Projective special unitary group:PSU(3,3)

This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
View a complete list of particular groups (this is a very huge list!)[SHOW MORE]

VIEW FACTS ABOUT THIS GROUP: All factsGroup property satisfactionsSubgroup property satisfactionsGroup property dissatisfactionsSubgroup property satisfactions
VIEW DEFINITIONS USING THIS AS EXAMPLE: All terms |Group properties |Subgroup properties|
VIEW FACTS USING THIS AS EXAMPLE: All facts |Group property non-implications |Subgroup property non-implications |Group metaproperty dissatisfactionsSubgroup metaproperty dissatisfactions

Definition

This group is defined in the following equivalent ways:

• It is the projective special unitary group of degree three for the quadratic extension field:F9 over field:F3, i.e., the group $PSU(3,3)$.
• It is the special unitary group of degree three for the quadratic extension field:F9 over field:F3, i.e., the group $SU(3,3)$.

Arithmetic functions

Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 6048#Arithmetic functions

Function	Value	Similar groups	Explanation
order (number of elements, equivalently, cardinality or size of underlying set)	6048	groups with same order	As $SU(3,q),q=3$: PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE] One of the people editing this page intended to fill in this information at a later stage, but hasn't gotten around to doing it yet. If you see this placeholder for a long time, file an error report at the error reporting page.
exponent of a group	168	groups with same order and exponent of a group | groups with same exponent of a group	As $SU(3,q),q=3$: PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE] One of the people editing this page intended to fill in this information at a later stage, but hasn't gotten around to doing it yet. If you see this placeholder for a long time, file an error report at the error reporting page.

Group properties

Property	Satisfied?	Explanation
abelian group	No
nilpotent group	No
solvable group	No
simple group, simple non-abelian group	Yes	projective special unitary group is simple

GAP implementation

Description	Functions used
PerfectGroup(6048,1)	PerfectGroup
PSU(3,3)	PSU
SU(3,3)	SU