A suspected neo-Nazi who named his baby Adolf posed for a photo with the child whilst wearing Ku Klux Klan robes, a court heard.
Adam Thomas, 22, and his partner Claudia Patatas, 38, are on trial accused of being members of the "extreme and violent" far-right group National Action.
Thomas is facing a separate charge of possessing The Anarchist Cookbook, a terrorist document which contains bomb-making instructions.
Patatas had a WhatsApp conversation with a man named Darren Fletcher who has admitted being a member of National Action, Birmingham Crown Court heard on Wednesday.
The mother is alleged to have told him in the chat from February 2017: "And all Jews must be put to death."
When the jury was shown a photo of Thomas cradling his newborn baby, prosecution lawyer Barnaby Jameson said: "The suggestion is that is Mr Thomas and his child, whose middle name is Adolf."
The parents, from Banbury, Oxfordshire, wanted to honour the wartime Nazi leader Hitler, the court heard.
Turning to an image of a hooded man with a machete, Mr Jameson added: "There is a strong inference, and you'll appreciate this when you look inside the Thomas and Patatas' house, that that was taken inside their home, and that the person in the robes was Thomas."
The flag was shown hanging over a sofa on which there were two scatter cushions each bearing the Nazi swastika symbol.
Patatas and Thomas also allegedly had a poster stuck to their fridge reading "Britain is ours - the rest must go".
Thomas at one stage bemoaned he had to work with a "fat p***", the jury heard.
Daniel Bogunovic, 27, from Leicester is also in the dock facing the same charge of being a National Action member.
Fletcher, 28, from Wednesfield, Wolverhampton, had a race hate conviction for dressing as a Ku Klux Klansman.
He was also found guilty of hanging a stuffed toy resembling a black person from a noose on stage at a white pride event in 2013.
Patatas and Thomas were allegedly pictured at home with "vehement Nazi" Fletcher, who was holding a swastika flag and performing a Hitler-style salute over their baby.
It emerged in court that counter-terrorism officers from Prevent had visited the couple's home in October last year "due to concerns Ms Patatas may be involved in the extreme right wing".
An online chat message allegedly sent by Thomas showed he was unfazed.
He said: "I have my flags up, lol - and f*** social services, they have no basis of claim of anything."
Mr Jameson said on Tuesday that National Action is a group so "extreme and violent" it was banned by the government.
He added the organisation then tried to "shed one skin for another" in order to evade the law.
Mr Jameson said on Wednesday that Thomas, Patatas and Bogunovic were part of a successor organisation called the TripleK Mafia, in reference to the Ku Klux Klan.
The group was in effect still National Action in all but name, the court heard.
A member named Joel Wilmore had spelt the rebranded group's name wrong by writing "TrippleK" four times in their new posters, the jury was shown.