General linear group:GL(3,3)

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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:

1. It is the general linear group of degree three over field:F3.
2. It is the external direct product of projective special linear group:PSL(3,3) and cyclic group:Z2.

Arithmetic functions

Function	Value	Similar groups	Explanation
order (number of elements, equivalently, cardinality or size of underlying set)	11232	groups with same order	order of a general linear group of degree three over a finite field with $q$ elements is $(q^{3}-1)(q^{3}-q)(q^{3}-q^{2})$. For $q=3$, we get $(26)(24)(18)=11232$
exponent of a group	312	groups with same order and exponent of a group | groups with same exponent of a group

GAP implementation

Description	Functions used
GL(3,3) or GeneralLinearGroup(3,3)	GAP:GL