Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orbits classifying extensions of prime power order groups   The strong isomorphism classes of extensions of finite groups are
parametrized by orbits of a prescribed action on the second cohomology group.
We study these orbits in the case of extensions of a finite abelian $p$-group
by a cyclic factor of order $p$. As an application, we compute number and sizes
of these orbits when the initial $p$-group is generated by at most $3$
elements.

3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