TOPICS
Search

Fischer Groups


The Fischer groups are the three sporadic groups Fi_(22), Fi_(23), and Fi_(24)^'. These groups were discovered during the investigation of 3-transposition groups.

The Fischer groups are implemented in the Wolfram Language as FischerGroupFi22[], FischerGroupFi23[], and FischerGroupFi24Prime[].

The following table summarizes the orders of the Fischer groups.

grouporderfactorization
Fi_(22)645617516544002^(17)·3^9·5^2·7·11·13
Fi_(23)40894704732930048002^(18)·3^(13)·5^2·7·11·13·17·23
Fi_(24)^'12552057091906617212928002^(21)·3^(16)·5^2·7^3·11·13·17·23·29

The baby monster group is sometimes called Fischer's baby monster group.


See also

Baby Monster Group, Sporadic Group

Explore with Wolfram|Alpha

References

Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A. Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England: Clarendon Press, 1985.Wilson, R. A. "ATLAS of Finite Group Representation." http://brauer.maths.qmul.ac.uk/Atlas/v3/spor/.

Referenced on Wolfram|Alpha

Fischer Groups

Cite this as:

Weisstein, Eric W. "Fischer Groups." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FischerGroups.html

Subject classifications