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Apr 25, 2018 at 0:39 comment added YCor Its order is $486=2.3^5$; it seems it's the case $(p,s)=(3,2)$ of my family of examples.
Apr 24, 2018 at 13:43 history edited Peter Mueller CC BY-SA 3.0
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Apr 24, 2018 at 12:36 comment added Ville Salo Seems that $k(G) = 3$ for this group, so that answers my first question. Thanks! I must have had some problem in my GAP code (which does not surprise me, but certainly does embarrass me).
Apr 24, 2018 at 12:06 history answered Peter Mueller CC BY-SA 3.0