galoisgetname

Function: galoisgetname
Section: number_fields
C-Name: galoisgetname
Prototype: LL
Help: galoisgetname(a,b): query the galpol package for a string describing the
 group of order a with index b in the GAP4 Small Group library.
Doc: Query the \kbd{galpol} package for a string describing the group of order
 $a$ with index $b$ in the GAP4 Small Group library, by Hans Ulrich Besche,
 Bettina Eick and Eamonn O'Brien.
 The strings were generated using the GAP4 function \kbd{StructureDescription}.
 The command below outputs the names of all abstract groups of order 12:
 \bprog
 ? o = 12; N = galoisgetgroup(o); \\ # of abstract groups of order 12
 ? for(i=1, N, print(i, ". ", galoisgetname(o,i)))
 1. C3 : C4
 2. C12
 3. A4
 4. D12
 5. C6 x C2
 @eprog\noindent
 The current version of \kbd{galpol} supports groups of order $a\leq 143$.
 For $a \geq 16$, it is possible for different groups to have the same name:
 \bprog
 ? o = 20; N = galoisgetgroup(o);
 ? for(i=1, N, print(i, ". ", galoisgetname(o,i)))
 1. C5 : C4
 2. C20
 3. C5 : C4
 4. D20
 5. C10 x C2
 @eprog