Projective symplectic group:PSp(6,2)

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Definition

This group is defined in the following equivalent ways:

1. It is the projective symplectic group of degree six (i.e., arising from $6\times 6$ matrices) over field:F2. This is denoted $PSp(6,2)$ and the Chevalley notation is $C_{3}(2)$; however, it can also be described as $B_{3}(2)$ (see below).
2. It is the symplectic group of degree six (i.e., arising from $6\times 6$ matrices) over field:F2. This is denoted $Sp(6,2)$.
3. It is the Chevalley group of type B $B_{3}(2)$ over field:F2.

Equivalence of definitions

The equivalence of (1) and (2) follows from isomorphism between symplectic and projective symplectic group in characteristic two.

Arithmetic functions

Function	Value	Similar groups	Explanation
order (number of elements, equivalently, cardinality or size of underlying set)	1451520	groups with same order	As $Sp(2m,q),m=3,q=2$: $q^{m^{2}}\prod _{i=1}^{m}(q^{2i}-1)$ becomes $2^{3^{2}}(2^{2}-1)(2^{4}-1)(2^{6}-1)=(512)(3)(15)(63)=1451520$

GAP implementation

Description	Functions used
PSp(6,2)	PSp
Sp(6,2)	Sp