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Let  G  be a finite group and let    be the set of elements of primary, biprimary and triprimary order of  G . We prove the following statement: if the conjugacy class sizes of    are exactly    with    and   , then  G  is nilpotent and    for some prime  q . Some known results are generalized.

Finite groups with four class sizes of elements of order divisible by at most three distinct primes