Mathieu Groups

Author

Eric W. Weisstein
November 11, 2010

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GroupTheory/MathieuGroups.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/MathieuGroups.html.

©2010 Wolfram Research, Inc. except for portions noted otherwise

Order

m=Symbol/@Names["MathieuGroup*"]

Grid[{
#,
Transitivity[#[]],
Length[PermutationSupport[#[]]],
g=GroupOrder[#[]],
Times@@Superscript@@@FactorInteger[g]
}&/@m,Alignment->{{Left,Decimal,Decimal,Decimal,Left},Automatic},Dividers->All]//TraditionalForm

CayleyGraph

cg=CayleyGraph[MathieuGroupM11[]];//Timing

m11=UndirectedGraph[cg];

RecognizeGraph[m11]

Through[{VertexCount,EdgeCount}[cg]]

Tally[Sort[VertexDegree[m11]]]

VertexTransitiveQ[m11]//Timing

EdgeTransitiveQ[m11]//Timing

gr=AutomorphismGroup[m11];

GroupOrder[gr]