#2866⋊C₇ #11730738

order	896
isoclinism	isoclinic class of #2866⋊C₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₇ · Schur multiplier (H₂) = C₁

Aliases

Fitting, Sylow	#2866 ⋊ C₇
derived	C₄³ ⋊ C₂×C₇

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₄³	C₂×C₇
Frattini, socle	C₂³	C₂×AGL(1,𝔽₈)
Fitting	#2866	C₇
LCS	G ▷ C₄³
UCS	C₁

41 conjugacy classes of subgroups.

minimal degree	μ(G) = 56
transitive degree	μ_t(G) = 56

Polycyclic presentation:

2,7,2^6|c^2=fg,d^2=fgh,e^2=f,b^a=bfgh,c^a=cf,d^a=dgh,e^a=eh,c^b=dgh,d^b=cdeh,e^b=defh,f^b=gh,g^b=f,h^b=g

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(896, 5504);