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Illicit major is a logical fallacy committed in a categorical syllogism that is invalid because its major term is undistributed in the major premise but distributed in the conclusion. Example: In this argument, the major term is "mammals". This is distributed in the conclusion (the last statement) because we are making a claim about a property of all mammals: that they are not cats. However, it is not distributed in the major premise (the first statement) where we are only talking about a property of some mammals: Only some mammals are dogs. The error is in assuming that the converse of the first statement (that all mammals are dogs) is also true.
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