We have gathered enough knowledge to determine all groups of order less than 12. We do this `up to isomorphism': for each isomorphism class, we give one representative.

Theorem

The table below contains, up to isomorphism, all groups of order less than 12.


order
group
number
1
{e}
1
2
Z/2Z
1
3
Z/3Z
1
4
Z/4Z , (Z/2Z)2
2
5
Z/5Z
1
6
Z/6Z, S3
2
7
Z/7Z
1
8
Z/8Z, Z/4Z×Z/2Z, (Z/2Z)3, Q, D4
5
9
Z/9Z, (Z/3Z)2
2
10
Z/10Z, D5
2
11
Z/11Z
1