Without space parity inversion, it is not an irreducible representation.
The table also shows which irreducible representation transforms in the same way (on the right hand side of the tables).
The number of conjugacy classes and irreducible representations is 6.
The second means that irreducible representations will occur in dimensions greater than 1.
In this case, it suffices to understand only the irreducible representations.
An irreducible representation of G is completely determined by its character.
They are called different irreducible representations of the algebra.
The group has an irreducible representation of dimension 253 over the field with 3 elements.
In particular the double cover has an irreducible 6-dimensional representation over the field of 3 elements.
Such irreducible representations are often described as having class one.