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4 Conversion to other group libraries
 4.1 The Small Groups Library
 4.2 The Library of Finite Perfect Groups
 4.3 The Primitive Permutation Groups Library
 4.4 The Library of Transitive Groups
 4.5 The ATLAS of Group Representations

4 Conversion to other group libraries

4.1 The Small Groups Library

This library is provided by the SmallGrp package.

4.1-1 IdClassNrToIdGroup
‣ IdClassNrToIdGroup( k, i )( function )

Returns: a pair of integers [x, y] such that SmallGroup(x, y) is isomorphic to SmallClassNrGroup(k, i).

gap> IdClassNrToIdGroup( 9, 19 );
[ 192, 1025 ]
gap> IdClassNr( SmallGroup( 192, 1025 ) );
[ 9, 19 ]

4.2 The Library of Finite Perfect Groups

This library is provided by GAP itself.

4.2-1 IdClassNrToPerfGrp
‣ IdClassNrToPerfGrp( k, i )( function )

Returns: a pair of integers [x, y] such that PerfectGroup(x, y) is isomorphic to SmallClassNrGroup(k, i).

gap> IdClassNrToPerfGrp( 10, 36 );
[ 14520, 1 ]
gap> IdClassNr( PerfectGroup( 14520, 1 ) );
[ 10, 36 ]

4.3 The Primitive Permutation Groups Library

This library is provided by the PrimGrp package.

4.3-1 IdClassNrToPrimGrp
‣ IdClassNrToPrimGrp( k, i )( function )

Returns: a pair of integers [x, y] such that PrimitiveGroup(x, y) is isomorphic to SmallClassNrGroup(k, i).

gap> IdClassNrToPrimGrp( 9, 25 );
[ 49, 25 ]
gap> IdClassNr( PrimitiveGroup( 49, 25 ) );
[ 9, 25 ]

4.4 The Library of Transitive Groups

This library is provided by the TransGrp package.

4.4-1 IdClassNrToTransGrp
‣ IdClassNrToTransGrp( k, i )( function )

Returns: a pair of integers [x, y] such that TransitiveGroup(x, y) is isomorphic to SmallClassNrGroup(k, i).

gap> IdClassNrToTransGrp( 12, 46 );
[ 45, 314 ]
gap> IdClassNr( TransitiveGroup( 45, 314 ) );
[ 12, 46 ]

4.5 The ATLAS of Group Representations

This library is provided by the AtlasRep package.

4.5-1 IdClassNrToAtlasName
‣ IdClassNrToAtlasName( k, i )( function )

Returns: a string name such that AtlasGroup(name) is isomorphic to SmallClassNrGroup(k, i).

gap> IdClassNrToAtlasName( 11, 34 );
"L2(17)"
gap> IdClassNr( AtlasGroup( "L2(17)" ) );
[ 11, 34 ]
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