# What is the Schur multiplier of a finite group? [closed]

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 $$C_2$$?

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

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