One nuclear bomb could wipe out around 720,000 people in an average city.
Basically no survival within 2 km of the blast area (around 120,000 people killed)
and around half the people within 2 to 11km away from blast will be killed from burns, smoke, collapse building and radiations (around 500,000 killed)
Of course there are also aftermath of radiation, with dust and ashes travelling with wind, causing smaller no. of deaths outside 11km range (say 100,000 killed)
But some may survive if they managed to hide away from blast and radiation.
But it is also estimated a detonation of around 300 nukes in short period of time, at the right place/infrastructure, would clog the Earth's stratosphere and block sunlight, destroy planet's ozone layer and trigger drop in global temperature that could last 25 years, would destroy ecosystem and spark a global famine, and assume electricity, transportation, water, food production are knocked out too, and together with the spread of radiation, eventually would lead to extinction of humanity.
And Russia alone has possession of 6500 of nuclear warheads.
So we are basically fecked, if nuclear war happened.