The Intransitive Groups of Degree 9 |
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02 order 12 in G 18-3 isomorphism 3-1 isomorphism 9 which contain ab.ef abode ac.df acbd ad.be.cf alternating group B₁ order be.od C₁ C₂ order 108 constituent of degree contain a transitive contain the invariant contains no invariant Croups cyclic 3 group D₂ D5 order 40 degree 9 degree and order dihedral group direct product distinct invariant subgroups F₁ F₂ fh.gi G₁ G₁₂ G₂ groups of degree groups of order half its order intransitive groups invariant subgroup abc isomorphic to F isomorphism 34 isomorphism F leaves two distinct metacyclic group octic group one-third its order order 12 order 18 F order 24 order 9 permutation possible invariant sub possible invariant subgroup product of C₂ quotient group simple group stituent of degree subgroup of half subgroup of order Sylow subgroup symetric group third its order three invariant subgroups three possible invariant tive constituent transitive constituent