update

Client App/Program.cs

@@ -51,7 +51,7 @@ class Client
                 else if (text.StartsWith("/groups"))
                 {
                     // Запрос списка групп и клиентов
-                    byte[] data = Encoding.UTF8.GetBytes("/list");
+                    byte[] data = Encoding.UTF8.GetBytes("/groups");
                     stream.Write(data, 0, data.Length);
                 }
                 else

Server App/Program.cs

@@ -79,6 +79,12 @@ class Server
                     HandleGroupCommand(clientName, groupName);
                     SendClientList(stream);
                 }
+                else if (message.StartsWith("/groups"))
+                {
+                    string groupName = message.Substring(7);
+                    HandleGroupCommand(clientName, groupName);
+                    SendClientList(stream);
+                }
                 else if (message.StartsWith("/msg "))
                 {
                     string[] parts = message.Substring(5).Split(' ', 2);