Finite Group Databasebeta

← Group #7623027

Character table — Group #7623027

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1122222222222222222224444444444444444888888888888888888888888888888888881616161616161616
order122222222444444448888448888888888888822224444444888888881616161616161616161616161616161644444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111-1-111-1-11111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111-1-111-1-11111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111-1-111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111-1-111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111-1-1-1-1111-1-1-1-111111111111-1-1-1-1111-1-1-1-111-1-111-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111-1-1-1-1111-1-1-1-111111111111-1-1-1-1111-1-1-1-111-1-111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ111111-1-1-1-1111-1-1-1-111111111111-1-1-1-1111-1-1-1-1-1-111-1-1111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ121111-1-1-1-1111-1-1-1-111111111111-1-1-1-1111-1-1-1-1-1-111-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ131111-1-1-1-1111-1-1-1-111-1-111-1-1111-1-1-1-1-1-1-1111111-1-111-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ141111-1-1-1-1111-1-1-1-111-1-111-1-1111-1-1-1-1-1-1-1111111-1-111-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ151111-1-1-1-1111-1-1-1-111-1-111-1-1111-1-1-1-1-1-1-11111-1-111-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ161111-1-1-1-1111-1-1-1-111-1-111-1-1111-1-1-1-1-1-1-11111-1-111-1-111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ1711-1-111-1-11-1-111-1-1111111111-1-111-1-11-1-111-1-11-11-11-11-1-11-111-1-111-1-111-1-111-1-111-1-111-1-11-11-11-11-1
χ1811-1-111-1-11-1-111-1-1111111111-1-111-1-11-1-111-1-11-11-11-11-1-11-111-1-111-1-1-1-111-1-111-1-111-1-111-11-11-11-11
χ1911-1-111-1-11-1-111-1-1111111111-1-111-1-11-1-111-1-1-11-11-11-11-11-1-1-111-1-11111-1-111-1-111-1-111-1-1-11-11-11-11
χ2011-1-111-1-11-1-111-1-1111111111-1-111-1-11-1-111-1-1-11-11-11-11-11-1-1-111-1-111-1-111-1-111-1-111-1-1111-11-11-11-1
χ2111-1-111-1-11-1-111-1-111-1-111-1-11-1-111-1-1-111-1-1111-11-11-11-11-11-1-111-1-11111-1-111-1-1-1-111-1-1111-11-1-11-11
χ2211-1-111-1-11-1-111-1-111-1-111-1-11-1-111-1-1-111-1-1111-11-11-11-11-11-1-111-1-111-1-111-1-11111-1-111-1-1-11-111-11-1
χ2311-1-111-1-11-1-111-1-111-1-111-1-11-1-111-1-1-111-1-111-11-11-11-111-1111-1-111-1-111-1-111-1-1-1-111-1-111-11-111-11-1
χ2411-1-111-1-11-1-111-1-111-1-111-1-11-1-111-1-1-111-1-111-11-11-11-111-1111-1-111-1-1-1-111-1-11111-1-111-1-11-11-1-11-11
χ2511-1-1-1-1111-1-1-1-111111111111-1-1-1-1111-1-1-1-1111-1-111-1-11-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-111-1-11
χ2611-1-1-1-1111-1-1-1-111111111111-1-1-1-1111-1-1-1-1111-1-111-1-11-1-1111-1-1-1-111-1-11111-1-1-1-11111-1-1-111-1-111-1
χ2711-1-1-1-1111-1-1-1-111111111111-1-1-1-1111-1-1-1-111-111-1-111-1-1-11-1-11111-1-111-1-1-1-11111-1-1-1-111-111-1-111-1
χ2811-1-1-1-1111-1-1-1-111111111111-1-1-1-1111-1-1-1-111-111-1-111-1-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-11-1-111-1-11
χ2911-1-1-1-1111-1-1-1-11111-1-111-1-11-1-1-1-111-11111-1-11-1-111-1-1111-1-1-11111-1-111-1-1-1-111-1-11111-1-11-1-11-111-1
χ3011-1-1-1-1111-1-1-1-11111-1-111-1-11-1-1-1-111-11111-1-11-1-111-1-1111-1-1-11111-1-1-1-11111-1-111-1-1-1-111-111-11-1-11
χ3111-1-1-1-1111-1-1-1-11111-1-111-1-11-1-1-1-111-11111-1-1-111-1-111-111-111-1-1-1-11111-1-1-1-111-1-11111-1-1-111-11-1-11
χ3211-1-1-1-1111-1-1-1-11111-1-111-1-11-1-1-1-111-11111-1-1-111-1-111-111-111-1-1-1-111-1-11111-1-111-1-1-1-1111-1-11-111-1
χ332222222222222222222-2-2-2-2-2-2-2-2-2-2-2222222200000000-2-2-200000000000000000000000000000000
χ3422222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022200000000000000000000000000000000
χ352222-2-2-2-2222-2-2-2-22222-2-2-2-2-2-2-22222222-2-2-2-200000000-22200000000000000000000000000000000
χ362222-2-2-2-2222-2-2-2-222-2-2-2-222-2-2-22222-2-2-22222000000002-2-200000000000000000000000000000000
χ37222-22-22-2-22-22-22-22-2002200-22-22-22-20000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ38222-22-22-2-22-22-22-22-2002200-22-22-22-2000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ39222-22-22-2-22-22-22-22-200-2-2002-22-22-220000000222-2-2-2-2200000000000000000000000000000000000
