Outer linear group:OL(2,3)

From Groupprops
Jump to: navigation, search

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)