Can a group be recovered from its order and automorphism?
107511
If $G$ and $H$ are nonisomorphic group with same order then can we say that $Aut(G)$ is not isomorphic to $Aut(H)$?
88262
How to enumerate subgroups of each order of $S_4$ by hand
84132
Number of preimages of a group element under a homomorphism.
73988
Characterize the groups $G$ for which the map $\iota: G \to G$, sending $x \mapsto x^{-1}$ for all $x \in G$, is an automorphism of $G$
143550
Order of product of two elements in an abelian group
44361
An automorphism that has no fixed points except for the identity and is its own inverse implies commutativity
131946
Order of an Element Under a Homomorphism
8746
Groups of order $pq$ without using Sylow theorems
123796
Order of automorphism group of a $p$-group is divisible by $p$.
77757
Infer the second isomorphism theorem from the first one
133497
Group Membership Test for Permutations
85018
When is the automorphism group of the Cayley graph of $G$ just $G$?
114811
Characteristic subgroups and automorphisms
101079
Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$
63499
Groups of prime squared order
72853
What is the number of automorphisms (including identity) for permutation group $S_3$ on 3 letters?
72991
Is every group the automorphism group of a group?