Janko group:J4

Definition
This group, denoted $$J_4$$, is one of the Janko groups. Its existence was conjectured by Janko.

The order of the group is:

$$\! 86775571046077562880 = 2^{21} \cdot 3^3 \cdot 5 \cdot 7 \cdot 11^3 \cdot 23 \cdot 29 \cdot 31 \cdot 37 \cdot 4$$