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Mar 26, 2013 at 1:30 comment added Chandan Singh Dalawat For a complete classification of such extensions (of a cyclic group by a cyclic group), see for example Mark Reeder's notes on Group Theory (www2.bc.edu/~reederma/806.html). They arise naturally as Galois groups of tamely ramified extensions of local fields, for which see Chapter 16 of Hasse's Nnumber Theory.
Mar 25, 2013 at 9:25 history answered Pierre CC BY-SA 3.0