Janko group:J1

Definition
This group, denoted $$J_1$$, is one of the Janko groups. It was constructed by Janko.

The order of the group is:

$$\! 175560 = 2^3 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 19$$

The group is a finite simple non-abelian group and in fact it is one of the 26 sporadic simple groups.