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Second-metacyclic finite p-groups for odd primes

Croatian Mathematical Society and Department of Mathematics, University of Zagreb
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  • Finite Group
  • P-Group
  • Metacyclic
  • Second-Maximal Subgroup
  • Second-Metacyclic Subgroup.


A second-metacyclic finite p-group is a finite p-group which possesses a nonmetacyclic maximal subgroup, but all its subgroups of index p2 are metacyclic. In this article we determine up to isomorphism all second-metacyclic p-groups for odd primes p. There are ten such groups of order p4, for each prime p ≥ 3, and two such groups of order 35.

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