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Abstract Ferromagnetism can be characterized by various distinct phenomena such as non-zero magnetization (inducing magnetic attraction/repulsion), diagonal piezomagnetism, nonreciprocal circular dichroism (such as Faraday effect), odd-order (including linear) anomalous Hall effect, and magneto-optical Kerr effect. We identify all broken symmetries requiring each of the above phenomena, and also the relevant magnetic point groups (MPGs) with those broken symmetries. All ferromagnetic point groups, relevant for ferromagnets, ferrimagnets, and weak ferromagnets, can certainly exhibit all these phenomena, including non-zero magnetization. Some of the true antiferromagnets, which are defined as magnets with MPGs that do not belong to ferromagnetic point groups, can display these phenomena through magnetization induced by external perturbations such as applied current, light illumination, and uniaxial stress, which preserve the combined symmetry of spatial inversion together with time reversal. Such MPGs are identified for each external perturbation. Since high-density and ultrafast spintronic technologies can be enabled by antiferromagnets, our findings will be essential guidance for future magnetism-related science as well as technology.