They were basically a Microsoft of their century. A little less monopolistic perhaps as countries believed they should own they natural resources, unlike their data.

All companies with investors are evil, make no mistake.

They may have nice looking save the world charity campaigns, but once you get even close to affecting their revenue stream, the axe falls. The charity is only a publicity stunt to reduce wages.

Some level of government intervention is needed to control investor's greed.

It is just a question of business model: some business models are eviler than others. Making people pay for operating systems being possible the most evil of all.

One thing must be said however. You can learn a lot by working in a good company, because it ends up putting you in contact with practical real problems that you wouldn't otherwise see by just doing your own random low-tech startup. This is especially valuable if said company is also enlightened enough to use and contribute back to open source software, thus improving the world and paying back the moral debt of using other people's work for free.

Another important point to consider is who in the company is evil. In a sane tech company, the lowly engineers are going to be non-evil. And then the more you go up the management chain, the more aligned you have to be with investors, and thus the more and more evil you get. HR is just evil from the bottom though, it's just the nature of their job.

Many/most companies are unable to give any beauty to its employees.

Hiring is simply a process of "let's get this money making project working ASAP", bring people in, without considering Brooks's law.

And then when that happens, companies put people in extremely narrow knowledge areas, making them unable to see or participate in the bigger picture of things, unless they spend 10 years there and reach architect status.

This is perhaps particularly painful for high flying birds like Ciro Santilli.

Companies need a higher top to down force that attempts to actually teach the business and tech to every employee to counter the low level manager get things done now pressure.

Companies that are able to do that, will have many more employees with a sense of purpose, and with the ability to innovate. Those companies will win.

Contains the first sporadic groups discovered by far: 11 and 12 in 1861, and 22, 23 and 24 in 1973. And therefore presumably the simplest! The next sporadic ones discovered were the Janko groups, only in 1965!

Each $M_n$ is a permutation group on $n$ elements. There isn't an obvious algorithmic relationship between $n$ and the actual group.

TODO initial motivation? Why did Mathieu care about k-transitive groups?

Their; k-transitive group properties seem to be the main characterization, according to Wikipedia:Looking at the classification of k-transitive groups we see that the Mathieu groups are the only families of 4 and 5 transitive groups other than symmetric groups and alternating groups. 3-transitive is not as nice, so let's just say it is the stabilizer of $M_{23}$ and be done with it.