Similarities between communism and fascism

Is Communism the Fascism of the left spectrum? This one question has been pounding on my head for long. They have their differences of course. Well fascism as an ideology argues that certain hierarchies are natural and inevitable as part of the natural order of politics itself. Brushing egalitarianism aside, fascism extends its hands towards laisezz-faire capitalism, ethnocentrism and anti-elitism.
On the other hand communism is built upon socialist ideologies that are polar opposites of what fascism advocates. Egalitarianism, social ownership, secularism and what fascism generally loathes altogether.
But in reality,isn't  the means of achieving both the ideologies similar. Communism fueled by the Bolshevik revolution in 1917 against the Russian Czar and his family started spreading its tentacles in a vice like grip around the Russian subcontinent. Well here are few instances that tingled my doubts further.

Red Terror: Red terror took place immediately after the Bolsheviks took over Russia and affirmed their position in the political theater of the world. Around ten thousand to twelve thousand bourgeois Cossack' were rounded up declared "Enemies of the People" and executed by the Cheka, then Russia's secret police. Strangely Cheka seems familiar to another organization that had similar operations. They were known as the Gestapo.

Yezhovshchina: The biggest purge in the history of Red Soviet Russia. Stalin's atrocities in solidifying his positions led to the execution of 724,000 people in Russia, of which 700,000 were shot dead while the rest perished in the Gulags.

Great purge in Mongolia: Again under the direction of the victorious leader Stalin, in 1937 NKVD agents were sent to Mongolia and around 35,000 people were executed. Interesting fact to note here is that 18,000 were Buddhist Lamas.

Well enough about Russia, let's get on with one of the fastest growing economies of the current world China.

Land Reforms: Under another "revolutionary" leader Mao Zedong, Around one million peasants were killed to facilitate agrarian reform. Around 724,000 Kuomintang party members were killed as suppression of counter revolutionaries.

The Great Leap Forward: The great leap forward was the primary reason for the great Chinese famine. The government gave the lowest priority to "black elements" (rightists, religious leaders, rich peasants etc...) in the allocation of food. The death toll was around 45 million,with the party itself killing them by stringent rations. Also 2.5 million were summarily tortured and killed. Mao Zedong in a secret meeting in Shanghai ordered to procure one third of all the grains procured in the countryside. His words were "When there's not enough to eat people starve to death. It's better to let half of the people die, so the other half can eat their fill".

Tibetan purge: After the Chinese government settled down and took over Tibet they hunted Tibetans. Tibetans were shot, hung, quartered, crucified, burnt, maimed, beheaded and mutilated. As many as 92,000 murders out of a 6 million population was in the hands of Chinese officials. Ethnic cleansing. It does sound similar to a second world war dictator who killed 6 million Jews.

Tienanmen Square massacre:  The students in China assembled in Tienanmen square in 1989 to protest against the government and demand democracy and freedom of expression. It ended up in them getting killed by 300,000 troops and even tanks rolling out. Pity! They forgot they were part of a communist regime. I'm forced to remember Benito Mussolini's regime.

Not only China and Russia, but also Cambodia, Vietnam, North Korea have similar stories to tell. If you are part of a communist regime, you cannot question your government and its policies, cannot own property and must have blind faith that the Polit Bureau will take care of you while you swear allegiance to them. If you do not comply, you're an enemy of the state and you along with your family will be mercilessly wiped out. This all sounds strikingly familiar to the fascist regime of nationalism and ethnocentrism, in this case we can make it as party-centrism.

With respect to all the communists in the world, it's a bit rich that communists call a fascist, a fascist when communists themselves are indulging in fascism styled activities. I advice Communists to change their name to Narcissists and the Polit Bureau to Polit Reich. It will suit better.