Difference between revisions of "Suzuki sporadic group"
From Encyclopedia of Mathematics
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A [[Simple finite group|simple finite group]] of order | A [[Simple finite group|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 [[ | + | 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 [[ | + | For other sporadic groups, see [[Sporadic simple group]]. |
====Comments==== | ====Comments==== | ||
| − | Its Schur multiplier is | + | Its Schur multiplier is $ 6 $. |
| + | Its central covering is the automorphism group of the complex [[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> | ||
Latest revision as of 18:33, 4 May 2023
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=15515
Suzuki sporadic group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Suzuki_sporadic_group&oldid=15515