Conway group

The term Conway group is used for the three sporadic simple groups whose existence was discovered by John Horton Conway. They are all related to the Leech lattice.

Group information	Symbol for group	Order	Prime factorization	Brief description/definition of the group
Conway group:Co1	$\operatorname {Co} _{1}$	4157776806543360000	[SHOW MORE] $2^{21}\cdot 3^{9}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 13\cdot 23$	inner automorphism group of Conway group:Co0, which in turn is defined as the group of automorphisms of the Leech lattice.
Conway group:Co2	$\operatorname {Co} _{2}$	42305421312000	[SHOW MORE] $2^{18}\cdot 3^{6}\cdot 5^{3}\cdot 7\cdot 11\cdot 23$	subgroup of $\operatorname {Co} _{0}$ consisting of automorphisms fixing a paticular vector of norm 4. (Note that since this intersects the center trivially, it can also be realized as a subgroup of $\operatorname {Co} _{1}$).
Conway group:Co3	$\operatorname {Co} _{3}$	495766656000	[SHOW MORE] $2^{10}\cdot 3^{7}\cdot 5^{3}\cdot 7\cdot 11\cdot 23$	subgroup of $\operatorname {Co} _{0}$ consisting of automorphisms fixing a particular vector of norm 6. (Note that since this intersects the center trivially, it can also be realized as a subgroup of $\operatorname {Co} _{1}$).