GAP:AsPermGroup

This article is about a GAP function.

Using this GAP function requires the loading of the following package: sonata

Definition

Package requirement

This function is available as part of the SONATA package.

Function type

The function takes as input a group (in any form) and outputs the group as a permutation group.

Examples of usage

gap> G := CyclicGroup(56);
<pc group of size 56 with 4 generators>
gap> H := AsPermGroup(G);
<permutation group of size 56 with 4 generators>
gap> GeneratorsOfGroup(H);
[ (1,29,15,43,8,36,22,50,2,30,16,44,9,37,23,51,3,31,17,45,10,38,24,52,4,32,18,
    46,11,39,25,53,5,33,19,47,12,40,26,54,6,34,20,48,13,41,27,55,7,35,21,49,
    14,42,28,56), (1,15,8,22,2,16,9,23,3,17,10,24,4,18,11,25,5,19,12,26,6,20,
    13,27,7,21,14,28)(29,43,36,50,30,44,37,51,31,45,38,52,32,46,39,53,33,47,
    40,54,34,48,41,55,35,49,42,56), (1,8,2,9,3,10,4,11,5,12,6,13,7,14)(15,22,
    16,23,17,24,18,25,19,26,20,27,21,28)(29,36,30,37,31,38,32,39,33,40,34,41,
    35,42)(43,50,44,51,45,52,46,53,47,54,48,55,49,56),
  (1,2,3,4,5,6,7)(8,9,10,11,12,13,14)(15,16,17,18,19,20,21)(22,23,24,25,26,27,
    28)(29,30,31,32,33,34,35)(36,37,38,39,40,41,42)(43,44,45,46,47,48,49)(50,
    51,52,53,54,55,56) ]
gap> IsomorphismGroups(G,H);
[ f4, f1*f2*f3 ] ->
[ (1,2,3,4,5,6,7)(8,9,10,11,12,13,14)(15,16,17,18,19,20,21)(22,23,24,25,26,27,
    28)(29,30,31,32,33,34,35)(36,37,38,39,40,41,42)(43,44,45,46,47,48,49)(50,
    51,52,53,54,55,56), (1,50,23,38,11,47,20,35)(2,51,24,39,12,48,21,29)(3,52,
    25,40,13,49,15,30)(4,53,26,41,14,43,16,31)(5,54,27,42,8,44,17,32)(6,55,28,
    36,9,45,18,33)(7,56,22,37,10,46,19,34) ]