Sporadic Group

Author

Eric W. Weisstein
September 24, 2003

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

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

©2005 Wolfram Research, Inc. except for portions noted otherwise

Table of Orders

orders={7920,95040,175560,443520,604800,10200960,44352000,50232960,244823040,898128000,4030387200,145926144000,448345497600,
460815505920,495766656000,42305421312000,64561751654400,
273030912000000,51765179004000000,90745943887872000,
4089470473293004800,4157776806543360000,
86775571046077562880,1255205709190661721292800,
4154781481226426191177580544000000,
808017424794512875886459904961710757005754368000000000};

mathworld={2^4 3^2 5 11 ,2^6 3^3 5 11,2^7 3^2 5 7 11,2^7 3^2 5 7 11 23,2^10 3^3 5 7 11 23,2^7 3^3 5^2 7,2^13 3^7 5^2 7 11 13,2^9 3^2 5^3 7 11,2^7 3^6 5^3 7 11,2^10 3^7 5^3 7 11 23,2^18 3^6 5^3 7 11 23,2^21 3^9 5^4 7^2 11 13 23,2^10 3^3 5^2 7^3 17,2^17 3^9 5^2 7 11 13,2^18 3^13 5^2 7 11 13 17 23,2^21 3^16 5^2 7^3 11 13 17 23 29,2^14 3^6 5^6 7 11 19,2^15 3^10 5^3 7^2 13 19 31,2^41 3^13 5^6 7^2 11 13 17 19 23 31 47,2^46 3^20 5^9 7^6 11^2 13^3 17 19 23 29 31 41 47 59 71,2^3 3 5 7 11 19,2^9 3^4 5 7^3 11 19 31,2^7 3^5 5 17 19,2^8 3^7 5^6 7 11 31 37 67,2^14 3^3 5^3 7 13 29,2^21 3^3 5 7 11^3 23 29 31 37 43};

Sort[mathworld]==orders

names={"(Subscript[M, 11])","(Subscript[M, 12])","(Subscript[M, 22])","(Subscript[M, 23])","(Subscript[M, 24])","(Subscript[J, 2])","Suz","HS","McL","(Subscript[Co, 3])","(Subscript[Co, 2])","(Subscript[Co, 1])","He","(Subscript[Fi, 22])","(Subscript[Fi, 23])","Fi(Subscript[', 24])","HN","Th","B","M","(Subscript[J, 1])","O'N","(Subscript[J, 3])","Ly","Ru","(Subscript[J, 4])"};

on=names[[Ordering[cur]]]

Transpose[{orders,on}]

MakeBoxes[times[x__],TraditionalForm]:=RowBox[Most@Flatten[Transpose[{{x}/.{
List[p_Integer,1]:>p,
List[p_Integer,k_Integer]:>SuperscriptBox[p,k]
},
Table["×",{Length[{x}]}]
}]
]]

{#[[1]],#[[2]],times@@FactorInteger[#[[2]]]}&/@Transpose[{on,orders}]//ColumnForm//TraditionalForm