What is the Order Of Symplectic Group(4,2) and Symplectic Group(4,3) from the Classical groups of Atlas?

Question

I have been working on Symplectic group of classical groups. I am trying to find Sylow-2 Subgroups of Symplectic Group(4,2) and Symplectic Grouop(4,3) through GAP, I am facing a problem regarding order of these groups. Order of Symplectic Group(4,2) and Symplectic Group(4,3) is 360 and 25920 respectively according to Atlas of Finite Groups but according to Gap calculations it is giving order of Symplectic Group(4,2) and Symplectic Group(4,3) is 720 and 51840 respectively. Help me of about the exact order of these groups. I am bit confuse between them.

Answer 1

Where exactly in the ATLAS did you find these assertions?

The group ${\rm Sp}(4,2)$ of symplectic matrices over the field of order $2$ has order $720$, and is isomorphic to $S_6$. So its commutator subgroup is isomorphic to the simple group $A_6$ of order $360$.

The group $G={\rm Sp}(4,3)$ has order $51480$. It has a centre of order $2$, and $G/Z(G)$ is the simple group ${\rm PSp}(4,3)$ of order $25920$. This simple group is denoted in the ATLAS by $S_4(3)$ (not ${\rm Sp}(4,3)$), so perhaps that is the source of your confusion.