We describe abstract groups using standard building blocks:

- $C_n$ denotes the cyclic group of order $n$
- $D_n$ denotes the dihedral group of order $2n$
- $A_n$ denotes the alternating group on $n$ letters
- $S_n$ denotes the symmetric group on $n$ letters

Groups $A$ and $B$ may be used to construct a larger group:

- $A\times B$ for the direct product of $A$ and $B$
- $A:B$ for the semidirect product of $A$ and $B$ (with normal subgroup $A$)
- $A.B$ an extension with normal subgroup $A$ and quotient isomorphic to $B$

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**Knowl status:**

- Review status: reviewed
- Last edited by John Jones on 2017-07-19 14:42:50

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