Higman-Sims Group

Author

Eric W. Weisstein
November 10, 2010

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

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

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

Order

GroupOrder[HigmanSimsGroupHS[]]

Transitivity

1-Transitive representation

GroupGenerators[HigmanSimsGroupHS[]]

PermutationSupport[HigmanSimsGroupHS[]]//Length

Transitivity[HigmanSimsGroupHS[]]

2-Transitive Representation

http://brauer.maths.qmul.ac.uk/Atlas/spor/HS/mag/HSG1-p176bB0.M

perm={{2,1,5,7,3,10,4,13,15,6,18,20,8,23,9,16,27,11,30,12,32,34,14,37,38,40,17,42,44,19,31,21,49,22,52,54,24,25,39,26,60,28,62,29,51,66,68,70,33,73,45,35,75,36,78,80,82,58,85,41,88,43,63,90,65,46,93,47,91,48,97,94,50,101,53,103,104,55,105,56,108,57,110,111,59,86,114,61,116,64,69,99,67,72,120,96,71,122,92,124,74,121,76,77,79,129,130,81,126,83,84,135,136,87,115,89,132,140,142,95,102,98,144,100,146,109,148,150,106,107,131,117,137,134,112,113,133,147,157,118,159,119,161,123,163,125,138,127,164,128,156,165,153,167,168,151,139,158,141,171,143,172,145,149,152,173,154,155,169,174,160,162,166,170,175,176},{3,4,6,8,9,11,12,14,16,17,19,21,22,24,25,26,28,29,1,31,33,35,36,2,39,41,40,43,45,46,47,48,50,51,53,55,56,57,58,59,5,61,63,64,65,67,69,71,72,7,49,74,76,77,79,81,83,84,86,87,37,89,10,91,92,30,75,94,95,96,98,99,100,102,66,13,101,88,106,107,42,109,68,15,112,113,115,90,73,117,118,18,119,38,20,121,93,123,34,125,116,126,127,128,114,23,97,131,132,133,134,124,27,137,104,138,139,141,80,85,140,143,32,145,62,147,149,60,151,111,152,153,154,155,129,156,142,54,78,158,44,160,103,162,120,130,52,110,122,148,136,161,166,150,146,135,169,70,170,105,171,173,164,174,175,82,167,176,163,165,108,159,168,157,172,144}};

gen=PermutationCycles/@perm

PermutationSupport[PermutationGroup[gen]]//Length

GroupOrder[PermutationGroup[gen]]

Transitivity[PermutationGroup[gen]]