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The smallest Frobenius group is the symmetric group of degree .
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A different permutation group isomorphic to the symmetric group of degree is a Frobenius group, but is not Frobenius as a permutation group.
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The dihedral group is Frobenius if, and only, if, is odd.
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We construct here a Frobenius subgroup of order in the first Janko group.
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However, this is not a Frobenius action; to get a Frobenius permutation group, use FrobeniusPermRep.
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Now we can compute the Frobenius kernel and complement, and determine their orders.
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Of course, we obtain the same result by computing the Frobenius kernel and complement of G itself.
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The Frobenius complement in a Frobenius dihedral group is a subgroup of order two.
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The Mathieu group of degree has a point stabilizer of order . (This is sometimes referred to as a Mathieu group of degree .)
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This point stabilizer is a Frobenius group.
Moreover, the action is Frobenius.
The Frobenius complement in is a quaternion group.
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