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In Mn-doped InSb single crystals an unusual, for nonmagnetic semiconductors, dependence on manganese concentration have been revealed for magnetization, conductivity, magnetoresistance and the Hall effect in the range NMn= (1÷2)×1017cm-3. Noticeable low temperature magnetization increase was observed at NMn≈1×1017cm-3. Strong correlation between magnetization, specific resistivity, Colossal Magnetoresistance (CMR) and the Hall constant as a function of manganese concentration in InSb(Mn) was revealed on the insulating side of the metal-insulator transition at Ncr=2×1017cm-3 and at temperature below 10K. Simultaneously, an onset of ferromagnetic-like response in the magnetic moment measurements of p-InSb(Mn) at NMn≤Ncr= 2×1017 cm-3 was registered. This experimental evidence fits the pattern of triplet excitons switching off from conductivity and demonstrates weak magnetic ordering. The coincidence in transport, magnetotransport properties of p-InSb(Mn) and uniaxially stressed p-InSb(Ge) crystals puts forward the idea that the unusual InSb(Mn) properties could be related to Jahn-Teller distortions caused by Mn.