Classifying Groups of Small Order

For groups of finite order there are only a finite number of groups, up to isomorphism. For example, ifprime, thenthe cyclic group of orderIfis not prime then more possibilities exist, but  there is still a finite number of possible groups up to isomorphism.

For groups up to order 8 these are:

Order

Groups

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Various methods exist for finding these groups – using Sylow's theorems, analysis of the conjugacy class equation, Lagrange's equation.

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