Can you show example a group of order $p^2$ besides $Z_{p^2} $ and $Z_p \oplus Z_p$?
3213
There exists only two groups of order $p^2$ up to isomorphism.
43580
Let $p$ be a prime number and $G$ a non abelian group or order $p^3$. Prove that $Z(G) = [G,G]$.
8742
Examples and further results about the order of the product of two elements in a group
38853
Cyclic group of prime order
62603
Characterizations of the $p$-Prüfer group
125640
Group of order $p^2$ is abelian.
33300
Showing order of $Z (G) =1$ or $pq$
92750
Groups where all elements are order 3
42389
If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
131204
A non-trivial normal subgroup N of a finite group G or order $p^n$ is such that $N\cap Z(G)\neq \{ 1\}$
61084
Examples of non-isomorphic fields with isomorphic group of units and additive group structure
41231
Subgroups of (Z,+) of order n
47239
For $p,q$ primes such that $q|p-1$, show there is only one non-abelian group of order $pq$, up to isomorphism
15341
Non-abelian finite group in which more than half of the elements have order $2$
141125
Group with order $p^2$ must be abelian . How to prove that?
8746
Groups of order $pq$ without using Sylow theorems
60075
Does there exist an $n$ such that all groups of order $n$ are Abelian?