χ40222-22-22-2-22-22-22-22-200-2-2002-22-22-220000000-2-2-22222-200000000000000000000000000000000000
χ41222-22-2-22-2-22-222-2-222200000000000-22-22-22-20000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ42222-22-2-22-2-22-222-2-222200000000000-22-22-22-20000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ43222-22-2-22-2-22-222-2-22-2-2000000000002-22-22-220000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ44222-22-2-22-2-22-222-2-22-2-2000000000002-22-22-220000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ45222-2-222-2-2-222-2-22-222200000000000-22-2-22-220000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ46222-2-222-2-2-222-2-22-222200000000000-22-2-22-220000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ47222-2-222-2-2-222-2-22-22-2-2000000000002-222-22-20000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ48222-2-222-2-2-222-2-22-22-2-2000000000002-222-22-20000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ49222-2-22-22-22-2-22-222-2002200-22-2-22-220000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ50222-2-22-22-22-2-22-222-2002200-22-2-22-22000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ51222-2-22-22-22-2-22-222-200-2-2002-222-22-2000000022-22-2-22-200000000000000000000000000000000000
χ52222-2-22-22-22-2-22-222-200-2-2002-222-22-20000000-2-22-222-2200000000000000000000000000000000000
χ5322-222-22-2-22-2-22-22-222200000000000-2-222-2-220000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ5422-222-22-2-22-2-22-22-222200000000000-2-222-2-220000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ5522-222-22-2-22-2-22-22-22-2-20000000000022-2-222-20000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ5622-222-22-2-22-2-22-22-22-2-20000000000022-2-222-20000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ5722-222-2-22-2-222-2-222-2002200-2-222-2-220000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ5822-222-2-22-2-222-2-222-2002200-2-222-2-22000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ5922-222-2-22-2-222-2-222-200-2-20022-2-222-200000002-222-22-2-200000000000000000000000000000000000
χ6022-222-2-22-2-222-2-222-200-2-20022-2-222-20000000-22-2-22-22200000000000000000000000000000000000
χ6122-22-222-2-2-22-222-22-2002200-2-22-222-20000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ6222-22-222-2-2-22-222-22-2002200-2-22-222-2000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ6322-22-222-2-2-22-222-22-200-2-20022-22-2-2200000002-2-2-2-222200000000000000000000000000000000000
χ6422-22-222-2-2-22-222-22-200-2-20022-22-2-220000000-22222-2-2-200000000000000000000000000000000000
χ6522-22-22-22-22-22-22-2-222200000000000-2-22-222-20000000000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000
χ6622-22-22-22-22-22-22-2-222200000000000-2-22-222-20000000000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000
χ6722-22-22-22-22-22-22-2-22-2-20000000000022-22-2-220000000000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000
χ6822-22-22-22-22-22-22-2-22-2-20000000000022-22-2-220000000000000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000
χ6922-2-222-2-22-2-222-2-22222-2-2-2-2-222-2-2222-2-222-2-2000000002-2200000000000000000000000000000000
χ7022-2-222-2-22-2-222-2-222-2-2-2-222-222-2-222-222-2-22200000000-22-200000000000000000000000000000000
χ7122-2-2-2-2222-2-2-2-2222222-2-2-2-2-22222-2-22-2-2-2-2220000000022-200000000000000000000000000000000
χ7222-2-2-2-2222-2-2-2-22222-2-2-2-222-22222-2-2-22222-2-200000000-2-2200000000000000000000000000000000
χ73444444-4-44-4-4-4-444-4-4000000000000000000000000000000000000000000000000000000000000000
χ744444-4-4444-4-444-4-4-4-4000000000000000000000000000000000000000000000000000000000000000
χ7544-4-44444444-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-4-4-4-44444444-4-4000000000000000000000000000000000000000000000000000000000000000
χ778-80000000000000004i2−4i24i2−4i24-4000000000000000000000000000000000000000000000000000000000
χ788-80000000000000004i2−4i2−4i24i2-44000000000000000000000000000000000000000000000000000000000
χ798-8000000000000000−4i24i24i2−4i2-44000000000000000000000000000000000000000000000000000000000
χ808-8000000000000000−4i24i2−4i24i24-4000000000000000000000000000000000000000000000000000000000

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