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I have a non-split extension $2^8\mathbin.(2^7\mathbin:\operatorname{Sp}(6,2))$ of $2^8$ by $2^7\mathbin:\operatorname{Sp}(6,2)$. The question is how does $2^7\mathbin:\operatorname{Sp}(6,2)$ act on $ …

Let $P$ be a special $p$-group $p^{n+m}$. So $P$ will have $p^m$ linear characters. How does one describe (or determine) the other ordinary irreducible characters of $P$ and will they all be faithf …

Let $G=p^{n+m}.Q$ be an extension group of the special $p$-group $p^{n+m}$ by a group $Q$. Now $p^{n+m}=p^n{{}^\cdot}p^m$. How does one show that $\frac{G}{p^n}\cong p^m.Q$? Or equivalently that $G \c …

Let $G=p^{1+2n}{.}Q$, $n>1$, be a finite extension group of an extra-special $p$-group $N=p^{1+2n}$ by a group $Q$, where $Q$ is a linear group of dimension $2n$ over $GF(p)$. It seems that the actio …

Let $G=2^{2n}{:}Sp_{2n}(2)$ be the split extension, where the symplectic group $Sp_{2n}(2)$ acts naturally on the vector space $2^{2n}$. With the aid of GAP it turns out that the automorphism group $\ …