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user 36466
5
votes
Accepted
Is there a maximal subgroup of depth 3?
As Noah points out, you are looking for some (core-free) maximal subgroup $H<G$ such that $1_H^G$ has nonzero inner product with every irreducible character.
Say $G=L_2(p)$ with $p$ prime and $p \equ …
- 3,571
3
votes
Accepted
Products of maximal inclusions of finite groups with a non-obvious intermediate
If I understand correctly, each $H_i$ is maximal in $G_i$ and core-free. In particular, unless $G_i$ has prime order $p$, $H_i$ is not normal in $G_i$.
Let $X$ be a subgroup of $G_1 \times G_2$. Fo …
- 3,571