3rd year mathematics undergraduate, particularly interested in abstract algebra.

Some group theory questions I've asked that provide info about classification of groups of orders, simplicity of them, etc, which I find interesting:

• Conjectures for finite groups that fail with large counterexamples

• For which $n$ in $2048 < n < 4096$ is the exact number of groups of order $n$ up to isomorphism currently unknown?

• To what extent can we determine the simplicity or non-simplicity of groups based on their prime decompositions?

• If $p>3$ is a prime congruent to $3 \bmod 4$, how can I prove that are there only two non-abelian groups of order $4p$?

• Non-abelian groups of order $27p$ for $p>3$ prime, $3 \nmid p-1$. Verification of conjecture and what is needed to prove it