I’ve seen that it is set to General most of the time, but not always.
Advocacy district related groups are set to Administrators only. Most other default groups are set to General by default. Automatically created center groups are set to the center's security category by default.
Admin created groups can vary. If you have group categorization turned on, that is you can see the security category drop down when created a group, there is no default as the security category is selected at the time of creation by the admin creating the group. If you do not have group categorization turned on, all admin created groups will be in General in most cases. If you have multicenter, when an admin is in a specific center, any group created will be in that center's security category by default.
Note that if you have group categorization turned on, the security category drop down will always show the first security category alphabetically in the drop down when the page to create a new group is first loaded.
If you do not have group categorization turned on, contact support to have it turned on.