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This operation table is abstractly the same as, or isomorphic to, the versions with the <math>\operatorname{E}_{ij}</math> operators and the <math>\operatorname{T}_{ij}</math> transformations that we discussed earlier. That is to say, the story is the same — only the names have been changed. An abstract group can have a multitude of significantly and superficially different representations. Even after we have long forgotten the details of the particular representation that we may have come in with, there are species of concrete representations, called the ''regular representations'', that are always readily available, as they can be generated from the mere data of the abstract operation table itself.
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For example, select a group element from the top margin of the Table,
For example, select a group element from the top margin of the Table,
and "consider its effects" on each of the group elements as they are
and "consider its effects" on each of the group elements as they are
