$G$ is the order $55$ group described by $G=\langle x,y \mid x^{11}=y^5=1, yxy^{-1}=x^4\rangle$. I am tasked with showing $|G/C(G)|=5$, but I don't know what $C(G)$ is supposed to be. It can't be the centre, as the centre is trivial - we need $|C(G)|=11$, but I cant think of what else it could be. Any advice?
2026-03-29 12:23:57.1774787037
Notation: What is $C(G)$?
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