#23847⋊C₇ #14267709

order	1792
automorphism	?
homology	Abelianization (H₁) = C₂×C₇ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, hypercenter	C₄	#401⋊C₇
commutator, cosocle, hypocenter	#2104	C₂×C₇
Frattini	C₂⁴	C₂×AGL(1,𝔽₈)
Fitting	#23847	C₇
socle	C₂	C₂×#401⋊C₇
prime radical	#2104⋊C₇	C₂
LCS	G ▷ #2104
UCS	C₁ ◁ C₄

58 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 32

Polycyclic presentation:

7,2^8|b^2=fgh,c^2=fg,d^2=f,e^2=i,b^a=cdfgh,c^a=beg,d^a=cei,f^a=fgi,g^a=hi,h^a=f,c^b=cf,d^b=dg,f^b=fi,g^b=gi,d^c=dh,h^c=hi,g^d=gi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1083481);