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In the book: J.H. Conway and R. T. Curtis and et al, Atlas of finite groups: Maximal Subgroups and Ordinary Characters for Simple Groups, Oxford University Press 1985.

Page:xvii,

"A central extension, or covering group, of $G$ is a group $H$ with a central subgroup $C$ whose quotient is $G$. It is called a proper covering group if $C$ is contained in the commutator subgroup of $H$. The groups $C$ that arise for proper covers of a group $G$ are each of them quotients of a largest one, called the Schur multiplier (or multiplicator), $Mult(G)$, of $G$."

But I don't understand this definition. For example:

Suppose that $H/T\cong A_{13}$ where $T\leqslant Z(H)\cap H'$. We know the Schur multiplier $Mult(A_{13})\cong C_2$.

Question: $T\cong 1$ or $C_2$?

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closed as too broad by Shaun, Xander Henderson, ancientmathematician, Thomas Shelby, Parcly Taxel Feb 27 at 6:22

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Please ask one question at a time. $\endgroup$ – Shaun Feb 24 at 12:20

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