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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