I'll post the relevant text below:

Command:

You speak a one-word command to a creature you can see within range. The target must succeed on a Wisdom saving throw or follow the command on its next turn...If the target can't follow your command, the spell ends.

Surprise:

If you're surprised, you can't move or take an action on your first turn of the combat, and you can't take a reaction until that turn ends. A member of a group can be surprised even if the other members aren't.

I'm unsure which effect is more specific, and therefore takes priority. I'm leaning towards Command, simply because Surprise functionally takes away a character's turn from themselves, but doesn't incapacitate them the way a Sleep spell would.

Command is specific, in that it acknowledges that the target may not be able to follow the Command. It does not provide any method for allowing the target to act when it is otherwise prohibited from taking an action.

Surprise tells you that the creature cannot take an action. Command tells you what to do if the target cannot follow the instruction.

While Surprise is not the same as Sleep, it still stops the surprised creature from acting. Due to this, they are unable to follow the Command, and the spell ends.

Result: The Surprised target fails to act, and the Command spell is wasted.

They follow the command if they are able to

The surprised condition prevents a creature from taking an action, moving or using a reaction until the end of their turn. Any command that requires a creature to do one of these thing will count as the target not be able to follow the command. Therefore the spell will fail. Not all command options require an action though. For example the typical commands given in the spell:

• 
  Approach: Requires the target to move, the spell fails.


• 
  Drop: Dropping an object doesn't require an action, the spell works.


• 
  Grovel: Falling prone required movement, the spell fails.


• 
  Halt: Doesn't move and takes no actions. It was going to do this anyway. The spell works but does nothing.

You can also give command that isn't one of the ones listed. Anything that would not require your action or move. Such as speaking (or not speaking) or any number of other things the player may think of. Note; you cannot use an Object Interaction as that must be taken during an action or your movement.

If you are going to cast Command on a surprised creature make sure it is something they can do without using their action of movement. Otherwise it will be a waste of a spell.

The surprised creature obeys the command. If it can't follow your command, then the spell ends.

While the argument as explored in the answer by Black Spike applies, the creature is still able to do Other Activity on their turn that is neither an action, a reaction, nor movement.

Command, PHB p. 223, does not provide the affected creature/s with the abilities to follow your command. If the creature/s can't follow your command, then the spell ends.

Other Activity on your Turn, PHB p. 190:

Your turn can include a variety of flourishes that require neither
your action nor your move.
You can communicate however you are able, through brief utterances and gestures, as you take your turn.
You can also interact with one object or feature of the environment for free, during either your move or your action.

If the command is as an example "Silence", then the creature would not be able to use their Other Activity to communicate.

The creature does not have an object or environment interaction, because it can't use their movement or their action.