An abstract group is a group characterized only by its abstract properties and not by the particular representations chosen for elements.
For example, there are two distinct abstract groups on four elements: the vierergruppe 
and the cyclic
group C4. A number of particular examples of the abstract group 
are the point groups 
(unfortunately, the symbols for the point groups 
are the same as those for the abstract cyclic groups 
to which they are isomorphic) and
.
Abstract Group
See also
Finite Group, GroupExplore with Wolfram|Alpha
References
Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 74 and 85, 1993.Referenced on Wolfram|Alpha
Abstract GroupCite this as:
Weisstein, Eric W. "Abstract Group." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AbstractGroup.html