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Following my previous question I have two questions:

1.the extensions of the group is associative or not, i.e. as we know by the notations of atlas if $S={\rm PSL}(2,q)$, where $q=p^f>9$, then $2.{\rm PSL}(2,q)\cong {\rm SL}(2,q)$, so $2.S.f\cong {\rm SL}.f$?

  1. Who we can determine the character degrees of $2.S.f$ as we stated above, in fact by "Character degrees of extensions of PSL 2 (q) and SL 2 (q); by Donald L. White, Journal of Group Theory 01/2013; 1(1). DOI: 10.1515/jgt-2012-0026 " we have the character degrees of the extensions of ${\rm SL}(2,q)$, but in that paper ${\rm SL}(2,q)\langle \delta\rangle\langle \varphi\rangle$ are considered. So how we can determine the character degrees of ${\rm SL}(2,q)\langle \varphi\rangle$?

Thanks for the answers in my previous question and for this ones.

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    $\begingroup$ In the paper, the character degrees of ${\rm SL}(2,q)\langle \delta^\alpha \rangle \langle \phi^\beta \rangle$ are determined for all $\alpha$ and $\beta$, so the case you are asking about is $\alpha=q-1$, $\beta=1$. $\endgroup$
    – Derek Holt
    Commented Oct 6, 2015 at 12:41

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