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Difference between revisions of "Suzuki sporadic group"

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A [[Simple finite group|simple finite group]] of order
 
A [[Simple finite group|simple finite group]] of order
  
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<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091520/s0915201.png" /></td> </tr></table>
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$$
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448  345  497  600  = 2  ^ {13} \cdot 3  ^ {7} \cdot 5  ^ {2} \cdot 7
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\cdot 11 \cdot 13 ,
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$$
  
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constructed by M. Suzuki as the primitive permutation group of degree 1782 with point stabilizer isomorphic to the [[Chevalley group|Chevalley group]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091520/s0915202.png" />.
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constructed by M. Suzuki as the primitive permutation group of degree 1782 with point stabilizer isomorphic to the [[Chevalley group|Chevalley group]] $  G _ {2} ( 4) $.
  
 
For other sporadic groups, see [[Sporadic simple group|Sporadic simple group]].
 
For other sporadic groups, see [[Sporadic simple group|Sporadic simple group]].
  
 
====Comments====
 
====Comments====
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Its Schur multiplier is <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091520/s0915203.png" />; its central covering is the automorphism group of the complex [[Leech lattice|Leech lattice]]. See [[#References|[a1]]].
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Its Schur multiplier is $  6 $;  
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its central covering is the automorphism group of the complex [[Leech lattice|Leech lattice]]. See [[#References|[a1]]].
  
 
====References====
 
====References====
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  J.H. Conway,  R.T. Curtis,  S.P. Norton,  R.A. Parker,  R.A. Wilson,  "Atlas of finite groups" , Clarendon Press  (1985)</TD></TR></table>
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  J.H. Conway,  R.T. Curtis,  S.P. Norton,  R.A. Parker,  R.A. Wilson,  "Atlas of finite groups" , Clarendon Press  (1985)</TD></TR></table>

Revision as of 08:24, 6 June 2020


A simple finite group of order

$$ 448 345 497 600 = 2 ^ {13} \cdot 3 ^ {7} \cdot 5 ^ {2} \cdot 7 \cdot 11 \cdot 13 , $$

constructed by M. Suzuki as the primitive permutation group of degree 1782 with point stabilizer isomorphic to the Chevalley group $ G _ {2} ( 4) $.

For other sporadic groups, see Sporadic simple group.

Comments

Its Schur multiplier is $ 6 $; its central covering is the automorphism group of the complex Leech lattice. See [a1].

References

[a1] J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker, R.A. Wilson, "Atlas of finite groups" , Clarendon Press (1985)
How to Cite This Entry:
Suzuki sporadic group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Suzuki_sporadic_group&oldid=48917
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