[GAP Forum] Solvable Groups

[Charles Wright]

Dear Vince,

It looks to me as if your groups are simply the solvable groups of odd 
order.

Subgroups of index 2 are normal, so you don't want any normal factor 
groups that are 2-groups. In particular, the Frattini factor group must 
have odd order. So the product of a 2-complement and the Frattini group 
must be the whole thing. But then the 2-complement is the whole group.

Am I missing something?

Charley

On 1/1/20 3:03 PM, Vince Giambalvo wrote:
> Dear Forum,
> As the title says, I am trying to study finite solvable groups with some nice (for me) properties that do not seem to be in the database. I don’t quite know which solvable group library, and or if there is another way.  “Not a direct product”, does seem to be in the libraries, and in addition if would like the Sylow 2 subgroup to be elementary abelian, and the group to have no subgroup of index 2. Does anyone have a suggestion for speeding up the search.
>
> Thanks for your help.
>   Vince Giambalvo
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