If order of group is $p^2$, where $p$ is prime, how can you deduce $G$ is isomorphic to $C_{p^2}$ or $C_p \times C_p$?
75127
Group $G$ of order $p^2$: $\;G\cong \mathbb Z_{p^2}$ or $G\cong \mathbb Z_p \times \mathbb Z_p$
105139
Verification of Proof that a nonabelian group G of order pq where p and q are primes has a trivial center
51373
$G$ non abelian, order $p^3$ ($p$ prime). Suppose that the center is $p^2$, prove that $\exists\ x$ outside of the center, of order p
71262
Subgroups of order $9$ isomorphic to $C_3 \times C_3$ in $S_6$
91085
how to find $|GL_2(F_p)|$
143314
Sylow subgroup of $S_{p^2}$
104080
Group with order $pq$ has subgroups of order $p$ and $q$
125640
Group of order $p^2$ is abelian.
70001
Any group of order $2p$ has a subgroup of order $p~$($p$ being a prime)
49162
Classify all groups with order $pq$, $p$ is not equal to $q$
117468
$o(g^{k})=\frac{o(g)}{\gcd(o(g),k)}$ order of a power of a group element.
79055
Orders of a symmetric group
63499
Groups of prime squared order
15526
Question on groups of order $pq$
107511
If $G$ and $H$ are nonisomorphic group with same order then can we say that $Aut(G)$ is not isomorphic to $Aut(H)$?
39719
If $g$ is a primitive root of $p^2$ where $p$ is an odd prime, why is $g$ a primitive root of $p^k$ for any $k \geq 1$?
99205
Group of order $p^k q$ where $p$ and $q$ are distinct primes - how to prove this property?