Finite non-solvable groups whose non-linear character degrees have the same number of distinct prime divisors are, up to abelian direct factors, exactly L2(4), L2(8), A7, S7, the central product of a cyclic 3-group with 3.A7, or A7 semidirect product with a cyclic 2-group acting non-trivially.
Willems , Blocks of defect zero and degree problems
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Non-solvable groups whose non-linear character degrees have the same number of different prime divisors
Finite non-solvable groups whose non-linear character degrees have the same number of distinct prime divisors are, up to abelian direct factors, exactly L2(4), L2(8), A7, S7, the central product of a cyclic 3-group with 3.A7, or A7 semidirect product with a cyclic 2-group acting non-trivially.