If 
is a group, then the extensions 
of 
of order 
with 
, where 
is the Frattini subgroup,
are called Frattini extensions.
Frattini Extension
See also
Frattini Factor, Frattini SubgroupExplore with Wolfram|Alpha
References
Besche, H.-U. and Eick, B. "Construction of Finite Groups." J. Symb. Comput. 27, 387-404, 1999.Gaschütz, W. "Über
-Untergruppen
endlicher Gruppen." Math. Z. 58, 160-170, 1953.Referenced on Wolfram|Alpha
Frattini ExtensionCite this as:
Weisstein, Eric W. "Frattini Extension." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FrattiniExtension.html