Outer linear group:OL(2,3)

Definition

This group is defined as the outer linear group of degree two over the field of three elements. It is denoted $OL(2,3)$.

Arithmetic functions

Function	Value	Explanation
order	96
exponent	24
nilpotency class	--	not a nilpotent group.
derived length	4	commutator subgroup is $SL(2,3)$.
Frattini length	2	Frattini subgroup is cyclic of order two.
Fitting length	3	Fitting subgroup is the quaternion group, and the quotient is dihedral of order twelve.
Composition length	6
max-length	6

GAP implementation

Group ID

This group can be defined using GAP's SmallGroup function:

SmallGroup(96,193)