## The Intransitive Groups of Degree 9 |

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_ is isomorphic 22 groups 3y ae 6-3 isomorphism 9 which contain ab.de ab.ef ab.fg abo.def abo)j abode aeb)(dfe alternating 4 group ao.df aobd be.od bo.Od conjugate invariant subgroups constituent of degree contain a transitive contain the alternating croup cyclic 3 group degree 9 degree and order dihedral group distinct groups dogree following list group of order groups of degree half its order half their order ia the direct iant subgroup intransitive groups isomorphism F letters one-third its order ootio group order 12 order 24 order 2l6 order 36 order 40 order 6 ia order 9 ordor oyolio possible invariant sub possible invariant subgroup product of Cz quotient group simple group stituent of decree subgroup of half subgroup of order Sylow subgroup synetrio tain third its order tho group three invariant subgroups three possible invariant throe tive constituent transitive constituent trill variant subgroup