Simple group name (reviewed)

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 $B$