i−2i2i−2i−2i2i2i0000000000000000000000000000-22-22000000000000002i−2i000000
χ3722-2-2222-2-22-2-22-22-2-2-222-222-22i−2i2i−2i−2i−2i2i2i00000000000000000000000022-2-200000000000000002i−2i00000000
χ3822-2-2222-2-22-2-22-22-2-2-222-222-22i−2i2i−2i−2i−2i2i2i000000000000000000000000-2-2220000000000000000−2i2i00000000
χ3922-2-2222-2-22-2-22-22-2-2-222-222-2−2i2i−2i2i2i2i−2i−2i00000000000000000000000022-2-20000000000000000−2i2i00000000
χ4022-2-2222-2-22-2-22-22-2-2-222-222-2−2i2i−2i2i2i2i−2i−2i000000000000000000000000-2-22200000000000000002i−2i00000000
χ4122-2-2-22-222-22-22-2-222-2222-2-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i000000002i−2i−2i2i000000000000000000002-2
χ4222-2-2-22-222-22-22-2-222-2222-2-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i00000000−2i2i2i−2i00000000000000000000-22
χ4322-2-2-22-222-22-22-2-222-2222-2-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i000000002i−2i−2i2i00000000000000000000-22
χ4422-2-2-22-222-22-22-2-222-2222-2-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i00000000−2i2i2i−2i000000000000000000002-2
χ452-22-2-2222-222-2-22-2-2-2-22-222-22000000000000000000002-22-22-22-200002i−2i2i−2i000000000000000000002i−2i0000
χ462-22-2-2222-222-2-22-2-2-2-22-222-22000000000000000000002-22-22-22-20000−2i2i−2i2i00000000000000000000−2i2i0000
χ472-22-2-2222-222-2-22-2-2-2-22-222-2200000000000000000000-22-22-22-2200002i−2i2i−2i00000000000000000000−2i2i0000
χ482-22-2-2222-222-2-22-2-2-2-22-222-2200000000000000000000-22-22-22-220000−2i2i−2i2i000000000000000000002i−2i0000
χ492-2-2222-22-2-222-2-22-22-2-22-22-22000000002i−2i2i−2i2-22-22-22-2000000002i−2i0000000000002i−2i2i−2i0000000000000000
χ502-2-2222-22-2-222-2-22-22-2-22-22-22000000002i−2i2i−2i-22-22-22-22000000002i−2i000000000000−2i2i−2i2i0000000000000000
χ512-2-2222-22-2-222-2-22-22-2-22-22-2200000000−2i2i−2i2i2-22-22-22-200000000−2i2i000000000000−2i2i−2i2i0000000000000000
χ522-2-2222-22-2-222-2-22-22-2-22-22-2200000000−2i2i−2i2i-22-22-22-2200000000−2i2i0000000000002i−2i2i−2i0000000000000000
χ532-2-2222-22-2-222-2-22-2-222-22-22-2000000002i−2i2i−2i000000002i−2i−2i2i2i−2i−2i2i−2i2i00000000000000002-22-2000000000000
χ542-2-2222-22-2-222-2-22-2-222-22-22-2000000002i−2i2i−2i00000000−2i2i2i−2i−2i2i2i−2i−2i2i0000000000000000-22-22000000000000
χ552-2-2222-22-2-222-2-22-2-222-22-22-200000000−2i2i−2i2i000000002i−2i−2i2i2i−2i−2i2i2i−2i0000000000000000-22-22000000000000
χ562-2-2222-22-2-222-2-22-2-222-22-22-200000000−2i2i−2i2i00000000−2i2i2i−2i−2i2i2i−2i2i−2i00000000000000002-22-2000000000000
χ572-2-22-222-222-22-2-2-22222-2-22-2-20000000000002i−2i2i−2i−2i2i−2i2i0000000000002i−2i−2i2i00000000000000000000002-200
χ582-2-22-222-222-22-2-2-22222-2-22-2-20000000000002i−2i2i−2i−2i2i−2i2i000000000000−2i2i2i−2i0000000000000000000000-2200
χ592-2-22-222-222-22-2-2-22222-2-22-2-2000000000000−2i2i−2i2i2i−2i2i−2i0000000000002i−2i−2i2i0000000000000000000000-2200
χ602-2-22-222-222-22-2-2-22222-2-22-2-2000000000000−2i2i−2i2i2i−2i2i−2i000000000000−2i2i2i−2i00000000000000000000002-200
χ612-2-2-2-2-2-22-22-2222220000000000002-22-22-2-222−2−222−2−222−2−22−222−20000000000002-22−2−222−2−22000000000000
χ622-2-2-2-2-2-22-22-2222220000000000002-22-22-2-22−222−2−222−2−222−22−2−220000000000002-2−222−2−222−2000000000000
χ632-2-2-2-2-2-22-22-2222220000000000002-22-2-222-22−2−222−2−222−2−22−222−2000000000000-22−222−2−222−2000000000000
χ642-2-2-2-2-2-22-22-2222220000000000002-22-2-222-2−222−2−222−2−222−22−2−22000000000000-222−2−222−2−22000000000000
χ652-2-2-2-2-2-22-22-222222000000000000-22-222-2-222−2−222−2−22−222−22−2−22000000000000-222−2−22−222−2000000000000
χ662-2-2-2-2-2-22-22-222222000000000000-22-222-2-22−222−2−222−22−2−22−222−2000000000000-22−222−22−2−22000000000000
χ672-2-2-2-2-2-22-22-222222000000000000-22-22-222-22−2−222−2−22−222−22−2−220000000000002-2−222−22−2−22000000000000
χ682-2-2-2-2-2-22-22-222222000000000000-22-22-222-2−222−2−222−22−2−22−222−20000000000002-22−2−22−222−2000000000000
χ694444-44-4-4-4-4-4444-4-4-4444-4-4-4400000000000000000000000000000000000000000000000000000000000000
χ70444-44-4-4-4-4444-4-4-44000000000000000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ71444-44-4-4-4-4444-4-4-4400000000000000000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ7244-444-4-4444-4-4-44-4-400000000000000000000000000002222−22−22−22−2222220000000000000000000000000000000000
χ7344-444-4-4444-4-4-44-4-40000000000000000000000000000−22−2222222222−22−220000000000000000000000000000000000
χ7444-44-4-44-4-4-44-4-4444000000004-4-440000000000000000000000000000000000000000000000000000000000
χ7544-44-4-44-4-4-44-4-444400000000-444-40000000000000000000000000000000000000000000000000000000000
χ7644-4-4-44-444-44-44-4-44-44-4-4-444400000000000000000000000000000000000000000000000000000000000000
χ774-4444-444-4-4-4-44-4-4400000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000
χ784-4444-444-4-4-4-44-4-440000000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000
χ794-444-4-4-4-4444-44-44-40000000000004i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ804-444-4-4-4-4444-44-44-4000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ814-44-444-4-44-4-4-4-44444-44-4-4-44400000000000000000000000000000000000000000000000000000000000000
χ824-44-444-4-44-4-4-4-4444-44-4444-4-400000000000000000000000000000000000000000000000000000000000000
χ834-44-4-4444-444-4-44-4-444-44-4-44-400000000000000000000000000000000000000000000000000000000000000
χ844-4-44-444-444-44-4-4-44-4-4-444-44400000000000000000000000000000000000000000000000000000000000000
χ854-4-4-44-44-44-44444-4-4000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ864-4-4-44-44-44-44444-4-400000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000

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