For any group $G$, the absolute center $L(G)$ of $G$ is defined as $$L(G) = \lbrace g\in G\mid \alpha(g)=g,\text{ for all }\alpha\in Aut(G) \rbrace,$$ where $Aut(G)$ denote the group of all automorphisms of $G$. Observe that $L(G)\leq Z(G)$, where $Z(G)$ denotes the center of $G$. The programme to calculate $L(G)$ for a finite $p$-group $G$ in Gap is known. I want to calculate the $L(G)$ of the following group but I don't know how to enter it in Gap: $$\Phi_2(22)= \langle a,b,c|[b,a]=a^p=c,b^{p^2}=c^p=1\rangle$$
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1$\begingroup$ I wonder if your question might fare better on MathSE. Both here & there have GAP tags (which you might add), but MSE has a higher volume of such questions. (I'm a little surprised there isn't a GAP Stack Exchange, as there is for Mathematica.) $\endgroup$– Brian HopkinsCommented Apr 16, 2019 at 18:08
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2$\begingroup$ I am doubtful whether questions of the type "how do I do this specific calculation in GAP?", which could reasonably be answered by (polite version) "look in the manual" are suitable for either MO or MSE. There is a fine line here, because they are suitable if there is some question of discussing which algorithms might apply. $\endgroup$– Derek HoltCommented Apr 16, 2019 at 22:16
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