Finite Group Databasebeta

← Group #499669

Character table — Group #499669

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222222222222244444444444444444444444444444444444444444444444416161616161616161616161616161616
order1222222244444444444444448888888888888888444444448888888816161616161616161616161616161616161616161616161616161616161616162222444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1111111-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-111
χ911111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11111
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ17222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ18222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2000000000000000022-2-222-2-2000000002222−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−20000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2000000000000000022-2-222-2-200000000−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−222220000000000000000
χ212222222222222222-2-2-2-2-2-2-2-20000000000000000-2-222-2-222000000002222−2−2−2−22222−2−2−2−2−2−2−2−22222−2−2−2−222220000000000000000
χ222222222222222222-2-2-2-2-2-2-2-20000000000000000-2-222-2-22200000000−2−2−2−22222−2−2−2−222222222−2−2−2−22222−2−2−2−20000000000000000
χ2322222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000022-2-2-2-222000000002222−2−2−2−2−2−2−2−222222222−2−2−2−2−2−2−2−222220000000000000000
χ2422222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000022-2-2-2-22200000000−2−2−2−222222222−2−2−2−2−2−2−2−222222222−2−2−2−20000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000-2-22222-2-2000000002222−2−2−2−2−2−2−2−22222−2−2−2−222222222−2−2−2−20000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000-2-22222-2-200000000−2−2−2−222222222−2−2−2−22222−2−2−2−2−2−2−2−222220000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ29222-2-2-2-222222-2-2-2-222-2-222-2-200000000000000000000000022-2-222-2-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ30222-2-2-2-222222-2-2-2-222-2-222-2-200000000000000000000000022-2-222-2-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ31222-2-2-2-222222-2-2-2-222-2-222-2-2000000000000000000000000-2-222-2-222i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ32222-2-2-2-222222-2-2-2-222-2-222-2-2000000000000000000000000-2-222-2-222−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ33222-2-2-2-222222-2-2-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ34222-2-2-2-222222-2-2-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ35222-2-2-2-222222-2-2-2-2-2-222-2-222-2-2-2-22222-2-2-2-2222200000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ36222-2-2-2-222222-2-2-2-2-2-222-2-222-2-2-2-22222-2-2-2-222220000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ37222-2-2-2-22-2-2-2-2222222-2-2-2-2222222-2-2-2-2-2-2-2-2222200000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ38222-2-2-2-22-2-2-2-2222222-2-2-2-2222222-2-2-2-2-2-2-2-222220000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ39222-2-2-2-22-2-2-2-2222222-2-2-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ40222-2-2-2-22-2-2-2-2222222-2-2-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ41222-2-2-2-22-2-2-2-22222-2-22222-2-200000000000000000000000022-2-2-2-222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ42222-2-2-2-22-2-2-2-22222-2-22222-2-200000000000000000000000022-2-2-2-222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ43222-2-2-2-22-2-2-2-22222-2-22222-2-2000000000000000000000000-2-22222-2-2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ44222-2-2-2-22-2-2-2-22222-2-22222-2-2000000000000000000000000-2-22222-2-2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ4522-222-2-2-22i2i−2i−2i2i2i−2i−2i00000000i2i2−i2−i2i2i2−i2−i222−2−222−2−2002-2002i−2i2−22−2i2−i2i2−i2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ50000000000000000
χ4622-222-2-2-22i2i−2i−2i2i2i−2i−2i00000000i2i2−i2−i2i2i2−i2−i222−2−222−2−2002-2002i−2i2−22−2i2−i2i2−i2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ50000000000000000
χ4722-222-2-2-22i2i−2i−2i2i2i−2i−2i00000000i2i2−i2−i2i2i2−i2−i222−2−222−2−200-2200−2i2i−22−22−i2i2−i2i2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ50000000000000000
χ4822-222-2-2-22i2i−2i−2i2i2i−2i−2i00000000i2i2−i2−i2i2i2−i2−i222−2−222−2−200-2200−2i2i−22−22−i2i2−i2i2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ50000000000000000
χ4922-222-2-2-22i2i−2i−2i2i2i−2i−2i00000000−i2−i2i2i2−i2−i2i2i2−2−222−2−222002-2002i−2i−22−22−i2i2−i2i2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ70000000000000000
χ5022-222-2-2-22i2i−2i−2i2i2i−2i−2i00000000−i2−i2i2i2−i2−i2i2i2−2−222−2−222002-2002i−2i−22−22−i2i2−i2i2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ70000000000000000
χ5122-222-2-2-22i2i−2i−2i2i2i−2i−2i00000000−i2−i2i2i2−i2−i2i2i2−2−222−2−22200-2200−2i2i2−22−2i2−i2i2−i2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ70000000000000000
χ5222-222-2-2-22i2i−2i−2i2i2i−2i−2i00000000−i2−i2i2i2−i2−i2i2i2−2−222−2−22200-2200−2i2i2−22−2i2−i2i2−i2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ70000000000000000
χ5322-222-2-2-2−2i−2i2i2i−2i−2i2i2i00000000i2i2−i2−i2i2i2−i2−i2−2−222−2−222002-200−2i2i−22−22i2−i2i2−i2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ70000000000000000
χ5422-222-2-2-2−2i−2i2i2i−2i−2i2i2i00000000i2i2−i2−i2i2i2−i2−i2−2−222−2−222002-200−2i2i−22−22i2−i2i2−i2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ70000000000000000
χ5522-222-2-2-2−2i−2i2i2i−2i−2i2i2i00000000i2i2−i2−i2i2i2−i2−i2−2−222−2−22200-22002i−2i2−22−2−i2i2−i2i2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ70000000000000000
χ5622-222-2-2-2−2i−2i2i2i−2i−2i2i2i00000000i2i2−i2−i2i2i2−i2−i2−2−222−2−22200-22002i−2i2−22−2−i2i2−i2i2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ70000000000000000
χ5722-222-2-2-2−2i−2i2i2i−2i−2i2i2i00000000−i2−i2i2i2−i2−i2i2i222−2−222−2−2002-200−2i2i2−22−2−i2i2−i2i2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ50000000000000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.