What are...sporadic groups?

Goal.
I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much.

This time.
What are...sporadic groups? Or: Weird, but interesting.

Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.

Slides.
http://www.dtubbenhauer.com/youtube.html

TeX files for the presentation.
https://github.com/dtubbenhauer/My-Te...

Thumbnail.
https://en.wikipedia.org/wiki/Hall%E2...

Main discussion.
https://en.wikipedia.org/wiki/Sporadi...
https://www.ams.org/journals/notices/...
https://en.wikipedia.org/wiki/Classif...
https://en.wikipedia.org/wiki/List_of...
https://en.wikipedia.org/wiki/Group_o...
https://plus.maths.org/content/enormo...

Background material.
https://en.wikipedia.org/wiki/Group_(...)
https://en.wikipedia.org/wiki/Simple_...
https://en.wikipedia.org/wiki/Normal_...
https://en.wikipedia.org/wiki/Finite_...
https://en.wikipedia.org/wiki/Composi...
https://en.wikipedia.org/wiki/Categor...
https://en.wikipedia.org/wiki/Mathieu...
https://en.wikipedia.org/wiki/Janko_g...
https://en.wikipedia.org/wiki/ATLAS_o...

Computer talk.
Run the below Magma code here: http://magma.maths.usyd.edu.au/calc/

G:=Group("M11");
CharacterTable(G)

M11 can be replaced by any other (not too large) sporadic group using the Atlas notation https://en.wikipedia.org/wiki/ATLAS_o....

Pictures used.
Picture from    • What is...the discrete periodic table?  
A zoom in and modification of the same picture
https://en.wikipedia.org/wiki/Klein_q...

Another zoom in and modification of the same picture
Picture from https://en.wikipedia.org/wiki/Janko_g...
https://en.wikipedia.org/wiki/Fano_pl...
More Fano planes
https://en.wikipedia.org/wiki/Hall%E2...

YouTube and co.
   • Sporadic groups  
   • Why Do Sporadic Groups Exist?  
   • Math talk: Sporadic groups and number...  
   • Sporadic Groups - Prof Richard Borche...  

#grouptheory
#combinatorics
#mathematics