7.3. Other groups

These are groups taken from the Atlas of Finite Group Representations (http://for.mat.bham.ac.uk/atlas/), in the section Miscellaneous Groups.

This is the exceptional twisted group Sz8 (the Suzuki group), which can be given in terms of permutations on 65 points.

In[241]:=

In[243]:=

PermDeg/@{g1, g2}

Out[243]=

{65, 65}

In[244]:=

myTiming[Sz8SGS = SchreierSims[{}, GenSet[g1, g2], 65] ;]

0.009850 Second

In[245]:=

Length/@Sz8SGS

Out[245]=

StrongGenSet[3, 5]

In[246]:=

OrderOfGroup[Sz8SGS]

Out[246]=

29120

This is the exceptional untwisted group G2(4), which can be given in terms of permutations on 416 points.

In[247]:=

In[249]:=

PermDeg/@{g1, g2}

Out[249]=

{414, 416}

In[250]:=

myTiming[G24SGS = SchreierSims[{}, GenSet[g1, g2], 416] ;]

3.204673 Second

In[251]:=

Length/@G24SGS

Out[251]=

StrongGenSet[4, 11]

In[252]:=

OrderOfGroup[G24SGS]

Out[252]=

251596800

The largest symplectic group given in the Atlas is S10. It can be represented using permutations of 496 points.

In[253]:=

In[255]:=

PermDeg/@{g1, g2}

Out[255]=

{496, 495}

In[256]:=

myTiming[S10SGS = SchreierSims[{}, GenSet[g1, g2], 496] ;]

21.573289 Second

In[257]:=

Length/@S10SGS

Out[257]=

StrongGenSet[10, 20]

In[258]:=

OrderOfGroup[S10SGS]

Out[258]=

24815256521932800

This is the exceptional twisted group T3D4, represented with permutations on 819 points.

In[259]:=

In[261]:=

PermDeg/@{g1, g2}

Out[261]=

{819, 818}

In[262]:=

myTiming[T3D4SGS = SchreierSims[{}, GenSet[g1, g2], 819] ;]

13.412142 Second

In[263]:=

Length/@T3D4SGS

Out[263]=

StrongGenSet[5, 14]

In[264]:=

OrderOfGroup[T3D4SGS]

Out[264]=

211341312

Go back to the original settings:

In[265]:=

SetOptions[Orbit, MathLink→False] ;

SetOptions[SchreierSims, MathLink→False] ;


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