Finite Group Databasebeta

← Group #316849

Character table — Group #316849

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888822444444448888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ9111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1
χ10111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ11111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111
χ12111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1722222222222-2-2-2-22-2-222-2-22222-2-2-2-2002-200000022-2-2000000000000000000000000
χ1822222222222-2-2-2-22-2-222-2-2-2-2-2-22222002-2000000-2-222000000000000000000000000
χ1922222222222-2-2-2-22-2-2-2-2222222-2-2-2-200-22000000-2-222000000000000000000000000
χ2022222222222-2-2-2-22-2-2-2-222-2-2-2-2222200-2200000022-2-2000000000000000000000000
χ2122222222-2-2-22222-2-2-222220000000022-2-2-2-222-2-20000000000000000000000000000
χ2222222222-2-2-22222-2-2-2222200000000-2-2-2-222-2-2220000000000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-2000000002222-2-2-2-2220000000000000000000000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-200000000-2-2222222-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-20000000000-2200000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-20000000000-220000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-22200000000002-200000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-22200000000002-20000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ29222-2-2-2-2200022-2-20002i−2i2i−2ii2i2−i2−i2i2i2−i2−i200002i−2i002-22−22−22−22−2i2−i2i2−i20000000000000000
χ30222-2-2-2-2200022-2-20002i−2i2i−2ii2i2−i2−i2i2i2−i2−i20000−2i2i00-222−22−2−22−22−i2i2−i2i20000000000000000
χ31222-2-2-2-2200022-2-20002i−2i2i−2i−i2−i2i2i2−i2−i2i2i200002i−2i002-2−22−22−22−22−i2i2−i2i20000000000000000
χ32222-2-2-2-2200022-2-20002i−2i2i−2i−i2−i2i2i2−i2−i2i2i20000−2i2i00-22−22−222−22−2i2−i2i2−i20000000000000000
χ33222-2-2-2-2200022-2-2000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i200002i−2i00-22−22−222−22−2−i2i2−i2i20000000000000000
χ34222-2-2-2-2200022-2-2000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i20000−2i2i002-2−22−22−22−22i2−i2i2−i20000000000000000
χ35222-2-2-2-2200022-2-2000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i200002i−2i00-222−22−2−22−22i2−i2i2−i20000000000000000
χ36222-2-2-2-2200022-2-2000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i20000−2i2i002-22−22−22−22−2−i2i2−i2i20000000000000000
χ37222-2-2-2-22000-2-2220002i−2i−2i2ii2i2−i2−i2−i2−i2i2i22-200002i−2i002−2−22i2−i2−i2i2−222−20000000000000000
χ38222-2-2-2-22000-2-2220002i−2i−2i2ii2i2−i2−i2−i2−i2i2i2-220000−2i2i002−2−22−i2i2i2−i22−2−220000000000000000
χ39222-2-2-2-22000-2-2220002i−2i−2i2i−i2−i2i2i2i2i2−i2−i22-200002i−2i00−222−2−i2i2i2−i22−2−220000000000000000
χ40222-2-2-2-22000-2-2220002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2-220000−2i2i00−222−2i2−i2−i2i2−222−20000000000000000
χ41222-2-2-2-22000-2-222000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i22-20000−2i2i00−222−2i2−i2−i2i22−2−220000000000000000
χ42222-2-2-2-22000-2-222000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2-2200002i−2i00−222−2−i2i2i2−i2−222−20000000000000000
χ43222-2-2-2-22000-2-222000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i22-20000−2i2i002−2−22−i2i2i2−i2−222−20000000000000000
χ44222-2-2-2-22000-2-222000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2-2200002i−2i002−2−22i2−i2−i2i22−2−220000000000000000
χ452-2-222-2-2222-22-22-2-22-200002i−2i2i−2i2i−2i2i−2i0000000000000000000000002i−2i2-20000000000
χ462-2-222-2-2222-22-22-2-22-200002i−2i2i−2i2i−2i2i−2i000000000000000000000000−2i2i-220000000000
χ472-2-222-2-2222-22-22-2-22-20000−2i2i−2i2i−2i2i−2i2i0000000000000000000000002i−2i-220000000000
χ482-2-222-2-2222-22-22-2-22-20000−2i2i−2i2i−2i2i−2i2i000000000000000000000000−2i2i2-20000000000
χ492-2-222-2-2222-2-22-22-2-2200002i−2i2i−2i−2i2i−2i2i00000000000000000000002i−2i00002-200000000
χ502-2-222-2-2222-2-22-22-2-2200002i−2i2i−2i−2i2i−2i2i0000000000000000000000−2i2i0000-2200000000
χ512-2-222-2-2222-2-22-22-2-220000−2i2i−2i2i2i−2i2i−2i00000000000000000000002i−2i0000-2200000000
χ522-2-222-2-2222-2-22-22-2-220000−2i2i−2i2i2i−2i2i−2i0000000000000000000000−2i2i00002-200000000
χ5344-44-44-4-44-440000-40000000000000000000000000000000000000000000022−22000000
χ5444-44-44-4-44-440000-400000000000000000000000000000000000000000000−2222000000
χ5544-44-44-4-4-44-40000400000000000000000000000000000000000000000000002i2−2i20000
χ5644-44-44-4-4-44-4000040000000000000000000000000000000000000000000000−2i22i20000
χ574-444-4-44-44-4-4000040000000000000000000000000000000000000000000000002i2−2i200
χ584-444-4-44-44-4-400004000000000000000000000000000000000000000000000000−2i22i200
χ594-444-4-44-4-4440000-40000000000000000000000000000000000000000000000000022−22
χ604-444-4-44-4-4440000-400000000000000000000000000000000000000000000000000−2222
χ614-4-444-4-44-4-444-44-44-4400000000000000000000000000000000000000000000000000
χ624-4-444-4-44-4-44-44-4444-400000000000000000000000000000000000000000000000000
χ634-4-4-4-44440004-4-44000000022−22−222222−22−222200000000000000000000000000000000000000
χ644-4-4-4-44440004-4-440000000−222222−22−222222−2200000000000000000000000000000000000000
χ654-4-4-4-4444000-444-4000000022−22−2222−222222−2200000000000000000000000000000000000000
χ664-4-4-4-4444000-444-40000000−222222−2222−22−222200000000000000000000000000000000000000
χ6788-8-88-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-888-8-8000000000000000000000000000000000000000000000000000000000000

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