How can I classify all almost simple groups with 15 or 16 conjugacy classes? A finite group $G$ is almost simple if there is a non-abelian simple group $S$ such that $S\trianglelefteq G\leq \operatorname{Aut}(S)$. We know that groups with at most 12 conjugacy classes are given in the paper "A. Vera López and J. Vera López, Classification of finite groups according to the number of conjugacy classes I, II, Israel J. Math.". Is there a GAP program to compute groups with 15 or 16 conjugacy classes?


closed as off-topic by ahulpke, José Carlos Santos, The Phenotype, Namaste, user1729 Jan 29 '18 at 10:17

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  • $\begingroup$ What is the context here? Is this a problem set in class, or is this a research problem? $\endgroup$ – user1729 Jan 25 '18 at 15:52
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    $\begingroup$ (Have you come across Vera-López, A. and Sangroniz, Josu, The finite groups with thirteen and fourteen conjugacy classes. Math. Nachr. 280 (2007), no. 5-6, 676–694. MR2308490) $\endgroup$ – user1729 Jan 25 '18 at 15:56
  • $\begingroup$ @user1729: That paper classified groups with 13 and 14 conjugacy classes. I need almost simple groups with 15 and 16 conjugacy classes. $\endgroup$ – M. R. Jan 25 '18 at 15:59
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    $\begingroup$ Naively this looks like a thesis problem given to a student, and there is no reason to expect that there would be a ready-made GAP function (or a written program) that solves the problem. On the other hand it is likely that computation will help, if only to eliminate cases. What have you tried so far? Are there parts of the degree 13,14 classification that used computation, or does the paper even contain software? Is there a particular computation you are stuck with? At the moment it looks like a prototypical ``Off Topic'' question that will get closed. $\endgroup$ – ahulpke Jan 26 '18 at 19:28