Billiard table manufacturers have produced convertible billiard tables (in the broad sense) that double as dining tables or as table tennis, foosball, or air hockey, tables, with removable hard tops. Home pool tables, which often lack a ball-return system, are commonly either 4 × 8 ft or 3.5 × 7 ft models, a medium between 3 × 6 ft. bar/pub tables and 4.5 × 9 ft tournament-size models. Low-end tables tend toward the smaller range, and may have MDF or wood beds as an alternative to slate; those with light-weight beds may be foldable for storage, as with table tennis. Miniature tables
Character table of the group "G" can be deduced from its character table: The character table does not in general determine the group up to isomorphism: for example, the quaternion group "Q" and the dihedral group of 8 elements ("D") have the same character table. Brauer asked whether the character table, together with the knowledge of how the powers of elements of its conjugacy classes are distributed, determines a finite group up to isomorphism. In 1964, this was answered in the negative by E. C. Dade. The linear characters form a character group, which has important number theoretic connections. The outer automorphism