Ground state: singlet or triplet

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In my book it is mentioned that for the two 1s electrons the ground state is the singlet while for the two 2p electrons the ground state could be either singlet or triplet.
Generally how can you determine whether the ground state is singlet or triplet?
 
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dextercioby
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By looking at the symmetry group of the theory: looking for all operators strongly commuting with the Hamiltonian.
 

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